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"proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "done", "discrepancy": false, "erdos_state": "disproved (Lean)", "erdos_url": "https://www.erdosproblems.com/16", "fc_has_proof": true, "fc_linked": true, "fc_theorem": "Erdos16.erdos_16", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos16.erdos_16", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": "plby", "machine_verdict": "unconditional", "named_assumptions": [], "non_kernel_axioms": [], "problem": 16, "proof_link": "https://github.com/danielchin/proofs/blob/main/Proofs/ErdosProblems/Erdos16.lean", "proof_links": [ { "complete": true, "conditional": false, "label": "plby/lean-proofs", 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null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 17, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/18", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos18.erdos_18a", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos18.erdos_18a", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 18, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "decidable", "erdos_url": "https://www.erdosproblems.com/19", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 19, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { 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"machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 22, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "falsifiable", "erdos_url": "https://www.erdosproblems.com/23", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos23.erdos_23", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos23.erdos_23", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 23, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "statement", "discrepancy": false, "erdos_state": "proved (Lean)", "erdos_url": "https://www.erdosproblems.com/24", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": "batch-3 draft for Erd\u0151s 24", "fidelity_source": "local", "gpt_erdos": null, "held_for_review": false, "machine_source": "plby", "machine_verdict": "unconditional", "named_assumptions": [], "non_kernel_axioms": [], "problem": 24, "proof_link": null, "proof_links": [ { "complete": true, "conditional": false, "label": "plby/lean-proofs", "partial": false, "source": "plby", "state": "complete", "url": "https://github.com/plby/lean-proofs/blob/main/src/v4.29.1/ErdosProblems/Erdos24.lean" }, { "complete": true, "conditional": false, "label": "Jayyhk/erdos-lean", "partial": false, "source": "jayyhk", "state": "complete", "url": "https://github.com/Jayyhk/erdos-lean/blob/main/problems/24/Erdos24.lean" } ], "recommended_action": "Write the FC statement and link the matching hosted proof.", "signed_by": "reviewer:will-blair", "signed_fidelity_verdict": "faithful", "wiki_ai_systems": [ "Aristotle" ], "wiki_claims_lean": true, "wiki_claims_solved": false, "wiki_color": "green", "wiki_humans": [], "wiki_outcome": "Formalization" }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/25", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos25.erdos_25", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos25.erdos_25", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 25, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "GPT-5.4 Pro" ], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": "yellow", "wiki_humans": [ "Przemek Chojecki" ], "wiki_outcome": "Partial result" }, { "bucket": "done", "discrepancy": false, "erdos_state": "disproved (Lean)", "erdos_url": "https://www.erdosproblems.com/26", "fc_has_proof": true, "fc_linked": true, "fc_theorem": "Erdos26.erdos_26.variants.tenenbaum", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos26.erdos_26.variants.tenenbaum", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": "alphaproof", "machine_verdict": "unconditional", "named_assumptions": [], "non_kernel_axioms": [], "problem": 26, "proof_link": "https://github.com/mo271/formal-conjectures/blob/09c54540aa51cb40dff73660c94a82e2631386f8/FormalConjectures/ErdosProblems/26.lean#L625", "proof_links": [ { "complete": true, "conditional": false, "label": "plby/lean-proofs", "partial": false, "source": "plby", "state": "complete", "url": "https://github.com/plby/lean-proofs/blob/main/src/v4.29.1/ErdosProblems/Erdos26.lean" }, { "complete": true, "conditional": false, "label": "Jayyhk/erdos-lean", "partial": false, "source": "jayyhk", "state": "complete", "url": "https://github.com/Jayyhk/erdos-lean/blob/main/problems/26/Erdos26.lean" } ], "recommended_action": "No action.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "Aristotle", "DeepMind prover agent" ], "wiki_claims_lean": true, "wiki_claims_solved": true, "wiki_color": "green", "wiki_humans": [], "wiki_outcome": "Solution to stronger problem" }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "disproved", "erdos_url": "https://www.erdosproblems.com/27", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 27, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/28", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos28.erdos_28", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos28.erdos_28", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 28, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "proved", "erdos_url": "https://www.erdosproblems.com/29", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 29, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/30", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos30.erdos_30", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos30.erdos_30", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 30, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "proved (Lean)", "erdos_url": "https://www.erdosproblems.com/31", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": "plby", "machine_verdict": "unconditional", "named_assumptions": [], "non_kernel_axioms": [], "problem": 31, "proof_link": null, "proof_links": [ { "complete": true, "conditional": false, "label": "plby/lean-proofs", "partial": false, "source": "plby", "state": "complete", "url": "https://github.com/plby/lean-proofs/blob/main/src/v4.29.1/ErdosProblems/Erdos31.lean" }, { "complete": true, "conditional": false, "label": "Jayyhk/erdos-lean", "partial": false, "source": "jayyhk", "state": "complete", "url": "https://github.com/Jayyhk/erdos-lean/blob/main/problems/31/Erdos31.lean" } ], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "Aristotle", "GPT" ], "wiki_claims_lean": true, "wiki_claims_solved": false, "wiki_color": "green", "wiki_humans": [], "wiki_outcome": "Formalization" }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/32", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos32.erdos_32", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos32.erdos_32", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 32, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/33", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos33.erdos_33", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos33.erdos_33", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 33, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "disproved (Lean)", "erdos_url": "https://www.erdosproblems.com/34", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": "plby", "machine_verdict": "unconditional", "named_assumptions": [], "non_kernel_axioms": [], "problem": 34, "proof_link": null, "proof_links": [ { "complete": true, "conditional": false, "label": "plby/lean-proofs", "partial": false, "source": "plby", "state": "complete", "url": "https://github.com/plby/lean-proofs/blob/main/src/v4.29.1/ErdosProblems/Erdos34.lean" }, { "complete": true, "conditional": false, "label": "Jayyhk/erdos-lean", "partial": false, "source": "jayyhk", "state": "complete", "url": "https://github.com/Jayyhk/erdos-lean/blob/main/problems/34/Erdos34.lean" } ], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "Aristotle" ], "wiki_claims_lean": true, "wiki_claims_solved": false, "wiki_color": "green", "wiki_humans": [], "wiki_outcome": "Formalization" }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "proved", "erdos_url": "https://www.erdosproblems.com/35", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 35, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "done", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/36", "fc_has_proof": true, "fc_linked": true, "fc_theorem": "Erdos36.M_two", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos36.M_two", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 36, "proof_link": "https://github.com/google-deepmind/formal-conjectures/pull/4153/commits/2ce2d6345d0fcf3b023fe35fde9a9a490b131a86", "proof_links": [], "recommended_action": "No action.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "AlphaEvolve", "GPT-5.5 Pro" ], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": "yellow", "wiki_humans": [], "wiki_outcome": "Slight improvement to past construction" }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "disproved", "erdos_url": "https://www.erdosproblems.com/37", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 37, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "done", "discrepancy": false, "erdos_state": "proved (Lean)", "erdos_url": "https://www.erdosproblems.com/38", "fc_has_proof": true, "fc_linked": true, "fc_theorem": "Erdos38.erdos_38", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos38.erdos_38", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": "plby", "machine_verdict": "unconditional", "named_assumptions": [], "non_kernel_axioms": [], "problem": 38, "proof_link": "https://www.erdosproblems.com/forum/thread/38#post-6131", "proof_links": [ { "complete": true, "conditional": false, "label": "plby/lean-proofs", "partial": false, "source": "plby", "state": "complete", "url": "https://github.com/plby/lean-proofs/blob/main/src/v4.29.1/ErdosProblems/Erdos38.lean" }, { "complete": true, "conditional": false, "label": "Jayyhk/erdos-lean", "partial": false, "source": "jayyhk", "state": "complete", "url": "https://github.com/Jayyhk/erdos-lean/blob/main/problems/38/Erdos38.lean" } ], "recommended_action": "No action.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "Aristotle", "GPT-5.5 Pro" ], "wiki_claims_lean": true, "wiki_claims_solved": true, "wiki_color": "green", "wiki_humans": [], "wiki_outcome": "Full solution" }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/39", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos39.erdos_39", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos39.erdos_39", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 39, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/40", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos40.erdos_40", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos40.erdos_40", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 40, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/41", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos41.erdos_41", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos41.erdos_41", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 41, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "done", "discrepancy": false, "erdos_state": "solved (Lean)", "erdos_url": "https://www.erdosproblems.com/42", "fc_has_proof": true, "fc_linked": true, "fc_theorem": "Erdos42.erdos_42", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos42.erdos_42", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": "plby", "machine_verdict": "unconditional", "named_assumptions": [], "non_kernel_axioms": [], "problem": 42, "proof_link": "https://github.com/Shashi456/erdos-formalizations/blob/main/Erdos/P42/CompactCayley/Proof.lean", "proof_links": [ { "complete": true, "conditional": false, "label": "plby/lean-proofs", "partial": false, "source": "plby", "state": "complete", "url": "https://github.com/plby/lean-proofs/blob/main/src/v4.29.1/ErdosProblems/Erdos42.lean" }, { "complete": true, "conditional": false, "label": "Jayyhk/erdos-lean", "partial": false, "source": "jayyhk", "state": "complete", "url": "https://github.com/Jayyhk/erdos-lean/blob/main/problems/42/Erdos42.lean" } ], "recommended_action": "No action.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "Codex", "GPT-5.2", "GPT-5.2 Pro", "GPT-5.5 Pro" ], "wiki_claims_lean": true, "wiki_claims_solved": true, "wiki_color": "green", "wiki_humans": [ "Harjas Sandhu" ], "wiki_outcome": "Full solution" }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "disproved", "erdos_url": "https://www.erdosproblems.com/43", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos43.erdos_43.parts.ii", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos43.erdos_43.parts.ii", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 43, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "Aristotle", "Claude" ], "wiki_claims_lean": true, "wiki_claims_solved": false, "wiki_color": "yellow", "wiki_humans": [], "wiki_outcome": "New proof of partial result (Lean)" }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/44", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos44.erdos_44", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos44.erdos_44", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 44, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "blocked-claim", "discrepancy": false, "erdos_state": "proved (Lean)", "erdos_url": "https://www.erdosproblems.com/45", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": "plby", "machine_verdict": "unconditional", "named_assumptions": [], "non_kernel_axioms": [], "problem": 45, "proof_link": null, "proof_links": [ { "complete": true, "conditional": false, "label": "plby/lean-proofs", "partial": false, "source": "plby", "state": "complete", "url": "https://github.com/plby/lean-proofs/blob/main/src/v4.29.1/ErdosProblems/Erdos45.lean" }, { "complete": true, "conditional": false, "label": "Jayyhk/erdos-lean", "partial": false, "source": "jayyhk", "state": "complete", "url": "https://github.com/Jayyhk/erdos-lean/blob/main/problems/45/Erdos45.lean" } ], "recommended_action": "Skip because a human claim exists outside an open PR.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "blocked-claim", "discrepancy": false, "erdos_state": "proved (Lean)", "erdos_url": "https://www.erdosproblems.com/46", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": "plby", "machine_verdict": "unconditional", "named_assumptions": [], "non_kernel_axioms": [], "problem": 46, "proof_link": null, "proof_links": [ { "complete": true, "conditional": false, "label": "plby/lean-proofs", "partial": false, "source": "plby", "state": "complete", "url": "https://github.com/plby/lean-proofs/blob/main/src/v4.29.1/ErdosProblems/Erdos46.lean" }, { "complete": true, "conditional": false, "label": "Jayyhk/erdos-lean", "partial": false, "source": "jayyhk", "state": "complete", "url": "https://github.com/Jayyhk/erdos-lean/blob/main/problems/46/Erdos46.lean" } ], "recommended_action": "Skip because a human claim exists outside an open PR.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "proved (Lean)", "erdos_url": "https://www.erdosproblems.com/47", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": "plby", "machine_verdict": "unconditional", "named_assumptions": [], "non_kernel_axioms": [], "problem": 47, "proof_link": null, "proof_links": [ { "complete": true, "conditional": false, "label": "plby/lean-proofs", "partial": false, "source": "plby", "state": "complete", "url": "https://github.com/plby/lean-proofs/blob/main/src/v4.29.1/ErdosProblems/Erdos47.lean" }, { "complete": true, "conditional": false, "label": "Jayyhk/erdos-lean", "partial": false, "source": "jayyhk", "state": "complete", "url": "https://github.com/Jayyhk/erdos-lean/blob/main/problems/47/Erdos47.lean" } ], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "proved", "erdos_url": "https://www.erdosproblems.com/48", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos48.erdos_48", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos48.erdos_48", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 48, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "proved", "erdos_url": "https://www.erdosproblems.com/49", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 49, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/50", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos50.erdos_50", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos50.erdos_50", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 50, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/51", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos51.erdos_51", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos51.erdos_51", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 51, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "ChatGPT free version" ], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/52", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos52.erdos_52", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos52.erdos_52", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 52, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "Claude Mythos", "GPT-5.5", "GPT-5.5 Pro" ], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": "yellow", "wiki_humans": [ "Boris Alexeev", "Carl Schildkraut", "Dmitrii Zhelezov", "Ingo Alth\u00f6fer", "Thomas Bloom", "Will Sawin" ], "wiki_outcome": "Solution to variant problem" }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "proved", "erdos_url": "https://www.erdosproblems.com/53", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 53, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "solved", "erdos_url": "https://www.erdosproblems.com/54", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 54, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "solved", "erdos_url": "https://www.erdosproblems.com/55", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 55, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "done", "discrepancy": false, "erdos_state": "disproved (Lean)", "erdos_url": "https://www.erdosproblems.com/56", "fc_has_proof": true, "fc_linked": true, "fc_theorem": "Erdos56.erdos_56", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos56.erdos_56", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": "plby", "machine_verdict": "unconditional", "named_assumptions": [], "non_kernel_axioms": [], "problem": 56, "proof_link": "https://github.com/plby/lean-proofs/blob/main/src/v4.24.0/ErdosProblems/Erdos56.lean", "proof_links": [ { "complete": true, "conditional": false, "label": "plby/lean-proofs", "partial": false, "source": "plby", "state": "complete", "url": "https://github.com/plby/lean-proofs/blob/main/src/v4.29.1/ErdosProblems/Erdos56.lean" }, { "complete": true, "conditional": false, "label": "Jayyhk/erdos-lean", "partial": false, "source": "jayyhk", "state": "complete", "url": "https://github.com/Jayyhk/erdos-lean/blob/main/problems/56/Erdos56.lean" } ], "recommended_action": "No action.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "Aristotle", "GPT" ], "wiki_claims_lean": true, "wiki_claims_solved": false, "wiki_color": "green", "wiki_humans": [], "wiki_outcome": "Formalization" }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "proved", "erdos_url": "https://www.erdosproblems.com/57", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 57, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "proved", "erdos_url": "https://www.erdosproblems.com/58", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 58, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "disproved", "erdos_url": "https://www.erdosproblems.com/59", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 59, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/60", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 60, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/61", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos61.erdos_61", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos61.erdos_61", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 61, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/62", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 62, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "proved", "erdos_url": "https://www.erdosproblems.com/63", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 63, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "falsifiable", "erdos_url": "https://www.erdosproblems.com/64", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos64.erdos_64", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos64.erdos_64", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 64, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/65", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 65, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/66", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos66.erdos_66", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos66.erdos_66", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 66, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "proved", "erdos_url": "https://www.erdosproblems.com/67", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos67.erdos_67", "fc_url": 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"machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 68, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "proved", "erdos_url": "https://www.erdosproblems.com/69", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos69.erdos_69", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos69.erdos_69", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 69, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted 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null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "statement", "discrepancy": false, "erdos_state": "proved (Lean)", "erdos_url": "https://www.erdosproblems.com/71", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 71, "proof_link": null, "proof_links": [ { "complete": true, "conditional": false, "label": "Jayyhk/erdos-lean", "partial": false, "source": "jayyhk", "state": "complete", "url": "https://github.com/Jayyhk/erdos-lean/blob/main/problems/71/Erdos71.lean" } ], "recommended_action": "Write the FC statement and link the matching hosted proof.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "Aristotle", "Claude Opus 4.7", "GPT-5.5" ], "wiki_claims_lean": true, "wiki_claims_solved": false, "wiki_color": "green", "wiki_humans": [], "wiki_outcome": "Formalization" }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "proved", "erdos_url": "https://www.erdosproblems.com/72", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 72, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "proved", "erdos_url": "https://www.erdosproblems.com/73", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 73, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/74", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos74.erdos_74", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos74.erdos_74", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 74, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/75", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos75.erdos_75", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos75.erdos_75", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 75, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "Aletheia", "GPT-5.4 Pro" ], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": "yellow", "wiki_humans": [], "wiki_outcome": "Solution to variant problem (implicit in literature)" }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "proved", "erdos_url": "https://www.erdosproblems.com/76", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 76, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/77", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 77, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/78", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": "hidden_constraints", "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 78, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "proved", "erdos_url": "https://www.erdosproblems.com/79", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 79, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/80", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 80, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/81", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 81, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "Aristotle", "GPT-5.5 Pro" ], "wiki_claims_lean": true, "wiki_claims_solved": false, "wiki_color": "yellow", "wiki_humans": [ "Wouter van Doorn" ], "wiki_outcome": "Partial result (Lean)" }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/82", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos82.erdos_82", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos82.erdos_82", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 82, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "proved", "erdos_url": "https://www.erdosproblems.com/83", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 83, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/84", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 84, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/85", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos85.erdos_85", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos85.erdos_85", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 85, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/86", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 86, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/87", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 87, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "proved", "erdos_url": "https://www.erdosproblems.com/88", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 88, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/89", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos89.erdos_89", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos89.erdos_89", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 89, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "in-pr", "discrepancy": true, "erdos_state": "disproved (Lean)", "erdos_url": "https://www.erdosproblems.com/90", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos90.erdos_90", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos90.erdos_90", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": "jayyhk", "machine_verdict": "conditional", "named_assumptions": [], "non_kernel_axioms": [ "Erdos90.golod_shafarevich_inequality", "Erdos90.shafarevich_relation_rank_bound" ], "problem": 90, "proof_link": null, "proof_links": [ { "complete": false, "conditional": true, "label": "Jayyhk/erdos-lean", "partial": false, "source": "jayyhk", "state": "axiomatic", "url": "https://github.com/Jayyhk/erdos-lean/blob/main/problems/90/Erdos90.lean" } ], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "Aleph Prover", "Claude Mythos", "GPT-5.5 Pro", "OpenAI internal model" ], "wiki_claims_lean": true, "wiki_claims_solved": true, "wiki_color": "green", "wiki_humans": [ "Carl Schildkraut", "Eric Naslund", "Ingo Alth\u00f6fer", "Michael Emmerich", "Paata Ivanisvili", "Tomasz Kania", "Tseng", "Will Sawin", "leloy", "mlewko", "norxornor", "spiderduckpig" ], "wiki_outcome": "Full solution" }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/91", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos91.erdos_91", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos91.erdos_91", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": "hidden_constraints", "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 91, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "disproved", "erdos_url": "https://www.erdosproblems.com/92", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos92.erdos_92.variants.strong", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos92.erdos_92.variants.strong", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 92, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "statement", "discrepancy": false, "erdos_state": "proved (Lean)", "erdos_url": "https://www.erdosproblems.com/93", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": "batch-3 draft for Erd\u0151s 93", "fidelity_source": "local", "gpt_erdos": null, "held_for_review": false, "machine_source": "plby", "machine_verdict": "unconditional", "named_assumptions": [], "non_kernel_axioms": [], "problem": 93, "proof_link": null, "proof_links": [ { "complete": true, "conditional": false, "label": "plby/lean-proofs", "partial": false, "source": "plby", "state": "complete", "url": "https://github.com/plby/lean-proofs/blob/main/src/v4.29.1/ErdosProblems/Erdos93.lean" }, { "complete": true, "conditional": false, "label": "Jayyhk/erdos-lean", "partial": false, "source": "jayyhk", "state": "complete", "url": "https://github.com/Jayyhk/erdos-lean/blob/main/problems/93/Erdos93.lean" } ], "recommended_action": "Write the FC statement and link the matching hosted proof.", "signed_by": "reviewer:will-blair", "signed_fidelity_verdict": "faithful", "wiki_ai_systems": [ "Aristotle", "Claude Opus 4.5", "Claude Opus 4.6", "Gemini 3 Flash", "Gemini 3 Pro", "Numina Lean Agent" ], "wiki_claims_lean": true, "wiki_claims_solved": false, "wiki_color": "green", "wiki_humans": [], "wiki_outcome": "Formalization" }, { "bucket": "hypothesis-conditional", "discrepancy": false, "erdos_state": "proved (Lean)", "erdos_url": "https://www.erdosproblems.com/94", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": "plby", "machine_verdict": "conditional", "named_assumptions": [ "hconv : Erdos94.ConvexPosition P" ], "non_kernel_axioms": [], "problem": 94, "proof_link": null, "proof_links": [ { "complete": true, "conditional": false, "label": "plby/lean-proofs", "partial": false, "source": "plby", "state": "complete", "url": "https://github.com/plby/lean-proofs/blob/main/src/v4.29.1/ErdosProblems/Erdos94.lean" }, { "complete": true, "conditional": false, "label": "Jayyhk/erdos-lean", "partial": false, "source": "jayyhk", "state": "complete", "url": "https://github.com/Jayyhk/erdos-lean/blob/main/problems/94/Erdos94.lean" } ], "recommended_action": "Do not add a formal_proof link; document or wait for an unconditional theorem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "Codex", "GPT-5.2 Thinking; Seed Prover" ], "wiki_claims_lean": true, "wiki_claims_solved": false, "wiki_color": "green", "wiki_humans": [], "wiki_outcome": "Formalization" }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "proved", "erdos_url": "https://www.erdosproblems.com/95", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 95, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/96", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos96.erdos_96", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos96.erdos_96", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 96, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "falsifiable", "erdos_url": "https://www.erdosproblems.com/97", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos97.erdos_97", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos97.erdos_97", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 97, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/98", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos98.erdos_98", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos98.erdos_98", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 98, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/99", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos99.erdos_99", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos99.erdos_99", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 99, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "done", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/100", "fc_has_proof": true, "fc_linked": true, "fc_theorem": "Erdos100.erdos_100_piepmeyer", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos100.erdos_100_piepmeyer", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 100, "proof_link": "https://github.com/theaustinhatfield/formal-conjectures/blob/solve-erdos-100-piepmeyer/FormalConjectures/ErdosProblems/100.lean", "proof_links": [], "recommended_action": "No action.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/101", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos101.erdos_101", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos101.erdos_101", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 101, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/102", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 102, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/103", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 103, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/104", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 104, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "disproved (Lean)", "erdos_url": "https://www.erdosproblems.com/105", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": "plby", "machine_verdict": "unconditional", "named_assumptions": [], "non_kernel_axioms": [], "problem": 105, "proof_link": null, "proof_links": [ { "complete": true, "conditional": false, "label": "plby/lean-proofs", "partial": false, "source": "plby", "state": "complete", "url": "https://github.com/plby/lean-proofs/blob/main/src/v4.29.1/ErdosProblems/Erdos105.lean" }, { "complete": true, "conditional": false, "label": "Jayyhk/erdos-lean", "partial": false, "source": "jayyhk", "state": "complete", "url": "https://github.com/Jayyhk/erdos-lean/blob/main/problems/105/Erdos105.lean" } ], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "Aristotle", "GPT Pro" ], "wiki_claims_lean": true, "wiki_claims_solved": false, "wiki_color": "green", "wiki_humans": [], "wiki_outcome": "Formalization" }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "falsifiable", "erdos_url": "https://www.erdosproblems.com/106", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 106, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "Aristotle" ], "wiki_claims_lean": true, "wiki_claims_solved": false, "wiki_color": "yellow", "wiki_humans": [], "wiki_outcome": "Formalization" }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "falsifiable", "erdos_url": "https://www.erdosproblems.com/107", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos107.erdos_107", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos107.erdos_107", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 107, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/108", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos108.erdos_108", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos108.erdos_108", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 108, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "proved", "erdos_url": "https://www.erdosproblems.com/109", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos109.erdos_109", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos109.erdos_109", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 109, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "disproved", "erdos_url": "https://www.erdosproblems.com/110", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 110, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/111", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 111, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/112", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 112, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "disproved", "erdos_url": "https://www.erdosproblems.com/113", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 113, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "falsifiable", "erdos_url": "https://www.erdosproblems.com/114", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 114, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "hypothesis-conditional", "discrepancy": false, "erdos_state": "proved (Lean)", "erdos_url": "https://www.erdosproblems.com/115", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": "plby", "machine_verdict": "conditional", "named_assumptions": [ "a : Erdos115.EremenkoLempertAtZeroStatement n" ], "non_kernel_axioms": [], "problem": 115, "proof_link": null, "proof_links": [ { "complete": true, "conditional": false, "label": "plby/lean-proofs", "partial": false, "source": "plby", "state": "complete", "url": "https://github.com/plby/lean-proofs/blob/main/src/v4.29.1/ErdosProblems/Erdos115.lean" }, { "complete": true, "conditional": false, "label": "Jayyhk/erdos-lean", "partial": false, "source": "jayyhk", "state": "complete", "url": "https://github.com/Jayyhk/erdos-lean/blob/main/problems/115/Erdos115.lean" } ], "recommended_action": "Do not add a formal_proof link; document or wait for an unconditional theorem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "Aristotle", "Claude Opus 4.6", "Claude Sonnet 4.6", "Gemini 3 Flash", "Gemini 3.1 Pro", "ulam.ai scaffold with Gemini 3 Flash and Gemini 3.1 Pro" ], "wiki_claims_lean": true, "wiki_claims_solved": false, "wiki_color": "green", "wiki_humans": [], "wiki_outcome": "Formalization" }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "proved", "erdos_url": "https://www.erdosproblems.com/116", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 116, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/117", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 117, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "disproved", "erdos_url": "https://www.erdosproblems.com/118", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 118, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/119", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos119.erdos_119.parts.ii", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos119.erdos_119.parts.ii", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 119, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/120", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos120.erdos_120", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos120.erdos_120", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 120, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "DeepMind prover agent" ], "wiki_claims_lean": true, "wiki_claims_solved": false, "wiki_color": "yellow", "wiki_humans": [], "wiki_outcome": "Solution to variant problem (Lean)" }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "disproved", "erdos_url": "https://www.erdosproblems.com/121", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 121, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/122", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 122, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/123", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos123.erdos_123", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos123.erdos_123", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 123, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/124", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos124.erdos124.converse", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos124.erdos124.converse", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": "plby", "machine_verdict": "unconditional", "named_assumptions": [], "non_kernel_axioms": [], "problem": 124, "proof_link": null, "proof_links": [ { "complete": false, "conditional": false, "label": "plby/lean-proofs", "partial": true, "source": "plby", "state": "partial", "url": "https://github.com/plby/lean-proofs/blob/main/src/v4.29.1/ErdosProblems/Erdos124.lean" } ], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "Aristotle" ], "wiki_claims_lean": true, "wiki_claims_solved": false, "wiki_color": "yellow", "wiki_humans": [], "wiki_outcome": 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false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 149, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "needs-human-match-check", "discrepancy": false, "erdos_state": "proved (Lean)", "erdos_url": "https://www.erdosproblems.com/150", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": "plby", "machine_verdict": "unconditional", "named_assumptions": [], "non_kernel_axioms": [], "problem": 150, "proof_link": null, "proof_links": [ { "complete": true, "conditional": false, "label": "plby/lean-proofs", "partial": false, "source": "plby", "state": "complete", "url": "https://github.com/plby/lean-proofs/blob/main/src/v4.29.1/ErdosProblems/Erdos150.lean" }, { "complete": true, "conditional": false, "label": "Jayyhk/erdos-lean", "partial": false, "source": "jayyhk", "state": "complete", "url": "https://github.com/Jayyhk/erdos-lean/blob/main/problems/150/Erdos150.lean" } ], "recommended_action": "Read the hosted theorem and boxed problem before deciding whether to link.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "Aristotle" ], "wiki_claims_lean": true, "wiki_claims_solved": false, "wiki_color": "green", "wiki_humans": [], "wiki_outcome": "Formalization" }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/151", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 151, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "done", "discrepancy": false, "erdos_state": "proved", "erdos_url": "https://www.erdosproblems.com/152", "fc_has_proof": true, "fc_linked": true, "fc_theorem": "Erdos152.erdos_152", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos152.erdos_152", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 152, "proof_link": "https://github.com/mo271/formal-conjectures/blob/29c60aa79729701905cf9e92517af23f588971f2/FormalConjectures/ErdosProblems/152.lean#L485", "proof_links": [], "recommended_action": "No action.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "DeepMind prover agent" ], "wiki_claims_lean": true, "wiki_claims_solved": true, "wiki_color": "green", "wiki_humans": [], "wiki_outcome": "Full solution (Lean)" }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/153", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos153.erdos_153", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos153.erdos_153", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 153, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "done", "discrepancy": false, "erdos_state": "proved (Lean)", "erdos_url": "https://www.erdosproblems.com/154", "fc_has_proof": true, "fc_linked": true, "fc_theorem": "Erdos154.erdos_154.variants.lindstrom", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos154.erdos_154.variants.lindstrom", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": "plby", "machine_verdict": "unconditional", "named_assumptions": [], "non_kernel_axioms": [], "problem": 154, "proof_link": "https://github.com/Woett/Lean-files/blob/main/ErdosProblem154.lean", "proof_links": [ { "complete": true, "conditional": false, "label": "plby/lean-proofs", "partial": false, "source": "plby", "state": "complete", "url": "https://github.com/plby/lean-proofs/blob/main/src/v4.29.1/ErdosProblems/Erdos154.lean" }, { "complete": true, "conditional": false, "label": "Jayyhk/erdos-lean", "partial": false, "source": "jayyhk", "state": "complete", "url": "https://github.com/Jayyhk/erdos-lean/blob/main/problems/154/Erdos154.lean" }, { "complete": true, "conditional": false, "label": "williamjblair/lean-proofs", "partial": false, "source": "vlp", "state": "axioms_clean", "url": "https://github.com/williamjblair/lean-proofs/blob/main/ErdosProblems/Erdos154Sumset.lean" } ], "recommended_action": "No action.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "Aristotle", "GPT" ], "wiki_claims_lean": true, "wiki_claims_solved": false, "wiki_color": "green", "wiki_humans": [], "wiki_outcome": "Formalization" }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/155", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos155.erdos_155", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos155.erdos_155", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 155, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/156", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos156.erdos_156", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos156.erdos_156", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 156, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "proved", "erdos_url": "https://www.erdosproblems.com/157", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 157, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/158", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos158.erdos_158", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos158.erdos_158", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 158, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/159", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 159, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/160", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos160.erdos_160.variants.known_lower", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos160.erdos_160.variants.known_lower", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 160, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/161", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": "typo", "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 161, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/162", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 162, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "proved", "erdos_url": "https://www.erdosproblems.com/163", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 163, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "statement", "discrepancy": false, "erdos_state": "proved (Lean)", "erdos_url": "https://www.erdosproblems.com/164", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": "batch-3 draft for Erd\u0151s 164", "fidelity_source": "local", "gpt_erdos": null, "held_for_review": false, "machine_source": "plby", "machine_verdict": "unconditional", "named_assumptions": [], "non_kernel_axioms": [], "problem": 164, "proof_link": null, "proof_links": [ { "complete": true, "conditional": false, "label": "plby/lean-proofs", "partial": false, "source": "plby", "state": "complete", "url": "https://github.com/plby/lean-proofs/blob/main/src/v4.29.1/ErdosProblems/Erdos164.lean" }, { "complete": true, "conditional": false, "label": "Jayyhk/erdos-lean", "partial": false, "source": "jayyhk", "state": "complete", "url": "https://github.com/Jayyhk/erdos-lean/blob/main/problems/164/Erdos164.lean" } ], "recommended_action": "Write the FC statement and link the matching hosted proof.", "signed_by": "reviewer:will-blair", "signed_fidelity_verdict": "faithful", "wiki_ai_systems": [ "Codex" ], "wiki_claims_lean": true, "wiki_claims_solved": false, "wiki_color": "green", "wiki_humans": [], "wiki_outcome": "Formalization" }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/165", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 165, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "Trellis" ], "wiki_claims_lean": true, "wiki_claims_solved": false, "wiki_color": "yellow", "wiki_humans": [], "wiki_outcome": "Formalization" }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "proved", "erdos_url": "https://www.erdosproblems.com/166", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 166, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "falsifiable", "erdos_url": "https://www.erdosproblems.com/167", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 167, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/168", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos168.F_eq_card", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos168.F_eq_card", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 168, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/169", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 169, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/170", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos170.trivial_ruler_is_perfect", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos170.trivial_ruler_is_perfect", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 170, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "proved", "erdos_url": "https://www.erdosproblems.com/171", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 171, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/172", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos172.erdos_172", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos172.erdos_172", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 172, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": 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"fc_has_proof": true, "fc_linked": true, "fc_theorem": "Erdos198.erdos_198.variants.concrete", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos198.erdos_198.variants.concrete", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": "plby", "machine_verdict": "unconditional", "named_assumptions": [], "non_kernel_axioms": [], "problem": 198, "proof_link": "https://github.com/mzhorvath1/formal-conjectures/blob/21f6780f84b406de468389571eb01717b8072f09/FormalConjectures/ErdosProblems/198.lean#L84", "proof_links": [ { "complete": true, "conditional": false, "label": "plby/lean-proofs", "partial": false, "source": "plby", "state": "complete", "url": "https://github.com/plby/lean-proofs/blob/main/src/v4.29.1/ErdosProblems/Erdos198.lean" }, { "complete": true, "conditional": false, "label": "Jayyhk/erdos-lean", "partial": false, "source": "jayyhk", "state": "complete", "url": "https://github.com/Jayyhk/erdos-lean/blob/main/problems/198/Erdos198.lean" } ], "recommended_action": "No action.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "AlphaProof", "Aristotle", "GPT" ], "wiki_claims_lean": true, "wiki_claims_solved": false, "wiki_color": "green", "wiki_humans": [], "wiki_outcome": "New proof found" }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "disproved (Lean)", "erdos_url": "https://www.erdosproblems.com/199", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": "plby", "machine_verdict": "unconditional", "named_assumptions": [], "non_kernel_axioms": [], "problem": 199, "proof_link": null, "proof_links": [ { "complete": true, "conditional": false, "label": "plby/lean-proofs", "partial": false, "source": "plby", "state": "complete", "url": "https://github.com/plby/lean-proofs/blob/main/src/v4.29.1/ErdosProblems/Erdos199.lean" }, { "complete": true, "conditional": false, "label": "Jayyhk/erdos-lean", "partial": false, "source": "jayyhk", "state": "complete", "url": "https://github.com/Jayyhk/erdos-lean/blob/main/problems/199/Erdos199.lean" } ], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "Aristotle" ], "wiki_claims_lean": true, "wiki_claims_solved": false, "wiki_color": "green", "wiki_humans": [], "wiki_outcome": "Formalization" }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/200", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos200.erdos_200", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos200.erdos_200", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 200, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/201", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 201, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "needs-human-match-check", "discrepancy": false, "erdos_state": "solved (Lean)", "erdos_url": "https://www.erdosproblems.com/202", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 202, "proof_link": null, "proof_links": [ { "complete": true, "conditional": false, "label": "plby/lean-proofs", "partial": false, "source": "plby", "state": "complete", "url": "https://github.com/plby/lean-proofs/blob/main/src/v4.29.1/ErdosProblems/Erdos202.lean" }, { "complete": true, "conditional": false, "label": "Jayyhk/erdos-lean", "partial": false, "source": "jayyhk", "state": "complete", "url": "https://github.com/Jayyhk/erdos-lean/blob/main/problems/202/Erdos202.lean" } ], "recommended_action": "Read the hosted theorem and boxed problem before deciding whether to link.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "GPT-5.4 Pro", "GPT-5.5 Pro", "Unspecified" ], "wiki_claims_lean": true, "wiki_claims_solved": true, "wiki_color": "green", "wiki_humans": [ "Boon Suan Ho", "Przemek Chojecki" ], "wiki_outcome": "Full solution" }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/203", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos203.erdos_203", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos203.erdos_203", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 203, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "done", "discrepancy": false, "erdos_state": "disproved (Lean)", "erdos_url": "https://www.erdosproblems.com/204", "fc_has_proof": true, "fc_linked": true, "fc_theorem": "Erdos204.erdos_204", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos204.erdos_204", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": "plby", "machine_verdict": "unconditional", "named_assumptions": [], "non_kernel_axioms": [], "problem": 204, "proof_link": "https://github.com/Woett/Lean-files/blob/main/ErdosProblem204.lean", "proof_links": [ { "complete": true, "conditional": false, "label": "plby/lean-proofs", "partial": false, "source": "plby", "state": "complete", "url": "https://github.com/plby/lean-proofs/blob/main/src/v4.29.1/ErdosProblems/Erdos204.lean" }, { "complete": true, "conditional": false, "label": "Jayyhk/erdos-lean", "partial": false, "source": "jayyhk", "state": "complete", "url": "https://github.com/Jayyhk/erdos-lean/blob/main/problems/204/Erdos204.lean" } ], "recommended_action": "No action.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "Aristotle" ], "wiki_claims_lean": true, "wiki_claims_solved": false, "wiki_color": "green", "wiki_humans": [], "wiki_outcome": "Formalization" }, { "bucket": "hypothesis-conditional", "discrepancy": false, "erdos_state": "disproved (Lean)", "erdos_url": "https://www.erdosproblems.com/205", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": "Treat as conditional until the hosted theorem is confirmed to have no non-problem hypothesis.", "fidelity_source": "local", "gpt_erdos": null, "held_for_review": false, "machine_source": "plby", "machine_verdict": "unconditional", "named_assumptions": [], "non_kernel_axioms": [], "problem": 205, "proof_link": null, "proof_links": [ { "complete": true, "conditional": false, "label": "plby/lean-proofs", "partial": false, "source": "plby", "state": "complete", "url": "https://github.com/plby/lean-proofs/blob/main/src/v4.29.1/ErdosProblems/Erdos205.lean" }, { "complete": true, "conditional": false, "label": "Jayyhk/erdos-lean", "partial": false, "source": "jayyhk", "state": "complete", "url": "https://github.com/Jayyhk/erdos-lean/blob/main/problems/205/Erdos205.lean" } ], "recommended_action": "Do not add a formal_proof link; document or wait for an unconditional theorem.", "signed_by": "reviewer:will-blair", "signed_fidelity_verdict": "variant", "wiki_ai_systems": [ "Aristotle", "GPT-5.2 Thinking" ], "wiki_claims_lean": true, "wiki_claims_solved": true, "wiki_color": "green", "wiki_humans": [], "wiki_outcome": "Full solution (Lean)" }, { "bucket": "statement", "discrepancy": false, "erdos_state": "disproved (Lean)", "erdos_url": "https://www.erdosproblems.com/206", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 206, "proof_link": null, "proof_links": [ { "complete": true, "conditional": false, "label": "plby/lean-proofs", "partial": false, "source": "plby", "state": "complete", "url": "https://github.com/plby/lean-proofs/blob/main/src/v4.29.1/ErdosProblems/Erdos206.lean" }, { "complete": true, "conditional": false, "label": "Jayyhk/erdos-lean", "partial": false, "source": "jayyhk", "state": "complete", "url": "https://github.com/Jayyhk/erdos-lean/blob/main/problems/206/Erdos206.lean" } ], "recommended_action": "Write the FC statement and link the matching hosted proof.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "Aristotle" ], "wiki_claims_lean": true, "wiki_claims_solved": false, "wiki_color": "green", "wiki_humans": [], "wiki_outcome": "Formalization" }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "proved", "erdos_url": "https://www.erdosproblems.com/207", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 207, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/208", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos208.erdos_208.variants.log_bound", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos208.erdos_208.variants.log_bound", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 208, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "statement", "discrepancy": false, "erdos_state": "disproved (Lean)", "erdos_url": "https://www.erdosproblems.com/209", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 209, "proof_link": null, "proof_links": [ { "complete": true, "conditional": false, "label": "Jayyhk/erdos-lean", "partial": false, "source": "jayyhk", "state": "complete", "url": "https://github.com/Jayyhk/erdos-lean/blob/main/problems/209/Erdos209.lean" } ], "recommended_action": "Write the FC statement and link the matching hosted proof.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "AxiomProver" ], "wiki_claims_lean": true, "wiki_claims_solved": false, "wiki_color": "green", "wiki_humans": [], "wiki_outcome": "Formalization" }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "proved", "erdos_url": "https://www.erdosproblems.com/210", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 210, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "proved", "erdos_url": "https://www.erdosproblems.com/211", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 211, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/212", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos212.erdos_212", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos212.erdos_212", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 212, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/213", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos213.erdos_213", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos213.erdos_213", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 213, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "mismatch", "discrepancy": false, "erdos_state": "proved (Lean)", "erdos_url": "https://www.erdosproblems.com/214", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": "Hosted proof is complete, but proves an existential coloring result rather than the universal boxed problem.", "fidelity_source": "local", "gpt_erdos": null, "held_for_review": false, "machine_source": "plby", "machine_verdict": "unconditional", "named_assumptions": [], "non_kernel_axioms": [], "problem": 214, "proof_link": null, "proof_links": [ { "complete": true, "conditional": false, "label": "plby/lean-proofs", "partial": false, "source": "plby", "state": "complete", "url": "https://github.com/plby/lean-proofs/blob/main/src/v4.29.1/ErdosProblems/Erdos214.lean" }, { "complete": true, "conditional": false, "label": "Jayyhk/erdos-lean", "partial": false, "source": "jayyhk", "state": "complete", "url": "https://github.com/Jayyhk/erdos-lean/blob/main/problems/214/Erdos214.lean" } ], "recommended_action": "Skip until a hosted proof matches the boxed FC statement.", "signed_by": "reviewer:will-blair", "signed_fidelity_verdict": "unfaithful", "wiki_ai_systems": [ "Aristotle" ], "wiki_claims_lean": true, "wiki_claims_solved": false, "wiki_color": "green", "wiki_humans": [], "wiki_outcome": "Formalization" }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "proved", "erdos_url": "https://www.erdosproblems.com/215", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 215, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "disproved", "erdos_url": "https://www.erdosproblems.com/216", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 216, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/217", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 217, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/218", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos218.erdos_218.variants.le", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos218.erdos_218.variants.le", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 218, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "GPT" ], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": "yellow", "wiki_humans": [], "wiki_outcome": "Conditional solution" }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "proved", "erdos_url": "https://www.erdosproblems.com/219", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos219.erdos_219", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos219.erdos_219", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 219, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "proved", "erdos_url": "https://www.erdosproblems.com/220", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 220, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "proved (Lean)", "erdos_url": "https://www.erdosproblems.com/221", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": "plby", "machine_verdict": "unconditional", "named_assumptions": [], "non_kernel_axioms": [], "problem": 221, "proof_link": null, "proof_links": [ { "complete": true, "conditional": false, "label": "plby/lean-proofs", "partial": false, "source": "plby", "state": "complete", "url": "https://github.com/plby/lean-proofs/blob/main/src/v4.29.1/ErdosProblems/Erdos221.lean" }, { "complete": true, "conditional": false, "label": "Jayyhk/erdos-lean", "partial": false, "source": "jayyhk", "state": "complete", "url": "https://github.com/Jayyhk/erdos-lean/blob/main/problems/221/Erdos221.lean" } ], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "Aristotle" ], "wiki_claims_lean": true, "wiki_claims_solved": false, "wiki_color": "green", "wiki_humans": [], "wiki_outcome": "Formalization" }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/222", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 222, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "solved", "erdos_url": "https://www.erdosproblems.com/223", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 223, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "proved (Lean)", "erdos_url": "https://www.erdosproblems.com/224", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": "plby", "machine_verdict": "conditional", "named_assumptions": [ "hNo : Erdos224.NoObtuse A" ], "non_kernel_axioms": [], "problem": 224, "proof_link": null, "proof_links": [ { "complete": true, "conditional": false, "label": "plby/lean-proofs", "partial": false, "source": "plby", "state": "complete", "url": "https://github.com/plby/lean-proofs/blob/main/src/v4.29.1/ErdosProblems/Erdos224.lean" }, { "complete": true, "conditional": false, "label": "Jayyhk/erdos-lean", "partial": false, "source": "jayyhk", "state": "complete", "url": "https://github.com/Jayyhk/erdos-lean/blob/main/problems/224/Erdos224.lean" } ], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "Codex", "GPT-5.2 Thinking" ], "wiki_claims_lean": true, "wiki_claims_solved": false, "wiki_color": "green", "wiki_humans": [], "wiki_outcome": "New proof found (Lean)" }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "proved", "erdos_url": "https://www.erdosproblems.com/225", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 225, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "proved (Lean)", "erdos_url": "https://www.erdosproblems.com/226", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": "plby", "machine_verdict": "unconditional", "named_assumptions": [], "non_kernel_axioms": [], "problem": 226, "proof_link": null, "proof_links": [ { "complete": true, "conditional": false, "label": "plby/lean-proofs", "partial": false, "source": "plby", "state": "complete", "url": "https://github.com/plby/lean-proofs/blob/main/src/v4.29.1/ErdosProblems/Erdos226.lean" }, { "complete": true, "conditional": false, "label": "Jayyhk/erdos-lean", "partial": false, "source": "jayyhk", "state": "complete", "url": "https://github.com/Jayyhk/erdos-lean/blob/main/problems/226/Erdos226.lean" } ], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "Aristotle" ], "wiki_claims_lean": true, "wiki_claims_solved": false, "wiki_color": "green", "wiki_humans": [], "wiki_outcome": "Formalization" }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "disproved", "erdos_url": "https://www.erdosproblems.com/227", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 227, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "proved", "erdos_url": "https://www.erdosproblems.com/228", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos228.erdos_228", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos228.erdos_228", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 228, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "done", "discrepancy": false, "erdos_state": "proved (Lean)", "erdos_url": "https://www.erdosproblems.com/229", "fc_has_proof": true, "fc_linked": true, "fc_theorem": "Erdos229.erdos_229", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos229.erdos_229", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": "plby", "machine_verdict": "unconditional", "named_assumptions": [], "non_kernel_axioms": [], "problem": 229, "proof_link": "https://github.com/plby/lean-proofs/blob/main/src/v4.24.0/ErdosProblems/Erdos229.lean", "proof_links": [ { "complete": true, "conditional": false, "label": "plby/lean-proofs", "partial": false, "source": "plby", "state": "complete", "url": "https://github.com/plby/lean-proofs/blob/main/src/v4.29.1/ErdosProblems/Erdos229.lean" }, { "complete": true, "conditional": false, "label": "Jayyhk/erdos-lean", "partial": false, "source": "jayyhk", "state": "complete", "url": "https://github.com/Jayyhk/erdos-lean/blob/main/problems/229/Erdos229.lean" } ], "recommended_action": "No action.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "Aristotle" ], "wiki_claims_lean": true, "wiki_claims_solved": false, "wiki_color": "green", "wiki_humans": [], "wiki_outcome": "Formalization" }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "disproved", "erdos_url": "https://www.erdosproblems.com/230", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 230, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "docstring", "discrepancy": false, "erdos_state": "disproved (Lean)", "erdos_url": "https://www.erdosproblems.com/231", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 231, "proof_link": null, "proof_links": [ { "complete": false, "conditional": true, "label": "Jayyhk/erdos-lean", "partial": false, "source": "jayyhk", "state": "trust_extended", "url": "https://github.com/Jayyhk/erdos-lean/blob/main/problems/231/Erdos231.lean" } ], "recommended_action": "Add only a docstring note if useful; do not add formal_proof.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "Aristotle" ], "wiki_claims_lean": true, "wiki_claims_solved": false, "wiki_color": "green", "wiki_humans": [], "wiki_outcome": "Formalization" }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "proved", "erdos_url": "https://www.erdosproblems.com/232", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 232, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "done", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/233", "fc_has_proof": true, "fc_linked": true, "fc_theorem": "Erdos233.erdos_233.variants.lower_bound", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos233.erdos_233.variants.lower_bound", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 233, "proof_link": "https://github.com/mzhorvath1/formal-conjectures/blob/032848c62fdf4c422bb0ee6663dc8d009d456c2c/FormalConjectures/ErdosProblems/233.lean#L57", "proof_links": [], "recommended_action": "No action.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "GPT-5.2 Pro" ], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/234", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos234.erdos_234", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos234.erdos_234", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 234, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "proved", "erdos_url": "https://www.erdosproblems.com/235", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 235, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/236", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos236.erdos_236", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos236.erdos_236", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 236, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "docstring", "discrepancy": false, "erdos_state": "proved (Lean)", "erdos_url": "https://www.erdosproblems.com/237", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": "plby", "machine_verdict": "conditional", "named_assumptions": [], "non_kernel_axioms": [ "maynard_tao" ], "problem": 237, "proof_link": null, "proof_links": [ { "complete": false, "conditional": true, "label": "plby/lean-proofs", "partial": false, "source": "plby", "state": "conditional", "url": "https://github.com/plby/lean-proofs/blob/main/src/v4.29.1/ErdosProblems/Erdos237.lean" }, { "complete": false, "conditional": true, "label": "Jayyhk/erdos-lean", "partial": false, "source": "jayyhk", "state": "axiomatic", "url": "https://github.com/Jayyhk/erdos-lean/blob/main/problems/237/Erdos237.lean" } ], "recommended_action": "Add only a docstring note if useful; do not add formal_proof.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "Aristotle" ], "wiki_claims_lean": true, "wiki_claims_solved": false, "wiki_color": "green", "wiki_humans": [], "wiki_outcome": "Formalization" }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/238", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos238.erdos_238", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos238.erdos_238", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 238, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "proved", "erdos_url": "https://www.erdosproblems.com/239", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos239.erdos_239", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos239.erdos_239", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 239, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "proved", "erdos_url": "https://www.erdosproblems.com/240", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 240, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/241", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos241.erdos_241", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos241.erdos_241", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 241, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "falsifiable", "erdos_url": "https://www.erdosproblems.com/242", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos242.erdos_242", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos242.erdos_242", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 242, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/243", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos243.erdos_243", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos243.erdos_243", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 243, "proof_link": null, "proof_links": [], "recommended_action": "No action until a 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"signed_fidelity_verdict": null, "wiki_ai_systems": [ "Aristotle" ], "wiki_claims_lean": true, "wiki_claims_solved": false, "wiki_color": "green", "wiki_humans": [], "wiki_outcome": "Formalization" }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/269", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos269.erdos_269.variants.irrational", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos269.erdos_269.variants.irrational", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 269, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, 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"wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "proved", "erdos_url": "https://www.erdosproblems.com/277", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos277.erdos_277", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos277.erdos_277", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 277, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/278", 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], "recommended_action": "No action.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "Aristotle" ], "wiki_claims_lean": true, "wiki_claims_solved": false, "wiki_color": "green", "wiki_humans": [], "wiki_outcome": "Formalization" }, { "bucket": "partial", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/291", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos291.erdos_291.variants.shiu_heuristic_density_zero", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos291.erdos_291.variants.shiu_heuristic_density_zero", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": "plby", "machine_verdict": "unconditional", "named_assumptions": [], "non_kernel_axioms": [], "problem": 291, "proof_link": null, "proof_links": [ { "complete": false, "conditional": false, "label": "plby/lean-proofs", "partial": true, "source": "plby", 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"wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/293", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 293, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "proved", "erdos_url": "https://www.erdosproblems.com/294", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 294, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/295", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos295.erdos_295", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos295.erdos_295", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], 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null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 308, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "disproved", "erdos_url": "https://www.erdosproblems.com/309", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 309, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, 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"machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 312, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/313", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos313.erdos_313", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos313.erdos_313", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 313, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "statement", "discrepancy": false, "erdos_state": "proved (Lean)", "erdos_url": "https://www.erdosproblems.com/314", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": "batch-3 draft for Erd\u0151s 314", "fidelity_source": "local", "gpt_erdos": null, "held_for_review": false, "machine_source": "plby", "machine_verdict": "unconditional", "named_assumptions": [], "non_kernel_axioms": [], "problem": 314, "proof_link": null, "proof_links": [ { "complete": true, "conditional": false, "label": "plby/lean-proofs", "partial": false, "source": "plby", "state": "complete", "url": "https://github.com/plby/lean-proofs/blob/main/src/v4.29.1/ErdosProblems/Erdos314.lean" }, { "complete": true, "conditional": false, "label": 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"complete": true, "conditional": false, "label": "plby/lean-proofs", "partial": false, "source": "plby", "state": "complete", "url": "https://github.com/plby/lean-proofs/blob/main/src/v4.29.1/ErdosProblems/Erdos315.lean" }, { "complete": true, "conditional": false, "label": "Jayyhk/erdos-lean", "partial": false, "source": "jayyhk", "state": "complete", "url": "https://github.com/Jayyhk/erdos-lean/blob/main/problems/315/Erdos315.lean" } ], "recommended_action": "Write the FC statement and link the matching hosted proof.", "signed_by": "reviewer:will-blair", "signed_fidelity_verdict": "faithful", "wiki_ai_systems": [ "Aristotle" ], "wiki_claims_lean": true, "wiki_claims_solved": false, "wiki_color": "green", "wiki_humans": [], "wiki_outcome": "Formalization" }, { "bucket": "done", "discrepancy": false, "erdos_state": "disproved (Lean)", "erdos_url": "https://www.erdosproblems.com/316", "fc_has_proof": true, "fc_linked": true, "fc_theorem": "Erdos316.erdos_316", "fc_url": 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[], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/317", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos317.erdos_317", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos317.erdos_317", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 317, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": 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"proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/321", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos321.erdos_321", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos321.erdos_321", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 321, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/322", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 322, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/323", "fc_has_proof": false, "fc_linked": false, "fc_theorem": 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null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 324, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/325", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos325.erdos_325", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos325.erdos_325", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 325, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/326", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos326.erdos_326", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos326.erdos_326", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 326, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "Aristotle", "Codex", "GPT-5.5" ], "wiki_claims_lean": true, "wiki_claims_solved": true, "wiki_color": "green", "wiki_humans": [ "Aron Bhalla" ], "wiki_outcome": "Full solution (Lean)" }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/327", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 327, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "GPT-5.5", "Rethlas" ], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": "white", "wiki_humans": [ "Yu Leon Liu" ], "wiki_outcome": "Candidate partial result" }, { "bucket": "statement", "discrepancy": false, "erdos_state": "disproved (Lean)", 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"recommended_action": "No action.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "Aristotle" ], "wiki_claims_lean": true, "wiki_claims_solved": false, "wiki_color": "green", "wiki_humans": [], "wiki_outcome": "Formalization" }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/332", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos332.erdos_332", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos332.erdos_332", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": "non_improving", "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 332, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "statement", "discrepancy": false, "erdos_state": "disproved (Lean)", "erdos_url": "https://www.erdosproblems.com/333", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": "batch-3 draft for Erd\u0151s 333", "fidelity_source": "local", "gpt_erdos": null, "held_for_review": false, "machine_source": "plby", "machine_verdict": "unconditional", "named_assumptions": [], "non_kernel_axioms": [], "problem": 333, "proof_link": null, "proof_links": [ { "complete": true, "conditional": false, "label": "plby/lean-proofs", "partial": false, "source": "plby", "state": "complete", "url": "https://github.com/plby/lean-proofs/blob/main/src/v4.29.1/ErdosProblems/Erdos333.lean" }, { "complete": true, "conditional": false, "label": "Jayyhk/erdos-lean", "partial": false, "source": "jayyhk", "state": "complete", "url": 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"wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/335", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": "subtle_error", "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 335, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/336", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 336, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "mismatch", "discrepancy": false, "erdos_state": "disproved (Lean)", "erdos_url": "https://www.erdosproblems.com/337", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": "Hosted proof is a counterexample/existence theorem and needs a fresh match-check before linking to the FC statement.", "fidelity_source": "local", "gpt_erdos": null, "held_for_review": false, "machine_source": 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"signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/341", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos341.erdos_341", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos341.erdos_341", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 341, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "in-pr", 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"proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "done", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/349", "fc_has_proof": true, "fc_linked": true, "fc_theorem": "Erdos349.int_coeff_ge_two_not_isGoodPair", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos349.int_coeff_ge_two_not_isGoodPair", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 349, "proof_link": "https://github.com/cepadugato/formal-conjectures/blob/erdos-349-integer-characterization-proof/FormalConjectures/ErdosProblems/349.lean", "proof_links": [], "recommended_action": "No action.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "GPT-5.2 Thinking" ], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": "yellow", "wiki_humans": [], "wiki_outcome": "Improved partial result" }, { "bucket": "done", "discrepancy": false, "erdos_state": "proved (Lean)", "erdos_url": "https://www.erdosproblems.com/350", "fc_has_proof": true, "fc_linked": true, "fc_theorem": "Erdos350.erdos_350", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos350.erdos_350", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": "plby", "machine_verdict": "conditional", "named_assumptions": [ "hA : Erdos350.DecidableDistinctSubsetSums A" ], "non_kernel_axioms": [], "problem": 350, "proof_link": "https://github.com/XC0R/formal-conjectures/blob/ba788c9124b563bce98a3413d474b3a2731fd0af/FormalConjectures/ErdosProblems/350.lean#L226", 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"wiki_color": "green", "wiki_humans": [], "wiki_outcome": "Formalization" }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/354", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos354.erdos_354.parts.i", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos354.erdos_354.parts.i", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 354, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "done", "discrepancy": false, "erdos_state": "proved (Lean)", "erdos_url": 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"recommended_action": "No action.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "Aristotle", "Gemini 3" ], "wiki_claims_lean": true, "wiki_claims_solved": false, "wiki_color": "green", "wiki_humans": [], "wiki_outcome": "Formalization" }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "proved", "erdos_url": "https://www.erdosproblems.com/356", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 356, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/357", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos357.erdos_357.variants.monotone.parts.ii.littleO_version", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos357.erdos_357.variants.monotone.parts.ii.littleO_version", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 357, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "proved", "erdos_url": "https://www.erdosproblems.com/358", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos358.erdos_358.variants.prime_set_density_representation", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos358.erdos_358.variants.prime_set_density_representation", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 358, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "GPT-5.2 Pro", "GPT-5.2 Thinking" ], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [ "Nat Sothanaphan" ], "wiki_outcome": null }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/359", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos359.erdos_359.variants.isGoodFor_1_asymptotic", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos359.erdos_359.variants.isGoodFor_1_asymptotic", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 359, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "solved", "erdos_url": "https://www.erdosproblems.com/360", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 360, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/361", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos361.erdos_361.bigO", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos361.erdos_361.bigO", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 361, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "proved", "erdos_url": "https://www.erdosproblems.com/362", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 362, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "disproved (Lean)", "erdos_url": "https://www.erdosproblems.com/363", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": "plby", "machine_verdict": "unconditional", "named_assumptions": [], "non_kernel_axioms": [], "problem": 363, "proof_link": null, "proof_links": [ { "complete": true, "conditional": false, "label": "plby/lean-proofs", "partial": false, "source": "plby", "state": "complete", "url": "https://github.com/plby/lean-proofs/blob/main/src/v4.29.1/ErdosProblems/Erdos363.lean" }, { "complete": true, "conditional": false, "label": "Jayyhk/erdos-lean", "partial": false, "source": "jayyhk", "state": "complete", "url": "https://github.com/Jayyhk/erdos-lean/blob/main/problems/363/Erdos363.lean" } ], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "Aristotle" ], "wiki_claims_lean": true, "wiki_claims_solved": false, "wiki_color": "green", "wiki_humans": [], "wiki_outcome": "Formalization" }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "verifiable", "erdos_url": "https://www.erdosproblems.com/364", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos364.erdos_364", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos364.erdos_364", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 364, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/365", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 365, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "verifiable", "erdos_url": "https://www.erdosproblems.com/366", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos366.erdos_366", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos366.erdos_366", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 366, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "Automated research pipeline" ], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": "yellow", "wiki_humans": [], "wiki_outcome": "Conditional partial result" }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/367", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": "plby", "machine_verdict": "unconditional", "named_assumptions": [], "non_kernel_axioms": [], "problem": 367, "proof_link": null, "proof_links": [ { "complete": false, "conditional": false, "label": "plby/lean-proofs", "partial": true, "source": "plby", "state": "partial", "url": "https://github.com/plby/lean-proofs/blob/main/src/v4.29.1/ErdosProblems/Erdos367.lean" } ], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "Aristotle", "Gemini Deep Think" ], "wiki_claims_lean": true, "wiki_claims_solved": false, "wiki_color": "yellow", "wiki_humans": [ "Boris Alexeev", "Terence Tao", "Wouter van Doorn" ], "wiki_outcome": "Partial result" }, { "bucket": "partial", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/368", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": "plby", "machine_verdict": "unconditional", "named_assumptions": [], "non_kernel_axioms": [], "problem": 368, "proof_link": null, "proof_links": [ { "complete": false, "conditional": false, "label": "plby/lean-proofs", "partial": true, "source": "plby", "state": "partial", "url": "https://github.com/plby/lean-proofs/blob/main/src/v4.29.1/ErdosProblems/Erdos368.lean" } ], "recommended_action": "Only link a correctly stated variant after a per-problem review.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "Aristotle" ], "wiki_claims_lean": true, "wiki_claims_solved": false, "wiki_color": "yellow", "wiki_humans": [], "wiki_outcome": "Formalization" }, { "bucket": "statement", "discrepancy": false, "erdos_state": "proved (Lean)", "erdos_url": "https://www.erdosproblems.com/369", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": "batch-3 draft for Erd\u0151s 369", "fidelity_source": "local", "gpt_erdos": "hidden_constraints", "held_for_review": false, "machine_source": "plby", "machine_verdict": "unconditional", "named_assumptions": [], "non_kernel_axioms": [], "problem": 369, "proof_link": null, "proof_links": [ { "complete": true, "conditional": false, "label": "plby/lean-proofs", "partial": false, "source": "plby", "state": "complete", "url": "https://github.com/plby/lean-proofs/blob/main/src/v4.29.1/ErdosProblems/Erdos369.lean" }, { "complete": true, "conditional": false, "label": "Jayyhk/erdos-lean", "partial": false, "source": "jayyhk", "state": "complete", "url": "https://github.com/Jayyhk/erdos-lean/blob/main/problems/369/Erdos369.lean" } ], "recommended_action": "Write the FC statement and link the matching hosted proof.", "signed_by": "reviewer:will-blair", "signed_fidelity_verdict": "faithful", "wiki_ai_systems": [ "Aristotle", "GPT" ], "wiki_claims_lean": true, "wiki_claims_solved": true, "wiki_color": "green", "wiki_humans": [ "Sky Yang" ], "wiki_outcome": "Full solution" }, { "bucket": "done", "discrepancy": false, "erdos_state": "proved (Lean)", "erdos_url": "https://www.erdosproblems.com/370", "fc_has_proof": true, "fc_linked": true, "fc_theorem": "Erdos370.erdos_370", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos370.erdos_370", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": "plby", "machine_verdict": "unconditional", "named_assumptions": [], "non_kernel_axioms": [], "problem": 370, "proof_link": "https://github.com/XC0R/formal-conjectures/blob/f58dea7d2cc5c9da2e050ec80a73e838b54a6dd2/FormalConjectures/ErdosProblems/370.lean#L73", "proof_links": [ { "complete": true, "conditional": false, "label": "plby/lean-proofs", "partial": false, "source": "plby", "state": "complete", "url": "https://github.com/plby/lean-proofs/blob/main/src/v4.29.1/ErdosProblems/Erdos370.lean" }, { "complete": true, "conditional": false, "label": "Jayyhk/erdos-lean", "partial": false, "source": "jayyhk", "state": "complete", "url": "https://github.com/Jayyhk/erdos-lean/blob/main/problems/370/Erdos370.lean" } ], "recommended_action": "No action.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "Aristotle", "GPT" ], "wiki_claims_lean": true, "wiki_claims_solved": false, "wiki_color": "green", "wiki_humans": [], "wiki_outcome": "Formalization" }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/371", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos371.erdos_371", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos371.erdos_371", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 371, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "proved", "erdos_url": "https://www.erdosproblems.com/372", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 372, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/373", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos373.erdos_373", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos373.erdos_373", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 373, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/374", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 374, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "GPT-5.4 Pro" ], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": "yellow", "wiki_humans": [ "Terence Tao" ], "wiki_outcome": "Partial result" }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "falsifiable", "erdos_url": "https://www.erdosproblems.com/375", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos375.erdos_375", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos375.erdos_375", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 375, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/376", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos376.erdos_376", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos376.erdos_376", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 376, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/377", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos377.erdos_377", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos377.erdos_377", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 377, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "proved", "erdos_url": "https://www.erdosproblems.com/378", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 378, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "done", "discrepancy": false, "erdos_state": "proved (Lean)", "erdos_url": "https://www.erdosproblems.com/379", "fc_has_proof": true, "fc_linked": true, "fc_theorem": "Erdos379.erdos_379", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos379.erdos_379", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, 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"held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 404, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "proved", "erdos_url": "https://www.erdosproblems.com/405", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 405, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/406", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos406.erdos_406", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos406.erdos_406", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 406, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "proved", "erdos_url": "https://www.erdosproblems.com/407", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 407, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/408", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 408, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/409", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos409.erdos_409.variants.sigma_isBigO", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos409.erdos_409.variants.sigma_isBigO", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 409, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/410", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos410.erdos_410", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos410.erdos_410", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 410, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/411", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 411, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "Claude" ], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [ "hoodieuser" ], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/412", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos412.erdos_412", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos412.erdos_412", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 412, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/413", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos413.erdos_413.parts.ii", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos413.erdos_413.parts.ii", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 413, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/414", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos414.erdos_414", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos414.erdos_414", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 414, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/415", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 415, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "GPT-5.4 Pro" ], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": "yellow", "wiki_humans": [ "Przemek Chojecki" ], "wiki_outcome": "Partial result" }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/416", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos416.erdos_416.variants.Maier_Pomerance", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos416.erdos_416.variants.Maier_Pomerance", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 416, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/417", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos417.erdos_417.parts.i", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos417.erdos_417.parts.i", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 417, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "done", "discrepancy": false, "erdos_state": "proved (Lean)", "erdos_url": "https://www.erdosproblems.com/418", "fc_has_proof": true, "fc_linked": true, "fc_theorem": "Erdos418.erdos_418", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos418.erdos_418", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": "plby", "machine_verdict": "conditional", "named_assumptions": [], "non_kernel_axioms": [ "_private.ErdosProblems.Erdos418.0.Erdos418.computation_lemma_check._native.native_decide.ax_1_1" ], "problem": 418, "proof_link": "https://github.com/plby/lean-proofs/blob/main/src/v4.24.0/ErdosProblems/Erdos418.lean", "proof_links": [ { "complete": false, "conditional": true, "label": "plby/lean-proofs", "partial": false, "source": "plby", "state": "conditional", "url": "https://github.com/plby/lean-proofs/blob/main/src/v4.29.1/ErdosProblems/Erdos418.lean" }, { "complete": false, "conditional": true, "label": "Jayyhk/erdos-lean", "partial": false, "source": "jayyhk", "state": "trust_extended", "url": "https://github.com/Jayyhk/erdos-lean/blob/main/problems/418/Erdos418.lean" } ], "recommended_action": "No action.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "Aristotle", "GPT" ], "wiki_claims_lean": true, "wiki_claims_solved": false, "wiki_color": "green", "wiki_humans": [], "wiki_outcome": "Formalization" }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "solved (Lean)", "erdos_url": "https://www.erdosproblems.com/419", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": "plby", "machine_verdict": "unconditional", "named_assumptions": [], "non_kernel_axioms": [], "problem": 419, "proof_link": null, "proof_links": [ { "complete": true, "conditional": false, "label": "plby/lean-proofs", "partial": false, "source": "plby", "state": "complete", "url": "https://github.com/plby/lean-proofs/blob/main/src/v4.29.1/ErdosProblems/Erdos419.lean" }, { "complete": true, "conditional": false, "label": "Jayyhk/erdos-lean", "partial": false, "source": "jayyhk", "state": "complete", "url": "https://github.com/Jayyhk/erdos-lean/blob/main/problems/419/Erdos419.lean" } ], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "Aristotle" ], "wiki_claims_lean": true, "wiki_claims_solved": false, "wiki_color": "green", "wiki_humans": [], "wiki_outcome": "Formalization" }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/420", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 420, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/421", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos421.erdos_421", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos421.erdos_421", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 421, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/422", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos422.erdos_422", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos422.erdos_422", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 422, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/423", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 423, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "GPT-5.2 Thinking", "GPT-5.4 Thinking" ], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": "yellow", "wiki_humans": [ "Nat Sothanaphan", "Quanyu Tang" ], "wiki_outcome": "Partial result" }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/424", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos424.erdos_424", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos424.erdos_424", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 424, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/425", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 425, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "Aristotle", "GPT" ], "wiki_claims_lean": true, "wiki_claims_solved": false, "wiki_color": "green", "wiki_humans": [], "wiki_outcome": "Formalization" }, { "bucket": "statement", "discrepancy": false, "erdos_state": "disproved (Lean)", "erdos_url": "https://www.erdosproblems.com/426", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 426, "proof_link": null, "proof_links": [ { "complete": true, "conditional": false, "label": "plby/lean-proofs", "partial": false, "source": "plby", "state": "complete", "url": "https://github.com/plby/lean-proofs/blob/main/src/v4.29.1/ErdosProblems/Erdos426.lean" }, { "complete": true, "conditional": false, "label": "Jayyhk/erdos-lean", "partial": false, "source": "jayyhk", "state": "complete", "url": "https://github.com/Jayyhk/erdos-lean/blob/main/problems/426/Erdos426.lean" } ], "recommended_action": "Write the FC statement and link the matching hosted proof.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "Aristotle" ], "wiki_claims_lean": true, "wiki_claims_solved": false, "wiki_color": "green", "wiki_humans": [], "wiki_outcome": "Formalization" }, { "bucket": "done", "discrepancy": false, "erdos_state": "proved (Lean)", "erdos_url": "https://www.erdosproblems.com/427", "fc_has_proof": true, "fc_linked": true, "fc_theorem": "Erdos427.erdos_427", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos427.erdos_427", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": "plby", "machine_verdict": "conditional", "named_assumptions": [], "non_kernel_axioms": [ "shiu_consecutive_primes" ], "problem": 427, "proof_link": "https://gist.githubusercontent.com/JohnEdwardJennings/e2c6ef0daab55857b7cc9d340de7af84/raw/8ff97800e38582c71246a238e7541a9d69488cbd/Erdos427.lean", "proof_links": [ { "complete": false, "conditional": true, "label": "plby/lean-proofs", "partial": false, "source": "plby", "state": "conditional", "url": "https://github.com/plby/lean-proofs/blob/main/src/v4.29.1/ErdosProblems/Erdos427.lean" }, { "complete": false, "conditional": true, "label": "Jayyhk/erdos-lean", "partial": false, "source": "jayyhk", "state": "axiomatic", "url": "https://github.com/Jayyhk/erdos-lean/blob/main/problems/427/Erdos427.lean" } ], "recommended_action": "No action.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "Aristotle" ], "wiki_claims_lean": true, "wiki_claims_solved": false, "wiki_color": "green", "wiki_humans": [], "wiki_outcome": "Formalization" }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/428", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos428.erdos_428", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos428.erdos_428", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 428, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "statement", "discrepancy": false, "erdos_state": "disproved (Lean)", "erdos_url": "https://www.erdosproblems.com/429", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": "batch-3 draft for Erd\u0151s 429", "fidelity_source": "local", "gpt_erdos": null, "held_for_review": false, "machine_source": "plby", "machine_verdict": "unconditional", "named_assumptions": [], "non_kernel_axioms": [], "problem": 429, "proof_link": null, "proof_links": [ { "complete": true, "conditional": false, "label": "plby/lean-proofs", "partial": false, "source": "plby", "state": "complete", "url": "https://github.com/plby/lean-proofs/blob/main/src/v4.29.1/ErdosProblems/Erdos429.lean" }, { "complete": true, "conditional": false, "label": "Jayyhk/erdos-lean", "partial": false, "source": "jayyhk", "state": "complete", "url": "https://github.com/Jayyhk/erdos-lean/blob/main/problems/429/Erdos429.lean" } ], "recommended_action": "Write the FC statement and link the matching hosted proof.", "signed_by": "reviewer:will-blair", "signed_fidelity_verdict": "faithful", "wiki_ai_systems": [ "Aristotle" ], "wiki_claims_lean": true, "wiki_claims_solved": false, "wiki_color": "green", "wiki_humans": [], "wiki_outcome": "Formalization" }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/430", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 430, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/431", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 431, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/432", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 432, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "GPT-5.5 Pro" ], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": "white", "wiki_humans": [ "Sungchul Lee" ], "wiki_outcome": "Candidate partial result" }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "proved (Lean)", "erdos_url": "https://www.erdosproblems.com/433", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": "plby", "machine_verdict": "conditional", "named_assumptions": [], "non_kernel_axioms": [ "Finset.add_kneser" ], "problem": 433, "proof_link": null, "proof_links": [ { "complete": false, "conditional": true, "label": "plby/lean-proofs", "partial": false, "source": "plby", "state": "conditional", "url": "https://github.com/plby/lean-proofs/blob/main/src/v4.29.1/ErdosProblems/Erdos433.lean" }, { "complete": true, "conditional": false, "label": "Jayyhk/erdos-lean", "partial": false, "source": "jayyhk", "state": "complete", "url": "https://github.com/Jayyhk/erdos-lean/blob/main/problems/433/Erdos433.lean" } ], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "Aristotle", "Claude Opus 4.8", "Claude Sonnet 4.6", "Gemini 3 Flash", "Gemini 3.1 Pro", "Project Numina" ], "wiki_claims_lean": true, "wiki_claims_solved": false, "wiki_color": "green", "wiki_humans": [], "wiki_outcome": "Formalization" }, { "bucket": "done", "discrepancy": false, "erdos_state": "proved (Lean)", "erdos_url": "https://www.erdosproblems.com/434", "fc_has_proof": true, "fc_linked": true, "fc_theorem": "Erdos434.erdos_434.parts.i", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos434.erdos_434.parts.i", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": "plby", "machine_verdict": "conditional", "named_assumptions": [], "non_kernel_axioms": [ "Finset.add_kneser" ], "problem": 434, "proof_link": "https://www.erdosproblems.com/forum/thread/434#post-4437", "proof_links": [ { "complete": false, "conditional": true, "label": "plby/lean-proofs", "partial": false, "source": "plby", "state": "conditional", "url": "https://github.com/plby/lean-proofs/blob/main/src/v4.29.1/ErdosProblems/Erdos434.lean" }, { "complete": true, "conditional": false, "label": "Jayyhk/erdos-lean", "partial": false, "source": "jayyhk", "state": "complete", "url": "https://github.com/Jayyhk/erdos-lean/blob/main/problems/434/Erdos434.lean" } ], "recommended_action": "No action.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "Aristotle", "Claude Opus 4.8" ], "wiki_claims_lean": true, "wiki_claims_solved": false, "wiki_color": "green", "wiki_humans": [], "wiki_outcome": "Formalization" }, { "bucket": "statement", "discrepancy": false, "erdos_state": "proved (Lean)", "erdos_url": "https://www.erdosproblems.com/435", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": "batch-3 draft for Erd\u0151s 435", "fidelity_source": "local", "gpt_erdos": null, "held_for_review": false, "machine_source": "plby", "machine_verdict": "unconditional", "named_assumptions": [], "non_kernel_axioms": [], "problem": 435, "proof_link": null, "proof_links": [ { "complete": true, "conditional": false, "label": "plby/lean-proofs", "partial": false, "source": "plby", "state": "complete", "url": "https://github.com/plby/lean-proofs/blob/main/src/v4.29.1/ErdosProblems/Erdos435.lean" }, { "complete": true, "conditional": false, "label": "Jayyhk/erdos-lean", "partial": false, "source": "jayyhk", "state": "complete", "url": "https://github.com/Jayyhk/erdos-lean/blob/main/problems/435/Erdos435.lean" } ], "recommended_action": "Write the FC statement and link the matching hosted proof.", "signed_by": "reviewer:will-blair", "signed_fidelity_verdict": "faithful", "wiki_ai_systems": [ "Aristotle" ], "wiki_claims_lean": true, "wiki_claims_solved": false, "wiki_color": "green", "wiki_humans": [], "wiki_outcome": "Formalization" }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/436", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 436, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "proved", "erdos_url": "https://www.erdosproblems.com/437", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 437, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "solved", "erdos_url": "https://www.erdosproblems.com/438", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 438, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "proved", "erdos_url": "https://www.erdosproblems.com/439", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 439, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "solved", "erdos_url": "https://www.erdosproblems.com/440", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 440, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "disproved", "erdos_url": "https://www.erdosproblems.com/441", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 441, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "AxiomProver" ], "wiki_claims_lean": true, "wiki_claims_solved": false, "wiki_color": "yellow", "wiki_humans": [], "wiki_outcome": "Formalization" }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "disproved", "erdos_url": "https://www.erdosproblems.com/442", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos442.erdos_442", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos442.erdos_442", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 442, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "statement", "discrepancy": false, "erdos_state": "proved (Lean)", "erdos_url": "https://www.erdosproblems.com/443", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": "plby", "machine_verdict": "unconditional", "named_assumptions": [], "non_kernel_axioms": [], "problem": 443, "proof_link": null, "proof_links": [ { "complete": true, "conditional": false, "label": "plby/lean-proofs", "partial": false, "source": "plby", "state": "complete", "url": "https://github.com/plby/lean-proofs/blob/main/src/v4.29.1/ErdosProblems/Erdos443.lean" }, { "complete": true, "conditional": false, "label": "Jayyhk/erdos-lean", "partial": false, "source": "jayyhk", "state": "complete", "url": "https://github.com/Jayyhk/erdos-lean/blob/main/problems/443/Erdos443.lean" } ], "recommended_action": "Write the FC statement and link the matching hosted proof.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "Aristotle" ], "wiki_claims_lean": true, "wiki_claims_solved": false, "wiki_color": "green", "wiki_humans": [], "wiki_outcome": "Formalization" }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "proved", "erdos_url": "https://www.erdosproblems.com/444", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 444, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/445", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos445.erdos_445", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos445.erdos_445", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 445, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "solved", "erdos_url": "https://www.erdosproblems.com/446", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 446, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "proved (Lean)", "erdos_url": "https://www.erdosproblems.com/447", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": "plby", "machine_verdict": "unconditional", "named_assumptions": [], "non_kernel_axioms": [], "problem": 447, "proof_link": null, "proof_links": [ { "complete": true, "conditional": false, "label": "plby/lean-proofs", "partial": false, "source": "plby", "state": "complete", "url": "https://github.com/plby/lean-proofs/blob/main/src/v4.29.1/ErdosProblems/Erdos447.lean" }, { "complete": true, "conditional": false, "label": "Jayyhk/erdos-lean", "partial": false, "source": "jayyhk", "state": "complete", "url": "https://github.com/Jayyhk/erdos-lean/blob/main/problems/447/Erdos447.lean" } ], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "Aristotle" ], "wiki_claims_lean": true, "wiki_claims_solved": false, "wiki_color": "green", "wiki_humans": [], "wiki_outcome": "Formalization" }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "disproved", "erdos_url": "https://www.erdosproblems.com/448", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos448.erdos_448", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos448.erdos_448", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 448, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "disproved", "erdos_url": "https://www.erdosproblems.com/449", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 449, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/450", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 450, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/451", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 451, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "Aristotle", "GPT-5.5 Pro" ], "wiki_claims_lean": true, "wiki_claims_solved": false, "wiki_color": "yellow", "wiki_humans": [ "Quanyu Tang", "Wouter van Doorn" ], "wiki_outcome": "Partial result (Lean)" }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/452", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 452, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "disproved (Lean)", "erdos_url": "https://www.erdosproblems.com/453", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": "plby", "machine_verdict": "unconditional", "named_assumptions": [], "non_kernel_axioms": [], "problem": 453, "proof_link": null, "proof_links": [ { "complete": true, "conditional": false, "label": "plby/lean-proofs", "partial": false, "source": "plby", "state": "complete", "url": "https://github.com/plby/lean-proofs/blob/main/src/v4.29.1/ErdosProblems/Erdos453.lean" }, { "complete": true, "conditional": false, "label": "Jayyhk/erdos-lean", "partial": false, "source": "jayyhk", "state": "complete", "url": "https://github.com/Jayyhk/erdos-lean/blob/main/problems/453/Erdos453.lean" } ], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "Aristotle" ], "wiki_claims_lean": true, "wiki_claims_solved": false, "wiki_color": "green", "wiki_humans": [], "wiki_outcome": "Formalization" }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/454", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos454.erdos_454", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos454.erdos_454", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 454, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/455", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos455.erdos_455", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos455.erdos_455", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 455, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/456", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos456.erdos_456.parts.ii", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos456.erdos_456.parts.ii", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 456, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "GPT-5.5 Pro" ], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": "white", "wiki_humans": [ "David Turturean" ], "wiki_outcome": "Candidate partial result (solutions to first part and second part; conditional solution to third part)" }, { "bucket": "done", "discrepancy": false, "erdos_state": "proved (Lean)", "erdos_url": "https://www.erdosproblems.com/457", "fc_has_proof": true, "fc_linked": true, "fc_theorem": "Erdos457.erdos_457", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos457.erdos_457", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": "plby", "machine_verdict": "unconditional", "named_assumptions": [], "non_kernel_axioms": [], "problem": 457, "proof_link": "https://github.com/Woett/Lean-files/blob/main/ErdosProblem457.lean", "proof_links": [ { "complete": true, "conditional": false, "label": "plby/lean-proofs", "partial": false, "source": "plby", "state": "complete", "url": "https://github.com/plby/lean-proofs/blob/main/src/v4.29.1/ErdosProblems/Erdos457.lean" }, { "complete": true, "conditional": false, "label": "Jayyhk/erdos-lean", "partial": false, "source": "jayyhk", "state": "complete", "url": "https://github.com/Jayyhk/erdos-lean/blob/main/problems/457/Erdos457.lean" } ], "recommended_action": "No action.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "Aristotle", "GPT-5.2 Pro" ], "wiki_claims_lean": true, "wiki_claims_solved": true, "wiki_color": "green", "wiki_humans": [], "wiki_outcome": "Full solution (Lean)" }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "falsifiable", "erdos_url": "https://www.erdosproblems.com/458", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos458.erdos_458", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos458.erdos_458", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 458, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "done", "discrepancy": false, "erdos_state": "solved (Lean)", "erdos_url": "https://www.erdosproblems.com/459", "fc_has_proof": true, "fc_linked": true, "fc_theorem": "Erdos459.erdos_459", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos459.erdos_459", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": "plby", "machine_verdict": "unconditional", "named_assumptions": [], "non_kernel_axioms": [], "problem": 459, "proof_link": "https://github.com/Woett/Lean-files/blob/main/ErdosProblem459.lean", "proof_links": [ { "complete": true, "conditional": false, "label": "plby/lean-proofs", "partial": false, "source": "plby", "state": "complete", "url": "https://github.com/plby/lean-proofs/blob/main/src/v4.29.1/ErdosProblems/Erdos459.lean" }, { "complete": true, "conditional": false, "label": "Jayyhk/erdos-lean", "partial": false, "source": "jayyhk", "state": "complete", "url": "https://github.com/Jayyhk/erdos-lean/blob/main/problems/459/Erdos459.lean" } ], "recommended_action": "No action.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "Aristotle" ], "wiki_claims_lean": true, "wiki_claims_solved": false, "wiki_color": "green", "wiki_humans": [], "wiki_outcome": "Formalization" }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/460", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 460, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "GPT-5.2" ], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": "yellow", "wiki_humans": [ "Przemek Chojecki" ], "wiki_outcome": "Reduction to a simpler problem" }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/461", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 461, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/462", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 462, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/463", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos463.erdos_463", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos463.erdos_463", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 463, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "statement", "discrepancy": false, "erdos_state": "proved (Lean)", "erdos_url": "https://www.erdosproblems.com/464", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 464, "proof_link": null, "proof_links": [ { "complete": true, "conditional": false, "label": "Jayyhk/erdos-lean", "partial": false, "source": "jayyhk", "state": "complete", "url": "https://github.com/Jayyhk/erdos-lean/blob/main/problems/464/Erdos464.lean" } ], "recommended_action": "Write the FC statement and link the matching hosted proof.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "Aristotle" ], "wiki_claims_lean": true, "wiki_claims_solved": false, "wiki_color": "green", "wiki_humans": [], "wiki_outcome": "Formalization" }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "proved", "erdos_url": "https://www.erdosproblems.com/465", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 465, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "proved", "erdos_url": "https://www.erdosproblems.com/466", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 466, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/467", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 467, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/468", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 468, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/469", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos469.erdos_469", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos469.erdos_469", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 469, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/470", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos470.erdos_470.parts.ii", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos470.erdos_470.parts.ii", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 470, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "proved", "erdos_url": "https://www.erdosproblems.com/471", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 471, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/472", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 472, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "proved", "erdos_url": "https://www.erdosproblems.com/473", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 473, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "not provable", "erdos_url": "https://www.erdosproblems.com/474", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 474, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "decidable", "erdos_url": "https://www.erdosproblems.com/475", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 475, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "proved (Lean)", "erdos_url": "https://www.erdosproblems.com/476", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": "plby", "machine_verdict": "unconditional", "named_assumptions": [], "non_kernel_axioms": [], "problem": 476, "proof_link": null, "proof_links": [ { "complete": true, "conditional": false, "label": "plby/lean-proofs", "partial": false, "source": "plby", "state": "complete", "url": "https://github.com/plby/lean-proofs/blob/main/src/v4.29.1/ErdosProblems/Erdos476.lean" }, { "complete": true, "conditional": false, "label": "Jayyhk/erdos-lean", "partial": false, "source": "jayyhk", "state": "complete", "url": "https://github.com/Jayyhk/erdos-lean/blob/main/problems/476/Erdos476.lean" } ], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "Aristotle" ], "wiki_claims_lean": true, "wiki_claims_solved": false, "wiki_color": "green", "wiki_humans": [], "wiki_outcome": "Formalization" }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/477", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos477.erdos_477", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos477.erdos_477", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 477, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "AlphaProof" ], "wiki_claims_lean": true, "wiki_claims_solved": false, "wiki_color": "yellow", "wiki_humans": [], "wiki_outcome": "Solution to variant problem (Lean)" }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/478", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 478, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/479", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos479.erdos_479", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos479.erdos_479", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 479, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "proved", "erdos_url": "https://www.erdosproblems.com/480", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos480.erdos_480", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos480.erdos_480", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 480, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "Aristotle" ], "wiki_claims_lean": true, "wiki_claims_solved": false, "wiki_color": "green", "wiki_humans": [], "wiki_outcome": "Formalization" }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "proved (Lean)", "erdos_url": "https://www.erdosproblems.com/481", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": "plby", "machine_verdict": "unconditional", "named_assumptions": [], "non_kernel_axioms": [], "problem": 481, "proof_link": null, "proof_links": [ { "complete": true, "conditional": false, "label": "plby/lean-proofs", "partial": false, "source": "plby", "state": "complete", "url": "https://github.com/plby/lean-proofs/blob/main/src/v4.29.1/ErdosProblems/Erdos481.lean" }, { "complete": true, "conditional": false, "label": "Jayyhk/erdos-lean", "partial": false, "source": "jayyhk", "state": "complete", "url": "https://github.com/Jayyhk/erdos-lean/blob/main/problems/481/Erdos481.lean" } ], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "Aristotle", "Claude" ], "wiki_claims_lean": true, "wiki_claims_solved": false, "wiki_color": "green", "wiki_humans": [], "wiki_outcome": "Formalization" }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "solved", "erdos_url": "https://www.erdosproblems.com/482", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 482, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/483", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 483, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "statement", "discrepancy": false, "erdos_state": "proved (Lean)", "erdos_url": "https://www.erdosproblems.com/484", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": "plby", "machine_verdict": "unconditional", "named_assumptions": [], "non_kernel_axioms": [], "problem": 484, "proof_link": null, "proof_links": [ { "complete": true, "conditional": false, "label": "plby/lean-proofs", "partial": false, "source": "plby", "state": "complete", "url": "https://github.com/plby/lean-proofs/blob/main/src/v4.29.1/ErdosProblems/Erdos484.lean" }, { "complete": true, "conditional": false, "label": "Jayyhk/erdos-lean", "partial": false, "source": "jayyhk", "state": "complete", "url": "https://github.com/Jayyhk/erdos-lean/blob/main/problems/484/Erdos484.lean" } ], "recommended_action": "Write the FC statement and link the matching hosted proof.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "Aristotle" ], "wiki_claims_lean": true, "wiki_claims_solved": false, "wiki_color": "green", "wiki_humans": [], "wiki_outcome": "Formalization" }, { "bucket": "partial", "discrepancy": false, "erdos_state": "proved", "erdos_url": "https://www.erdosproblems.com/485", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": "plby", "machine_verdict": "unconditional", "named_assumptions": [], "non_kernel_axioms": [], "problem": 485, "proof_link": null, "proof_links": [ { "complete": false, "conditional": false, "label": "plby/lean-proofs", "partial": true, "source": "plby", "state": "partial", "url": "https://github.com/plby/lean-proofs/blob/main/src/v4.29.1/ErdosProblems/Erdos485.lean" } ], "recommended_action": "Only link a correctly stated variant after a per-problem review.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/486", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos486.erdos_486", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos486.erdos_486", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 486, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "statement", "discrepancy": false, "erdos_state": "proved (Lean)", "erdos_url": "https://www.erdosproblems.com/487", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": "plby", "machine_verdict": "unconditional", "named_assumptions": [], "non_kernel_axioms": [], "problem": 487, "proof_link": null, "proof_links": [ { "complete": true, "conditional": false, "label": "plby/lean-proofs", "partial": false, "source": "plby", "state": "complete", "url": "https://github.com/plby/lean-proofs/blob/main/src/v4.29.1/ErdosProblems/Erdos487.lean" }, { "complete": true, "conditional": false, "label": "Jayyhk/erdos-lean", "partial": false, "source": "jayyhk", "state": "complete", "url": "https://github.com/Jayyhk/erdos-lean/blob/main/problems/487/Erdos487.lean" } ], "recommended_action": "Write the FC statement and link the matching hosted proof.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "Aristotle" ], "wiki_claims_lean": true, "wiki_claims_solved": false, "wiki_color": "green", "wiki_humans": [], "wiki_outcome": "Formalization" }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "falsifiable", "erdos_url": "https://www.erdosproblems.com/488", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos488.erdos_488", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos488.erdos_488", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 488, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "Aristotle", "GPT-5.4" ], "wiki_claims_lean": true, "wiki_claims_solved": false, "wiki_color": "yellow", "wiki_humans": [ "Przemek Chojecki" ], "wiki_outcome": "New solution to variant problem (Lean)" }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/489", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos489.erdos_489", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos489.erdos_489", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 489, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "docstring", "discrepancy": false, "erdos_state": "proved (Lean)", "erdos_url": "https://www.erdosproblems.com/490", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 490, "proof_link": null, "proof_links": [ { "complete": false, "conditional": true, "label": "plby/lean-proofs", "partial": false, "source": "plby", "state": "conditional", "url": "https://github.com/plby/lean-proofs/blob/main/src/v4.29.1/ErdosProblems/Erdos490.lean" }, { "complete": false, "conditional": true, "label": "Jayyhk/erdos-lean", "partial": false, "source": "jayyhk", "state": "axiomatic", "url": "https://github.com/Jayyhk/erdos-lean/blob/main/problems/490/Erdos490.lean" } ], "recommended_action": "Add only a docstring note if useful; do not add formal_proof.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "Aristotle", "GPT-5.5 Pro" ], "wiki_claims_lean": true, "wiki_claims_solved": false, "wiki_color": "green", "wiki_humans": [], "wiki_outcome": "Formalization" }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "proved", "erdos_url": "https://www.erdosproblems.com/491", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 491, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "disproved", "erdos_url": "https://www.erdosproblems.com/492", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 492, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "done", "discrepancy": false, "erdos_state": "proved (Lean)", "erdos_url": "https://www.erdosproblems.com/493", "fc_has_proof": true, "fc_linked": true, "fc_theorem": "Erdos493.erdos_493", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos493.erdos_493", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": "plby", "machine_verdict": "unconditional", "named_assumptions": [], "non_kernel_axioms": [], "problem": 493, "proof_link": "https://github.com/plby/lean-proofs/blob/main/src/v4.29.1/ErdosProblems/Erdos493.lean", "proof_links": [ { "complete": true, "conditional": false, "label": "plby/lean-proofs", "partial": false, "source": "plby", "state": "complete", "url": "https://github.com/plby/lean-proofs/blob/main/src/v4.29.1/ErdosProblems/Erdos493.lean" }, { "complete": true, "conditional": false, "label": "Jayyhk/erdos-lean", "partial": false, "source": "jayyhk", "state": "complete", "url": "https://github.com/Jayyhk/erdos-lean/blob/main/problems/493/Erdos493.lean" } ], "recommended_action": "No action.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "Aristotle", "GPT", "Seed Prover" ], "wiki_claims_lean": true, "wiki_claims_solved": false, "wiki_color": "green", "wiki_humans": [], "wiki_outcome": "New or existing proof found (Lean)" }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "proved", "erdos_url": "https://www.erdosproblems.com/494", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos494.erdos_494.variants.k_eq_4_card_gt_12", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos494.erdos_494.variants.k_eq_4_card_gt_12", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 494, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/495", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos495.erdos_495", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos495.erdos_495", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 495, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "proved", "erdos_url": "https://www.erdosproblems.com/496", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 496, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "statement", "discrepancy": false, "erdos_state": "solved (Lean)", "erdos_url": "https://www.erdosproblems.com/497", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": "plby", "machine_verdict": "unconditional", "named_assumptions": [], "non_kernel_axioms": [], "problem": 497, "proof_link": null, "proof_links": [ { "complete": true, "conditional": false, "label": "plby/lean-proofs", "partial": false, "source": "plby", "state": "complete", "url": "https://github.com/plby/lean-proofs/blob/main/src/v4.29.1/ErdosProblems/Erdos497.lean" }, { "complete": true, "conditional": false, "label": "Jayyhk/erdos-lean", "partial": false, "source": "jayyhk", "state": "complete", "url": "https://github.com/Jayyhk/erdos-lean/blob/main/problems/497/Erdos497.lean" } ], "recommended_action": "Write the FC statement and link the matching hosted proof.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "Aristotle" ], "wiki_claims_lean": true, "wiki_claims_solved": false, "wiki_color": "green", "wiki_humans": [], "wiki_outcome": "Formalization" }, { "bucket": "statement", "discrepancy": false, "erdos_state": "proved (Lean)", "erdos_url": "https://www.erdosproblems.com/498", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": "plby", "machine_verdict": "unconditional", "named_assumptions": [], "non_kernel_axioms": [], "problem": 498, "proof_link": null, "proof_links": [ { "complete": true, "conditional": false, "label": "plby/lean-proofs", "partial": false, "source": "plby", "state": "complete", "url": "https://github.com/plby/lean-proofs/blob/main/src/v4.29.1/ErdosProblems/Erdos498.lean" }, { "complete": true, "conditional": false, "label": "Jayyhk/erdos-lean", "partial": false, "source": "jayyhk", "state": "complete", "url": "https://github.com/Jayyhk/erdos-lean/blob/main/problems/498/Erdos498.lean" } ], "recommended_action": "Write the FC statement and link the matching hosted proof.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "Aristotle", "Claude Opus", "Gemini Flash", "Gemini Pro" ], "wiki_claims_lean": true, "wiki_claims_solved": false, "wiki_color": "green", "wiki_humans": [], "wiki_outcome": "Formalization" }, { "bucket": "done", "discrepancy": false, "erdos_state": "proved (Lean)", "erdos_url": "https://www.erdosproblems.com/499", "fc_has_proof": true, "fc_linked": true, "fc_theorem": "Erdos499.erdos_499", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos499.erdos_499", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": "plby", "machine_verdict": "unconditional", "named_assumptions": [], "non_kernel_axioms": [], "problem": 499, "proof_link": "https://github.com/plby/lean-proofs/blob/main/src/v4.29.1/ErdosProblems/Erdos499.lean", "proof_links": [ { "complete": true, "conditional": false, "label": "plby/lean-proofs", "partial": false, "source": "plby", "state": "complete", "url": "https://github.com/plby/lean-proofs/blob/main/src/v4.29.1/ErdosProblems/Erdos499.lean" }, { "complete": true, "conditional": false, "label": "Jayyhk/erdos-lean", "partial": false, "source": "jayyhk", "state": "complete", "url": "https://github.com/Jayyhk/erdos-lean/blob/main/problems/499/Erdos499.lean" } ], "recommended_action": "No action.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "Aristotle" ], "wiki_claims_lean": true, "wiki_claims_solved": false, "wiki_color": "green", "wiki_humans": [], "wiki_outcome": "Formalization" }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/500", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 500, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/501", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos501.erdos_501", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos501.erdos_501", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 501, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "GPT-5.5 Pro" ], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": "white", "wiki_humans": [ "Sungchul Lee" ], "wiki_outcome": "Candidate conditional partial result (conditional solution to first part)" }, { "bucket": "statement", "discrepancy": false, "erdos_state": "solved (Lean)", "erdos_url": "https://www.erdosproblems.com/502", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": "plby", "machine_verdict": "unconditional", "named_assumptions": [], "non_kernel_axioms": [], "problem": 502, "proof_link": null, "proof_links": [ { "complete": true, "conditional": false, "label": "plby/lean-proofs", "partial": false, "source": "plby", "state": "complete", "url": "https://github.com/plby/lean-proofs/blob/main/src/v4.29.1/ErdosProblems/Erdos502.lean" }, { "complete": true, "conditional": false, "label": "Jayyhk/erdos-lean", "partial": false, "source": "jayyhk", "state": "complete", "url": "https://github.com/Jayyhk/erdos-lean/blob/main/problems/502/Erdos502.lean" } ], "recommended_action": "Write the FC statement and link the matching hosted proof.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "Aristotle" ], "wiki_claims_lean": true, "wiki_claims_solved": false, "wiki_color": "green", "wiki_humans": [], "wiki_outcome": "Formalization" }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/503", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos503.erdos_503", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos503.erdos_503", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 503, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "Aristotle", "GPT-5.4 Pro", "GPT-5.5 Pro" ], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": "yellow", "wiki_humans": [ "Junnosuke Koizumi", "Przemek Chojecki", "RealBelgian" ], "wiki_outcome": "Partial result" }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "solved", "erdos_url": "https://www.erdosproblems.com/504", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 504, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "done", "discrepancy": false, "erdos_state": "disproved (Lean)", "erdos_url": "https://www.erdosproblems.com/505", "fc_has_proof": true, "fc_linked": true, "fc_theorem": "Erdos505.erdos_505", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos505.erdos_505", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": "plby", "machine_verdict": "unconditional", "named_assumptions": [], "non_kernel_axioms": [], "problem": 505, "proof_link": "https://github.com/plby/lean-proofs/blob/96cd54930d844e3655e6bb89b96b65516397dae9/src/v4.24.0/ErdosProblems/Erdos505.lean#L1153", "proof_links": [ { "complete": true, "conditional": false, "label": "plby/lean-proofs", "partial": false, "source": "plby", "state": "complete", "url": "https://github.com/plby/lean-proofs/blob/main/src/v4.29.1/ErdosProblems/Erdos505.lean" }, { "complete": true, "conditional": false, "label": "Jayyhk/erdos-lean", "partial": false, "source": "jayyhk", "state": "complete", "url": "https://github.com/Jayyhk/erdos-lean/blob/main/problems/505/Erdos505.lean" } ], "recommended_action": "No action.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "Aristotle" ], "wiki_claims_lean": true, "wiki_claims_solved": false, "wiki_color": "green", "wiki_humans": [], "wiki_outcome": "Formalization" }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "decidable", "erdos_url": "https://www.erdosproblems.com/506", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 506, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/507", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos507.erdos_507.upper", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos507.erdos_507.upper", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 507, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "AlphaEvolve" ], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": "yellow", "wiki_humans": [], "wiki_outcome": "Surpassed some past constructions" }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/508", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos508.HadwigerNelsonProblem", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos508.HadwigerNelsonProblem", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 508, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/509", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos509.erdos_509", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos509.erdos_509", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 509, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/510", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos510.erdos_510", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos510.erdos_510", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 510, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "disproved", "erdos_url": "https://www.erdosproblems.com/511", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 511, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "statement", "discrepancy": false, "erdos_state": "proved (Lean)", "erdos_url": "https://www.erdosproblems.com/512", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 512, "proof_link": null, "proof_links": [ { "complete": true, "conditional": false, "label": "Jayyhk/erdos-lean", "partial": false, "source": "jayyhk", "state": "complete", "url": "https://github.com/Jayyhk/erdos-lean/blob/main/problems/512/Erdos512.lean" } ], "recommended_action": "Write the FC statement and link the matching hosted proof.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "Aristotle" ], "wiki_claims_lean": true, "wiki_claims_solved": false, "wiki_color": "green", "wiki_humans": [], "wiki_outcome": "Formalization" }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/513", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos513.erdos_513", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos513.erdos_513", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 513, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "GPT-5.2 Thinking" ], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": "yellow", "wiki_humans": [], "wiki_outcome": "Slight improvement to past construction" }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/514", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": "non_improving", "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 514, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "GPT-5.4 Pro", "GPT-5.5 Pro" ], "wiki_claims_lean": true, "wiki_claims_solved": false, "wiki_color": "yellow", "wiki_humans": [ "Przemek Chojecki", "Yuta Oriike" ], "wiki_outcome": "Partial result (solutions to first part and second part)" }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "proved", "erdos_url": "https://www.erdosproblems.com/515", "fc_has_proof": false, "fc_linked": false, 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[], "non_kernel_axioms": [], "problem": 516, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/517", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos517.erdos_517", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos517.erdos_517", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": "subtle_error", "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 517, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "proved", "erdos_url": "https://www.erdosproblems.com/518", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 518, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "proved (Lean)", "erdos_url": 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"wiki_claims_lean": true, "wiki_claims_solved": false, "wiki_color": "green", "wiki_humans": [], "wiki_outcome": "Formalization" }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/520", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos520.erdos_520", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos520.erdos_520", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 520, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/521", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 521, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "GPT-5.5 Pro" ], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": "yellow", "wiki_humans": [ "Vjekoslav Kova\u010d" ], "wiki_outcome": "Solution to variant problem" }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/522", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos522.erdos_522", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos522.erdos_522", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 522, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "proved", "erdos_url": "https://www.erdosproblems.com/523", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 523, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/524", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": "hidden_constraints", "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 524, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "GPT-5.2", "GPT-5.4 Pro", "Gemini", "Grok" ], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": "yellow", "wiki_humans": [ "Brayden Letwin", "Mehtaab Sawhney" ], "wiki_outcome": "Improved partial result" }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "proved", "erdos_url": "https://www.erdosproblems.com/525", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 525, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "solved", "erdos_url": "https://www.erdosproblems.com/526", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 526, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "proved", "erdos_url": "https://www.erdosproblems.com/527", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 527, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/528", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 528, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/529", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 529, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/530", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 530, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/531", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 531, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "done", "discrepancy": false, "erdos_state": "proved (Lean)", "erdos_url": "https://www.erdosproblems.com/532", "fc_has_proof": true, "fc_linked": true, "fc_theorem": "Erdos532.erdos_532", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos532.erdos_532", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": "plby", "machine_verdict": "unconditional", "named_assumptions": [], "non_kernel_axioms": [], "problem": 532, "proof_link": "https://github.com/plby/lean-proofs/blob/main/src/v4.29.1/ErdosProblems/Erdos532.lean", "proof_links": [ { "complete": true, "conditional": false, "label": "plby/lean-proofs", "partial": false, "source": "plby", "state": "complete", "url": "https://github.com/plby/lean-proofs/blob/main/src/v4.29.1/ErdosProblems/Erdos532.lean" }, { "complete": true, "conditional": false, "label": "Jayyhk/erdos-lean", "partial": false, "source": "jayyhk", "state": "complete", "url": "https://github.com/Jayyhk/erdos-lean/blob/main/problems/532/Erdos532.lean" } ], "recommended_action": "No action.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "disproved", "erdos_url": "https://www.erdosproblems.com/533", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": "subtle_error", "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 533, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "solved", "erdos_url": "https://www.erdosproblems.com/534", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 534, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/535", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos535.erdos_535", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos535.erdos_535", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 535, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "GPT-5.5 Thinking" ], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": "yellow", "wiki_humans": [ "Hrishi Sunder", "Kireet Cheri", "Sourish Kumrawat" ], "wiki_outcome": "Partial result (implicit in literature)" }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/536", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos536.erdos_536", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos536.erdos_536", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 536, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "Codex", "GPT-5.5 Pro" ], "wiki_claims_lean": true, "wiki_claims_solved": false, "wiki_color": "yellow", "wiki_humans": [], "wiki_outcome": "Partial result (Lean)" }, { "bucket": "statement", "discrepancy": false, "erdos_state": "disproved (Lean)", "erdos_url": "https://www.erdosproblems.com/537", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": "plby", "machine_verdict": "unconditional", "named_assumptions": [], "non_kernel_axioms": [], "problem": 537, "proof_link": null, "proof_links": [ { "complete": true, "conditional": false, "label": "plby/lean-proofs", "partial": false, "source": "plby", "state": "complete", "url": "https://github.com/plby/lean-proofs/blob/main/src/v4.29.1/ErdosProblems/Erdos537.lean" }, { "complete": true, "conditional": false, "label": "Jayyhk/erdos-lean", "partial": false, "source": "jayyhk", "state": "complete", "url": "https://github.com/Jayyhk/erdos-lean/blob/main/problems/537/Erdos537.lean" } ], "recommended_action": "Write the FC statement and link the matching hosted proof.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "Aristotle" ], "wiki_claims_lean": true, "wiki_claims_solved": false, "wiki_color": "green", "wiki_humans": [], "wiki_outcome": "Formalization" }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/538", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": "subtle_error", "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 538, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/539", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos539.erdos_539", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos539.erdos_539", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": "conditional_conjecture", "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 539, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "Codex", "GPT-5.5", "ProofCouncil" ], "wiki_claims_lean": true, "wiki_claims_solved": false, "wiki_color": "yellow", "wiki_humans": [], "wiki_outcome": "Partial result (Lean)" }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "proved (Lean)", "erdos_url": "https://www.erdosproblems.com/540", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": "plby", "machine_verdict": "unconditional", "named_assumptions": [], "non_kernel_axioms": [], "problem": 540, "proof_link": null, "proof_links": [ { "complete": true, "conditional": false, "label": "plby/lean-proofs", "partial": false, "source": "plby", "state": "complete", "url": "https://github.com/plby/lean-proofs/blob/main/src/v4.29.1/ErdosProblems/Erdos540.lean" }, { "complete": true, "conditional": false, "label": "Jayyhk/erdos-lean", "partial": false, "source": "jayyhk", "state": "complete", "url": "https://github.com/Jayyhk/erdos-lean/blob/main/problems/540/Erdos540.lean" } ], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "Aristotle" ], "wiki_claims_lean": true, "wiki_claims_solved": false, "wiki_color": "green", "wiki_humans": [], "wiki_outcome": "Formalization" }, { "bucket": "done", "discrepancy": false, "erdos_state": "proved (Lean)", "erdos_url": "https://www.erdosproblems.com/541", "fc_has_proof": true, "fc_linked": true, "fc_theorem": "Erdos541.erdos_541", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos541.erdos_541", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": "plby", "machine_verdict": "unconditional", "named_assumptions": [], "non_kernel_axioms": [], "problem": 541, "proof_link": "https://github.com/plby/lean-proofs/blob/main/src/v4.24.0/ErdosProblems/Erdos541.lean", "proof_links": [ { "complete": true, "conditional": false, "label": "plby/lean-proofs", "partial": false, "source": "plby", "state": "complete", "url": "https://github.com/plby/lean-proofs/blob/main/src/v4.29.1/ErdosProblems/Erdos541.lean" }, { "complete": true, "conditional": false, "label": "Jayyhk/erdos-lean", "partial": false, "source": "jayyhk", "state": "complete", "url": "https://github.com/Jayyhk/erdos-lean/blob/main/problems/541/Erdos541.lean" } ], "recommended_action": "No action.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "Aristotle", "GPT" ], "wiki_claims_lean": true, "wiki_claims_solved": false, "wiki_color": "green", "wiki_humans": [], "wiki_outcome": "Formalization" }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "solved", "erdos_url": "https://www.erdosproblems.com/542", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 542, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "disproved", "erdos_url": "https://www.erdosproblems.com/543", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 543, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "GPT-5.2 Pro" ], "wiki_claims_lean": false, "wiki_claims_solved": true, "wiki_color": "green", "wiki_humans": [], "wiki_outcome": "Full solution" }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/544", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 544, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/545", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 545, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "proved", "erdos_url": "https://www.erdosproblems.com/546", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 546, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "decidable", "erdos_url": "https://www.erdosproblems.com/547", "fc_has_proof": false, "fc_linked": false, 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"held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 580, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "solved", "erdos_url": "https://www.erdosproblems.com/581", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 581, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "statement", "discrepancy": false, "erdos_state": "proved (Lean)", "erdos_url": "https://www.erdosproblems.com/582", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": "plby", "machine_verdict": "unconditional", "named_assumptions": [], "non_kernel_axioms": [], "problem": 582, "proof_link": null, "proof_links": [ { "complete": true, "conditional": false, "label": "plby/lean-proofs", "partial": false, "source": "plby", "state": "complete", "url": "https://github.com/plby/lean-proofs/blob/main/src/v4.29.1/ErdosProblems/Erdos582.lean" }, { "complete": true, "conditional": false, "label": "Jayyhk/erdos-lean", "partial": false, "source": "jayyhk", "state": "complete", "url": 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false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/584", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 584, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/585", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 585, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "disproved", "erdos_url": "https://www.erdosproblems.com/586", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 586, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "solved", "erdos_url": "https://www.erdosproblems.com/587", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos587.erdos_587.variants.nguyen_vu", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos587.erdos_587.variants.nguyen_vu", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 587, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/588", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 588, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/589", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, 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"proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "proved", "erdos_url": "https://www.erdosproblems.com/591", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos591.erdos_591", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos591.erdos_591", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": "literature", "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 591, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/592", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos592.erdos_592", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos592.erdos_592", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 592, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "open", "erdos_url": 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null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 595, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/596", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos596.erdos_596", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos596.erdos_596", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 596, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted 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"erdos_url": "https://www.erdosproblems.com/598", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos598.erdos_598", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos598.erdos_598", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 598, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "Aristotle", "GPT-5.4 Pro" ], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": "white", "wiki_humans": [ "Przemek Chojecki" ], "wiki_outcome": "Candidate partial result" }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "proved", "erdos_url": "https://www.erdosproblems.com/599", "fc_has_proof": false, "fc_linked": false, "fc_theorem": 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"non_kernel_axioms": [], "problem": 600, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/601", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 601, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/602", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos602.erdos_602", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos602.erdos_602", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": "subtle_error", "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 602, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/603", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 603, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "Codex", "GPT-5.4 Pro", "GPT-5.5" ], "wiki_claims_lean": true, "wiki_claims_solved": true, "wiki_color": "green", "wiki_humans": [ "Przemek Chojecki" ], "wiki_outcome": "Full solution" }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/604", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 604, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "proved", "erdos_url": "https://www.erdosproblems.com/605", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 605, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "solved", "erdos_url": "https://www.erdosproblems.com/606", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 606, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "proved", "erdos_url": "https://www.erdosproblems.com/607", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 607, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "disproved", "erdos_url": "https://www.erdosproblems.com/608", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 608, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/609", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 609, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "docstring", "discrepancy": false, "erdos_state": "proved (Lean)", "erdos_url": "https://www.erdosproblems.com/610", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 610, "proof_link": null, "proof_links": [ { "complete": false, "conditional": true, "label": "Jayyhk/erdos-lean", "partial": false, "source": "jayyhk", "state": "axiomatic", "url": "https://github.com/Jayyhk/erdos-lean/blob/main/problems/610/Erdos610.lean" } ], "recommended_action": "Add only a docstring note if useful; do not add formal_proof.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "Aristotle", "GPT-5.4 Pro" ], "wiki_claims_lean": true, "wiki_claims_solved": true, "wiki_color": "green", "wiki_humans": [ "Przemek Chojecki" ], "wiki_outcome": "Full solution (Lean) (implicit in literature)" }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/611", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 611, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/612", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 612, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "blocked-claim", "discrepancy": false, "erdos_state": "disproved (Lean)", "erdos_url": "https://www.erdosproblems.com/613", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos613.erdos_613", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos613.erdos_613", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": "jayyhk", "machine_verdict": "unconditional", "named_assumptions": [], "non_kernel_axioms": [], "problem": 613, "proof_link": null, "proof_links": [ { "complete": true, "conditional": false, "label": "plby/lean-proofs", "partial": false, "source": "plby", "state": "complete", "url": "https://github.com/plby/lean-proofs/blob/main/src/v4.29.1/ErdosProblems/Erdos613.lean" }, { "complete": true, "conditional": false, "label": "Jayyhk/erdos-lean", "partial": false, "source": "jayyhk", "state": "complete", "url": "https://github.com/Jayyhk/erdos-lean/blob/main/problems/613/Erdos613.lean" } ], "recommended_action": "Skip because a human claim exists outside an open PR.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "GPT Pro" ], "wiki_claims_lean": true, "wiki_claims_solved": false, "wiki_color": "green", "wiki_humans": [], "wiki_outcome": "Formalization" }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/614", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 614, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "disproved", "erdos_url": "https://www.erdosproblems.com/615", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos615.erdos_615", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos615.erdos_615", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 615, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/616", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 616, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "Claude Sonnet 4.5", "GPT-5.2 Pro", "Gemini 3 Pro" ], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "falsifiable", "erdos_url": "https://www.erdosproblems.com/617", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos617.erdos_617", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos617.erdos_617", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 617, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "statement", "discrepancy": false, "erdos_state": "proved (Lean)", "erdos_url": "https://www.erdosproblems.com/618", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": "plby", "machine_verdict": "unconditional", "named_assumptions": [], "non_kernel_axioms": [], "problem": 618, "proof_link": null, "proof_links": [ { "complete": true, "conditional": false, "label": "plby/lean-proofs", "partial": false, "source": "plby", "state": "complete", "url": "https://github.com/plby/lean-proofs/blob/main/src/v4.29.1/ErdosProblems/Erdos618.lean" }, { "complete": true, "conditional": false, "label": "Jayyhk/erdos-lean", "partial": false, "source": "jayyhk", "state": "complete", "url": "https://github.com/Jayyhk/erdos-lean/blob/main/problems/618/Erdos618.lean" } ], "recommended_action": "Write the FC statement and link the matching hosted proof.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "Aristotle" ], "wiki_claims_lean": true, "wiki_claims_solved": false, "wiki_color": "green", "wiki_humans": [], "wiki_outcome": "Formalization" }, { "bucket": "done", "discrepancy": false, "erdos_state": "solved (Lean)", "erdos_url": "https://www.erdosproblems.com/619", "fc_has_proof": true, "fc_linked": true, "fc_theorem": "Erdos619.erdos_619", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos619.erdos_619", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 619, "proof_link": "https://github.com/nick-kuhn/erdos-619/blob/7f65718b8c1019ecc24e6c9a6b04ec4c66a4e26f/Solution.lean#L5869", "proof_links": [ { "complete": true, "conditional": false, "label": "Jayyhk/erdos-lean", "partial": false, "source": "jayyhk", "state": "complete", "url": "https://github.com/Jayyhk/erdos-lean/blob/main/problems/619/Erdos619.lean" } ], "recommended_action": "No action.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "Claude Fable 5", "Codex", "GPT-5.5" ], "wiki_claims_lean": true, "wiki_claims_solved": true, "wiki_color": "green", "wiki_humans": [], "wiki_outcome": "Full solution (Lean)" }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/620", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 620, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "statement", "discrepancy": false, "erdos_state": "proved (Lean)", "erdos_url": "https://www.erdosproblems.com/621", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 621, "proof_link": null, "proof_links": [ { "complete": true, "conditional": false, "label": "plby/lean-proofs", "partial": false, "source": "plby", "state": "complete", "url": "https://github.com/plby/lean-proofs/blob/main/src/v4.29.1/ErdosProblems/Erdos621.lean" }, { "complete": true, "conditional": false, "label": "Jayyhk/erdos-lean", "partial": false, "source": "jayyhk", "state": "complete", "url": "https://github.com/Jayyhk/erdos-lean/blob/main/problems/621/Erdos621.lean" } ], "recommended_action": "Write the FC statement and link the matching hosted proof.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "Aristotle" ], "wiki_claims_lean": true, "wiki_claims_solved": false, "wiki_color": "green", "wiki_humans": [], "wiki_outcome": "Formalization" }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "proved", "erdos_url": "https://www.erdosproblems.com/622", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 622, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/623", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos623.erdos_623", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos623.erdos_623", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 623, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "GPT-5.5 Pro" ], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": "white", "wiki_humans": [ "Sungchul Lee" ], "wiki_outcome": "Candidate full solution" }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/624", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos624.erdos_624", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos624.erdos_624", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 624, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/625", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 625, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/626", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 626, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/627", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 627, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "falsifiable", "erdos_url": "https://www.erdosproblems.com/628", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 628, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/629", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 629, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "GPT-5.4 Thinking", "Gemini 3.1 Pro" ], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": "yellow", "wiki_humans": [], "wiki_outcome": "Partial result" }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "proved", "erdos_url": "https://www.erdosproblems.com/630", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 630, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "proved", "erdos_url": "https://www.erdosproblems.com/631", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 631, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "disproved", "erdos_url": "https://www.erdosproblems.com/632", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 632, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "solved", "erdos_url": "https://www.erdosproblems.com/633", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos633.erdos_633", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos633.erdos_633", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 633, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/634", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 634, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/635", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 635, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "Aristotle", "GPT-5.2 Pro" ], "wiki_claims_lean": true, "wiki_claims_solved": false, "wiki_color": "yellow", "wiki_humans": [], "wiki_outcome": "Solution to one part of problem (Lean)" }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "proved", "erdos_url": "https://www.erdosproblems.com/636", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 636, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "proved", "erdos_url": "https://www.erdosproblems.com/637", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 637, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/638", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 638, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "statement", "discrepancy": false, "erdos_state": "proved (Lean)", "erdos_url": "https://www.erdosproblems.com/639", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 639, "proof_link": null, "proof_links": [ { "complete": true, "conditional": false, "label": "plby/lean-proofs", "partial": false, "source": "plby", "state": "complete", "url": "https://github.com/plby/lean-proofs/blob/main/src/v4.29.1/ErdosProblems/Erdos639.lean" }, { "complete": true, "conditional": false, "label": "Jayyhk/erdos-lean", "partial": false, "source": "jayyhk", "state": "complete", "url": "https://github.com/Jayyhk/erdos-lean/blob/main/problems/639/Erdos639.lean" } ], "recommended_action": "Write the FC statement and link the matching hosted proof.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "Aristotle" ], "wiki_claims_lean": true, "wiki_claims_solved": false, "wiki_color": "green", "wiki_humans": [], "wiki_outcome": "Formalization" }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/640", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 640, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "disproved", "erdos_url": "https://www.erdosproblems.com/641", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 641, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/642", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 642, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/643", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 643, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/644", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 644, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "done", "discrepancy": false, "erdos_state": "proved (Lean)", "erdos_url": "https://www.erdosproblems.com/645", "fc_has_proof": true, "fc_linked": true, "fc_theorem": "Erdos645.erdos_645", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos645.erdos_645", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": "plby", "machine_verdict": "unconditional", "named_assumptions": [], "non_kernel_axioms": [], "problem": 645, "proof_link": "https://github.com/plby/lean-proofs/blob/main/src/v4.24.0/ErdosProblems/Erdos645.lean", "proof_links": [ { "complete": true, "conditional": false, "label": "plby/lean-proofs", "partial": false, "source": "plby", "state": "complete", "url": "https://github.com/plby/lean-proofs/blob/main/src/v4.29.1/ErdosProblems/Erdos645.lean" }, { "complete": true, "conditional": false, "label": "Jayyhk/erdos-lean", "partial": false, "source": "jayyhk", "state": "complete", "url": "https://github.com/Jayyhk/erdos-lean/blob/main/problems/645/Erdos645.lean" } ], "recommended_action": "No action.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "Aristotle", "GPT" ], "wiki_claims_lean": true, "wiki_claims_solved": false, "wiki_color": "green", "wiki_humans": [], "wiki_outcome": "Formalization" }, { "bucket": "statement", "discrepancy": false, "erdos_state": "proved (Lean)", "erdos_url": "https://www.erdosproblems.com/646", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": "plby", "machine_verdict": "unconditional", "named_assumptions": [], "non_kernel_axioms": [], "problem": 646, "proof_link": null, "proof_links": [ { "complete": true, "conditional": false, "label": "plby/lean-proofs", "partial": false, "source": "plby", "state": "complete", "url": "https://github.com/plby/lean-proofs/blob/main/src/v4.29.1/ErdosProblems/Erdos646.lean" }, { "complete": true, "conditional": false, "label": "Jayyhk/erdos-lean", "partial": false, "source": "jayyhk", "state": "complete", "url": "https://github.com/Jayyhk/erdos-lean/blob/main/problems/646/Erdos646.lean" } ], "recommended_action": "Write the FC statement and link the matching hosted proof.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "Aristotle" ], "wiki_claims_lean": true, "wiki_claims_solved": false, "wiki_color": "green", "wiki_humans": [], "wiki_outcome": "Formalization" }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "verifiable", "erdos_url": "https://www.erdosproblems.com/647", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos647.erdos_647", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos647.erdos_647", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": "conditional_conjecture", "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 647, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "ChatGPT Deep research", "DeepSeek DeepThink", "Gemini" ], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "statement", "discrepancy": false, "erdos_state": "solved (Lean)", "erdos_url": "https://www.erdosproblems.com/648", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": "plby", "machine_verdict": "unconditional", "named_assumptions": [], "non_kernel_axioms": [], "problem": 648, "proof_link": null, "proof_links": [ { "complete": true, "conditional": false, "label": "plby/lean-proofs", "partial": false, "source": "plby", "state": "complete", "url": "https://github.com/plby/lean-proofs/blob/main/src/v4.29.1/ErdosProblems/Erdos648.lean" }, { "complete": true, "conditional": false, "label": "Jayyhk/erdos-lean", "partial": false, "source": "jayyhk", "state": "complete", "url": "https://github.com/Jayyhk/erdos-lean/blob/main/problems/648/Erdos648.lean" } ], "recommended_action": "Write the FC statement and link the matching hosted proof.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "Aristotle" ], "wiki_claims_lean": true, "wiki_claims_solved": false, "wiki_color": "green", "wiki_humans": [], "wiki_outcome": "Formalization" }, { "bucket": "statement", "discrepancy": false, "erdos_state": "disproved (Lean)", "erdos_url": "https://www.erdosproblems.com/649", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": "plby", "machine_verdict": "unconditional", "named_assumptions": [], "non_kernel_axioms": [], "problem": 649, "proof_link": null, "proof_links": [ { "complete": true, "conditional": false, "label": "plby/lean-proofs", "partial": false, "source": "plby", "state": "complete", "url": "https://github.com/plby/lean-proofs/blob/main/src/v4.29.1/ErdosProblems/Erdos649.lean" }, { "complete": true, "conditional": false, "label": "Jayyhk/erdos-lean", "partial": false, "source": "jayyhk", "state": "complete", "url": "https://github.com/Jayyhk/erdos-lean/blob/main/problems/649/Erdos649.lean" } ], "recommended_action": "Write the FC statement and link the matching hosted proof.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "Aristotle", "GPT" ], "wiki_claims_lean": true, "wiki_claims_solved": false, "wiki_color": "green", "wiki_humans": [], "wiki_outcome": "Formalization" }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "solved (Lean)", "erdos_url": "https://www.erdosproblems.com/650", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": "plby", "machine_verdict": "unconditional", "named_assumptions": [], "non_kernel_axioms": [], "problem": 650, "proof_link": null, "proof_links": [ { "complete": true, "conditional": false, "label": "plby/lean-proofs", "partial": false, "source": "plby", "state": "complete", "url": "https://github.com/plby/lean-proofs/blob/main/src/v4.29.1/ErdosProblems/Erdos650.lean" }, { "complete": true, "conditional": false, "label": "Jayyhk/erdos-lean", "partial": false, "source": "jayyhk", "state": "complete", "url": "https://github.com/Jayyhk/erdos-lean/blob/main/problems/650/Erdos650.lean" } ], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "Aristotle", "GPT-5.4 Pro" ], "wiki_claims_lean": true, "wiki_claims_solved": true, "wiki_color": "green", "wiki_humans": [], "wiki_outcome": "Full solution (stronger than literature)" }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "disproved", "erdos_url": "https://www.erdosproblems.com/651", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 651, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "proved", "erdos_url": "https://www.erdosproblems.com/652", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": "new_proof", "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 652, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/653", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos653.erdos_653", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos653.erdos_653", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 653, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/654", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 654, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "Aletheia" ], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": "yellow", "wiki_humans": [], "wiki_outcome": "Partial result" }, { "bucket": "done", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/655", "fc_has_proof": true, "fc_linked": true, "fc_theorem": "Erdos655.erdos_655", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos655.erdos_655", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": "non_improving", "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 655, "proof_link": "https://github.com/AlperTheKing/formal-conjectures/blob/4aaaf544b6ed0ef22580787a8d8a19e85dc49556/FormalConjectures/ErdosProblems/655.lean", "proof_links": [], "recommended_action": "No action.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "proved", "erdos_url": "https://www.erdosproblems.com/656", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 656, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/657", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 657, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "statement", "discrepancy": false, "erdos_state": "proved (Lean)", "erdos_url": "https://www.erdosproblems.com/658", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": "plby", "machine_verdict": "unconditional", "named_assumptions": [], "non_kernel_axioms": [], "problem": 658, "proof_link": null, "proof_links": [ { "complete": false, "conditional": true, "label": "plby/lean-proofs", "partial": false, "source": "plby", "state": "conditional", "url": "https://github.com/plby/lean-proofs/blob/main/src/v4.29.1/ErdosProblems/Erdos658.lean" }, { "complete": false, "conditional": true, "label": "Jayyhk/erdos-lean", "partial": false, "source": "jayyhk", "state": "axiomatic", "url": "https://github.com/Jayyhk/erdos-lean/blob/main/problems/658/Erdos658.lean" } ], "recommended_action": "Write the FC statement and link the matching hosted proof.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "Aristotle" ], "wiki_claims_lean": true, "wiki_claims_solved": false, "wiki_color": "green", "wiki_humans": [], "wiki_outcome": "Formalization" }, { "bucket": "docstring", "discrepancy": true, "erdos_state": "proved (Lean)", "erdos_url": "https://www.erdosproblems.com/659", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos659.erdos_659", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos659.erdos_659", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": "plby", "machine_verdict": "conditional", "named_assumptions": [], "non_kernel_axioms": [ "bernays" ], "problem": 659, "proof_link": null, "proof_links": [ { "complete": false, "conditional": true, "label": "plby/lean-proofs", "partial": false, "source": "plby", "state": "conditional", "url": "https://github.com/plby/lean-proofs/blob/main/src/v4.29.1/ErdosProblems/Erdos659.lean" }, { "complete": false, "conditional": true, "label": "Jayyhk/erdos-lean", "partial": false, "source": "jayyhk", "state": "axiomatic", "url": "https://github.com/Jayyhk/erdos-lean/blob/main/problems/659/Erdos659.lean" } ], "recommended_action": "Add only a docstring note if useful; do not add formal_proof.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "Aletheia", "Aristotle", "Gemini 3" ], "wiki_claims_lean": true, "wiki_claims_solved": true, "wiki_color": "green", "wiki_humans": [ "Benjamin Grayzel" ], "wiki_outcome": "Full solution" }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/660", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 660, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/661", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 661, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/662", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": "typo", "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 662, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/663", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 663, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "disproved", "erdos_url": "https://www.erdosproblems.com/664", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 664, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/665", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": "hidden_constraints", "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 665, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "statement", "discrepancy": false, "erdos_state": "disproved (Lean)", "erdos_url": "https://www.erdosproblems.com/666", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": "plby", "machine_verdict": "unconditional", "named_assumptions": [], "non_kernel_axioms": [], "problem": 666, "proof_link": null, "proof_links": [ { "complete": true, "conditional": false, "label": "plby/lean-proofs", "partial": false, "source": "plby", "state": "complete", "url": "https://github.com/plby/lean-proofs/blob/main/src/v4.29.1/ErdosProblems/Erdos666.lean" }, { "complete": true, "conditional": false, "label": "Jayyhk/erdos-lean", "partial": false, "source": "jayyhk", "state": "complete", "url": "https://github.com/Jayyhk/erdos-lean/blob/main/problems/666/Erdos666.lean" } ], "recommended_action": "Write the FC statement and link the matching hosted proof.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "Aristotle" ], "wiki_claims_lean": true, "wiki_claims_solved": false, "wiki_color": "green", "wiki_humans": [], "wiki_outcome": "Formalization" }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/667", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 667, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/668", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 668, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/669", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 669, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/670", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 670, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/671", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 671, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "Codex", "GPT-5.5 Pro" ], "wiki_claims_lean": true, "wiki_claims_solved": false, "wiki_color": "white", "wiki_humans": [], "wiki_outcome": "Candidate full solution (Lean)" }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "verifiable", "erdos_url": "https://www.erdosproblems.com/672", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos672.erdos_672", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos672.erdos_672", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 672, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "proved", "erdos_url": "https://www.erdosproblems.com/673", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 673, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "statement", "discrepancy": false, "erdos_state": "proved (Lean)", "erdos_url": "https://www.erdosproblems.com/674", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": "plby", "machine_verdict": "unconditional", "named_assumptions": [], "non_kernel_axioms": [], "problem": 674, "proof_link": null, "proof_links": [ { "complete": true, "conditional": false, "label": "plby/lean-proofs", "partial": false, "source": "plby", "state": "complete", "url": "https://github.com/plby/lean-proofs/blob/main/src/v4.29.1/ErdosProblems/Erdos674.lean" }, { "complete": true, "conditional": false, "label": "Jayyhk/erdos-lean", "partial": false, "source": "jayyhk", "state": "complete", "url": "https://github.com/Jayyhk/erdos-lean/blob/main/problems/674/Erdos674.lean" } ], "recommended_action": "Write the FC statement and link the matching hosted proof.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/675", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 675, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "GPT-5.4 Pro" ], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": "yellow", "wiki_humans": [ "Boon Suan Ho" ], "wiki_outcome": "Partial result" }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/676", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 676, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/677", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos677.erdos_677", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos677.erdos_677", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 677, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "wont-fix", "discrepancy": false, "erdos_state": "proved (Lean)", "erdos_url": "https://www.erdosproblems.com/678", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos678.erdos_678", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos678.erdos_678", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": "plby", "machine_verdict": "unconditional", "named_assumptions": [], "non_kernel_axioms": [], "problem": 678, "proof_link": null, "proof_links": [ { "complete": true, "conditional": false, "label": "plby/lean-proofs", "partial": false, "source": "plby", "state": "complete", "url": "https://github.com/plby/lean-proofs/blob/main/src/v4.29.1/ErdosProblems/Erdos678.lean" }, { "complete": true, "conditional": false, "label": "Jayyhk/erdos-lean", "partial": false, "source": "jayyhk", "state": "complete", "url": "https://github.com/Jayyhk/erdos-lean/blob/main/problems/678/Erdos678.lean" } ], "recommended_action": "Skip.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "Aristotle" ], "wiki_claims_lean": true, "wiki_claims_solved": false, "wiki_color": "green", "wiki_humans": [], "wiki_outcome": "Formalization" }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/679", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 679, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "Aristotle" ], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": "yellow", "wiki_humans": [], "wiki_outcome": "Improved proof by reducing dependence on prime number theorem" }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/680", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos680.erdos_680.parts.i", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos680.erdos_680.parts.i", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 680, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/681", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos681.erdos_681", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos681.erdos_681", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 681, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "proved", "erdos_url": "https://www.erdosproblems.com/682", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 682, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/683", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos683.erdos_683", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos683.erdos_683", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 683, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/684", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 684, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "GPT-5.2 Thinking", "GPT-5.4 Thinking", "OpenAI internal model" ], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": "yellow", "wiki_humans": [ "Nat Sothanaphan", "Quanyu Tang" ], "wiki_outcome": "Partial result" }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/685", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 685, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/686", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos686.erdos_686", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos686.erdos_686", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": "hidden_constraints", "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 686, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "AlphaProof", "Claude", "GPT-5.2 Thinking", "GPT-5.4 Thinking", "Gemini Deep Think", "Seed 2.0 Pro" ], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": "yellow", "wiki_humans": [ "Adenwalla", "Malek Zribi", "Miklos", "Nat Sothanaphan", "Quanyu Tang", "Stijn Cambie", "Terence Tao", "Vjekoslav Kova\u010d", "Wouter van Doorn", "vilc" ], "wiki_outcome": "Various partial results" }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/687", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 687, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/688", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos688.erdos_688.parts.i.lower_bound", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos688.erdos_688.parts.i.lower_bound", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 688, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/689", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos689.erdos_689", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos689.erdos_689", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 689, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "Codex", "GPT-5.2", "GPT-5.5 Pro" ], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": "white", "wiki_humans": [ "Boris Alexeev", "Dogmachine", "Malek Zribi", "Mehtaab Sawhney", "Przemek Chojecki", "Terence Tao", "jleng01" ], "wiki_outcome": "Candidate full solution" }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "solved", "erdos_url": "https://www.erdosproblems.com/690", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": "hidden_constraints", "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 690, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "Multiscalar Fields System" ], "wiki_claims_lean": false, "wiki_claims_solved": true, "wiki_color": "green", "wiki_humans": [ "Davide Crapis", "Shouqiao Wang" ], "wiki_outcome": "Full solution" }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/691", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 691, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "statement", "discrepancy": false, "erdos_state": "disproved (Lean)", "erdos_url": "https://www.erdosproblems.com/692", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": "plby", "machine_verdict": "unconditional", "named_assumptions": [], "non_kernel_axioms": [], "problem": 692, "proof_link": null, "proof_links": [ { "complete": true, "conditional": false, "label": "plby/lean-proofs", "partial": false, "source": "plby", "state": "complete", "url": "https://github.com/plby/lean-proofs/blob/main/src/v4.29.1/ErdosProblems/Erdos692.lean" }, { "complete": true, "conditional": false, "label": "Jayyhk/erdos-lean", "partial": false, "source": "jayyhk", "state": "complete", "url": "https://github.com/Jayyhk/erdos-lean/blob/main/problems/692/Erdos692.lean" } ], "recommended_action": "Write the FC statement and link the matching hosted proof.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "Aristotle" ], "wiki_claims_lean": true, "wiki_claims_solved": false, "wiki_color": "green", "wiki_humans": [], "wiki_outcome": "Formalization" }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/693", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 693, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "docstring", "discrepancy": true, "erdos_state": "solved (Lean)", "erdos_url": "https://www.erdosproblems.com/694", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos694.erdos_694", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos694.erdos_694", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": "plby", "machine_verdict": "conditional", "named_assumptions": [], "non_kernel_axioms": [ "mertens_product", "linnik_dvd" ], "problem": 694, "proof_link": null, "proof_links": [ { "complete": false, "conditional": true, "label": "plby/lean-proofs", "partial": false, "source": "plby", "state": "conditional", "url": "https://github.com/plby/lean-proofs/blob/main/src/v4.29.1/ErdosProblems/Erdos694.lean" }, { "complete": false, "conditional": true, "label": "Jayyhk/erdos-lean", "partial": false, "source": "jayyhk", "state": "axiomatic", "url": "https://github.com/Jayyhk/erdos-lean/blob/main/problems/694/Erdos694.lean" } ], "recommended_action": "Add only a docstring note if useful; do not add formal_proof.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "Aristotle", "Claude Code", "Claude Opus 4.7", "GPT-5.5 Pro" ], "wiki_claims_lean": true, "wiki_claims_solved": true, "wiki_color": "green", "wiki_humans": [], "wiki_outcome": "Full solution" }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/695", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos695.erdos_695", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos695.erdos_695", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 695, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "solved (Lean)", "erdos_url": "https://www.erdosproblems.com/696", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 696, "proof_link": null, "proof_links": [ { "complete": false, "conditional": true, "label": "Jayyhk/erdos-lean", "partial": false, "source": "jayyhk", "state": "axiomatic", "url": "https://github.com/Jayyhk/erdos-lean/blob/main/problems/696/Erdos696.lean" } ], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "Aristotle", "Claude Code", "Claude Opus 4.7", "GPT-5.5 Pro" ], "wiki_claims_lean": true, "wiki_claims_solved": true, "wiki_color": "green", "wiki_humans": [ "David Turturean", "Jake Mallen" ], "wiki_outcome": "Full solution (Lean)" }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "proved", "erdos_url": "https://www.erdosproblems.com/697", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos697.erdos_697.variants.delta_lt", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos697.erdos_697.variants.delta_lt", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 697, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "statement", "discrepancy": false, "erdos_state": "proved (Lean)", "erdos_url": "https://www.erdosproblems.com/698", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": "plby", "machine_verdict": "unconditional", "named_assumptions": [], "non_kernel_axioms": [], "problem": 698, "proof_link": null, "proof_links": [ { "complete": true, "conditional": false, "label": "plby/lean-proofs", "partial": false, "source": "plby", "state": "complete", "url": "https://github.com/plby/lean-proofs/blob/main/src/v4.29.1/ErdosProblems/Erdos698.lean" }, { "complete": true, "conditional": false, "label": "Jayyhk/erdos-lean", "partial": false, "source": "jayyhk", "state": "complete", "url": "https://github.com/Jayyhk/erdos-lean/blob/main/problems/698/Erdos698.lean" } ], "recommended_action": "Write the FC statement and link the matching hosted proof.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "Aristotle" ], "wiki_claims_lean": true, "wiki_claims_solved": false, "wiki_color": "green", "wiki_humans": [], "wiki_outcome": "Formalization" }, { "bucket": "done", "discrepancy": false, "erdos_state": "falsifiable", "erdos_url": "https://www.erdosproblems.com/699", "fc_has_proof": true, "fc_linked": true, "fc_theorem": "Erdos699.sylvester_schur", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos699.sylvester_schur", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 699, "proof_link": "https://github.com/AllenGrahamHart/FormalConjectures-Bench/blob/482dacc4d9335240f26218cdc62032da3100392b/formalizations/erdos699/Erdos699Formalization.lean#L7679", "proof_links": [], "recommended_action": "No action.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/700", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos700.erdos_700.parts.ii", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos700.erdos_700.parts.ii", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 700, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/701", "fc_has_proof": false, "fc_linked": false, 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false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/710", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 710, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/711", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, 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"wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "proved", "erdos_url": "https://www.erdosproblems.com/718", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 718, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/719", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 719, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "proved", "erdos_url": "https://www.erdosproblems.com/720", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 720, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted 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"conditional": false, "label": "plby/lean-proofs", "partial": false, "source": "plby", "state": "complete", "url": "https://github.com/plby/lean-proofs/blob/main/src/v4.29.1/ErdosProblems/Erdos756.lean" }, { "complete": true, "conditional": false, "label": "Jayyhk/erdos-lean", "partial": false, "source": "jayyhk", "state": "complete", "url": "https://github.com/Jayyhk/erdos-lean/blob/main/problems/756/Erdos756.lean" } ], "recommended_action": "Write the FC statement and link the matching hosted proof.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "Aristotle" ], "wiki_claims_lean": true, "wiki_claims_solved": false, "wiki_color": "green", "wiki_humans": [], "wiki_outcome": "Formalization" }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/757", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos757.erdos_757", "fc_url": 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"wiki_outcome": null }, { "bucket": "statement", "discrepancy": false, "erdos_state": "proved (Lean)", "erdos_url": "https://www.erdosproblems.com/760", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 760, "proof_link": null, "proof_links": [ { "complete": true, "conditional": false, "label": "plby/lean-proofs", "partial": false, "source": "plby", "state": "complete", "url": "https://github.com/plby/lean-proofs/blob/main/src/v4.29.1/ErdosProblems/Erdos760.lean" }, { "complete": true, "conditional": false, "label": "Jayyhk/erdos-lean", "partial": false, "source": "jayyhk", "state": "complete", "url": "https://github.com/Jayyhk/erdos-lean/blob/main/problems/760/Erdos760.lean" } ], "recommended_action": "Write the FC statement and link the matching hosted 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"wiki_outcome": null }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/768", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 768, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "GPT" ], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": "white", "wiki_humans": [ "Eric Li" ], "wiki_outcome": "Candidate full solution" }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/769", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 769, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/770", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos770.erdos_770.parts.ii", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos770.erdos_770.parts.ii", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], 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"label": "Jayyhk/erdos-lean", "partial": false, "source": "jayyhk", "state": "complete", "url": "https://github.com/Jayyhk/erdos-lean/blob/main/problems/775/Erdos775.lean" } ], "recommended_action": "Write the FC statement and link the matching hosted proof.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "Aristotle" ], "wiki_claims_lean": true, "wiki_claims_solved": false, "wiki_color": "green", "wiki_humans": [], "wiki_outcome": "Formalization" }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/776", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 776, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "GPT-5.2 Thinking" ], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": "yellow", "wiki_humans": [ "Quanyu Tang", "Yixin He" ], "wiki_outcome": "Partial result" }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "solved", "erdos_url": "https://www.erdosproblems.com/777", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 777, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/778", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 778, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "falsifiable", "erdos_url": "https://www.erdosproblems.com/779", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos779.erdos_779", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos779.erdos_779", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 779, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "proved", "erdos_url": "https://www.erdosproblems.com/780", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 780, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "disproved", "erdos_url": "https://www.erdosproblems.com/781", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 781, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/782", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 782, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "solved", "erdos_url": "https://www.erdosproblems.com/783", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": "subtle_error", "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 783, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "GPT-5.2" ], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": "yellow", "wiki_humans": [], "wiki_outcome": "Partial result" }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "solved", "erdos_url": "https://www.erdosproblems.com/784", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 784, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "hypothesis-conditional", "discrepancy": false, "erdos_state": "proved (Lean)", "erdos_url": "https://www.erdosproblems.com/785", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": "plby", "machine_verdict": "conditional", "named_assumptions": [ "h_hyp : Erdos785.exact_complements A B" ], "non_kernel_axioms": [], "problem": 785, "proof_link": null, "proof_links": [ { "complete": true, "conditional": false, "label": "plby/lean-proofs", "partial": false, "source": "plby", "state": "complete", "url": "https://github.com/plby/lean-proofs/blob/main/src/v4.29.1/ErdosProblems/Erdos785.lean" }, { "complete": true, "conditional": false, "label": "Jayyhk/erdos-lean", "partial": false, "source": "jayyhk", "state": "complete", "url": "https://github.com/Jayyhk/erdos-lean/blob/main/problems/785/Erdos785.lean" } ], "recommended_action": "Do not add a formal_proof link; document or wait for an unconditional theorem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "Aristotle" ], "wiki_claims_lean": true, "wiki_claims_solved": false, "wiki_color": "green", "wiki_humans": [], "wiki_outcome": "Formalization" }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/786", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos786.erdos_786.parts.i", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos786.erdos_786.parts.i", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 786, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/787", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 787, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/788", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": "partial_literature", "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 788, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "Aristotle", "GPT-5.2 Pro" ], "wiki_claims_lean": true, "wiki_claims_solved": false, "wiki_color": "yellow", "wiki_humans": [], "wiki_outcome": "New partial result" }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/789", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos789.erdos_789", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos789.erdos_789", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 789, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/790", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 790, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/791", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 791, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/792", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": "non_improving", "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 792, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/793", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 793, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "disproved (Lean)", "erdos_url": "https://www.erdosproblems.com/794", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": "plby", "machine_verdict": "unconditional", "named_assumptions": [], "non_kernel_axioms": [], "problem": 794, "proof_link": null, "proof_links": [ { "complete": true, "conditional": false, "label": "plby/lean-proofs", "partial": false, "source": "plby", "state": "complete", "url": "https://github.com/plby/lean-proofs/blob/main/src/v4.29.1/ErdosProblems/Erdos794.lean" }, { "complete": true, "conditional": false, "label": "Jayyhk/erdos-lean", "partial": false, "source": "jayyhk", "state": "complete", "url": "https://github.com/Jayyhk/erdos-lean/blob/main/problems/794/Erdos794.lean" } ], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "Aristotle" ], "wiki_claims_lean": true, "wiki_claims_solved": false, "wiki_color": "green", "wiki_humans": [], "wiki_outcome": "Formalization" }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "proved", "erdos_url": "https://www.erdosproblems.com/795", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 795, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/796", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": "non_improving", "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 796, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "proved", "erdos_url": "https://www.erdosproblems.com/797", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 797, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "statement", "discrepancy": false, "erdos_state": "proved (Lean)", "erdos_url": "https://www.erdosproblems.com/798", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": "plby", "machine_verdict": "unconditional", "named_assumptions": [], "non_kernel_axioms": [], "problem": 798, "proof_link": null, "proof_links": [ { "complete": true, "conditional": false, "label": "plby/lean-proofs", "partial": false, "source": "plby", "state": "complete", "url": "https://github.com/plby/lean-proofs/blob/main/src/v4.29.1/ErdosProblems/Erdos798.lean" }, { "complete": true, "conditional": false, "label": "Jayyhk/erdos-lean", "partial": false, "source": "jayyhk", "state": "complete", "url": "https://github.com/Jayyhk/erdos-lean/blob/main/problems/798/Erdos798.lean" } ], "recommended_action": "Write the FC statement and link the matching hosted proof.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "Aristotle" ], "wiki_claims_lean": true, "wiki_claims_solved": false, "wiki_color": "green", "wiki_humans": [], "wiki_outcome": "Formalization" }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "proved", "erdos_url": "https://www.erdosproblems.com/799", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 799, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "proved", "erdos_url": "https://www.erdosproblems.com/800", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 800, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "proved", "erdos_url": "https://www.erdosproblems.com/801", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 801, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/802", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 802, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "disproved", "erdos_url": "https://www.erdosproblems.com/803", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 803, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "disproved", "erdos_url": "https://www.erdosproblems.com/804", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 804, "proof_link": null, "proof_links": [], "recommended_action": "No action until 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"wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/809", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 809, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/810", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, 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"gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 814, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "disproved", "erdos_url": "https://www.erdosproblems.com/815", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 815, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "proved", "erdos_url": "https://www.erdosproblems.com/816", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 816, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/817", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos817.erdos_817", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos817.erdos_817", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 817, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "statement", "discrepancy": false, "erdos_state": "proved (Lean)", "erdos_url": "https://www.erdosproblems.com/818", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, 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"machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 820, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/821", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 821, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "proved", "erdos_url": "https://www.erdosproblems.com/822", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos822.erdos_822", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos822.erdos_822", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 822, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "proved", 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"non_kernel_axioms": [], "problem": 824, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "proved", "erdos_url": "https://www.erdosproblems.com/825", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos825.erdos_825", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos825.erdos_825", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 825, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/826", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos826.erdos_826", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos826.erdos_826", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 826, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/827", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 827, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "done", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/828", "fc_has_proof": true, "fc_linked": true, "fc_theorem": "Erdos828.erdos_828.variants.phi_dvd_self_iff_pow2_pow3", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos828.erdos_828.variants.phi_dvd_self_iff_pow2_pow3", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 828, "proof_link": "https://github.com/XC0R/formal-conjectures/blob/03e00cf8d44098d0fb06e891fca30c29769df619/FormalConjectures/ErdosProblems/828.lean#L49", "proof_links": [], "recommended_action": "No action.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/829", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos829.erdos_829", "fc_url": 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"proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "verifiable", "erdos_url": "https://www.erdosproblems.com/835", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos835.erdos_835", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos835.erdos_835", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 835, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "AlphaProof" ], 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"non_kernel_axioms": [], "problem": 838, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/839", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 839, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/840", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 840, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "solved", "erdos_url": "https://www.erdosproblems.com/841", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 841, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "proved", "erdos_url": "https://www.erdosproblems.com/842", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 842, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "proved", "erdos_url": "https://www.erdosproblems.com/843", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 843, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "statement", "discrepancy": false, "erdos_state": "proved (Lean)", "erdos_url": "https://www.erdosproblems.com/844", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": "plby", "machine_verdict": "unconditional", "named_assumptions": [], "non_kernel_axioms": [], "problem": 844, "proof_link": null, "proof_links": [ { "complete": true, "conditional": false, "label": "plby/lean-proofs", "partial": false, "source": "plby", "state": "complete", "url": "https://github.com/plby/lean-proofs/blob/main/src/v4.29.1/ErdosProblems/Erdos844.lean" }, { "complete": true, "conditional": false, "label": "Jayyhk/erdos-lean", "partial": false, "source": "jayyhk", "state": "complete", "url": "https://github.com/Jayyhk/erdos-lean/blob/main/problems/844/Erdos844.lean" } ], "recommended_action": "Write the FC statement and link the matching hosted proof.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "Aristotle" ], 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}, { "complete": true, "conditional": false, "label": "Jayyhk/erdos-lean", "partial": false, "source": "jayyhk", "state": "complete", "url": "https://github.com/Jayyhk/erdos-lean/blob/main/problems/845/Erdos845.lean" } ], "recommended_action": "No action.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "Aristotle" ], "wiki_claims_lean": true, "wiki_claims_solved": false, "wiki_color": "green", "wiki_humans": [], "wiki_outcome": "Formalization" }, { "bucket": "done", "discrepancy": false, "erdos_state": "disproved (Lean)", "erdos_url": "https://www.erdosproblems.com/846", "fc_has_proof": true, "fc_linked": true, "fc_theorem": "Erdos846.erdos_846", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos846.erdos_846", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": "plby", "machine_verdict": "unconditional", "named_assumptions": [], "non_kernel_axioms": [], "problem": 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"erdos_state": "disproved", "erdos_url": "https://www.erdosproblems.com/847", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos847.erdos_847", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos847.erdos_847", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": "literature", "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 847, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "done", "discrepancy": false, "erdos_state": "decidable", "erdos_url": "https://www.erdosproblems.com/848", "fc_has_proof": true, "fc_linked": true, "fc_theorem": "Erdos848.erdos_848.variants.asymptotic", "fc_url": 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"erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/849", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos849.erdos_849", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos849.erdos_849", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 849, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/850", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos850.erdos_850", "fc_url": 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"machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 851, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "GPT-5.2 Pro" ], "wiki_claims_lean": false, "wiki_claims_solved": true, "wiki_color": "green", "wiki_humans": [], "wiki_outcome": "Full solution (building upon Romanoff (1934))" }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/852", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 852, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "GPT-5.4", "GPT-5.5 Pro" ], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": "yellow", "wiki_humans": [ "Aron Bhalla", "David Turturean", "Przemek Chojecki" ], "wiki_outcome": "Partial result" }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/853", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos853.erdos_853.parts.i", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos853.erdos_853.parts.i", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 853, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/854", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 854, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/855", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos855.erdos_855", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos855.erdos_855", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 855, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/856", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 856, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "GPT-5.4 Pro" ], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": "white", "wiki_humans": [ "Przemek Chojecki" ], "wiki_outcome": "Candidate full solution" }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/857", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos857.erdos_857", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos857.erdos_857", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 857, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "solved", "erdos_url": "https://www.erdosproblems.com/858", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": "non_improving", "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 858, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "GPT-5.4 Pro" ], "wiki_claims_lean": false, "wiki_claims_solved": true, "wiki_color": "green", "wiki_humans": [ "Przemek Chojecki" ], "wiki_outcome": "Full solution" }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/859", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos859.erdos_859", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos859.erdos_859", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 859, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/860", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 860, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "solved", "erdos_url": "https://www.erdosproblems.com/861", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 861, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "statement", "discrepancy": false, "erdos_state": "solved (Lean)", "erdos_url": "https://www.erdosproblems.com/862", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": "plby", "machine_verdict": "unconditional", "named_assumptions": [], "non_kernel_axioms": [], "problem": 862, "proof_link": null, "proof_links": [ { "complete": true, "conditional": false, "label": "plby/lean-proofs", "partial": false, "source": "plby", "state": "complete", "url": "https://github.com/plby/lean-proofs/blob/main/src/v4.29.1/ErdosProblems/Erdos862.lean" }, { "complete": true, "conditional": false, "label": "Jayyhk/erdos-lean", "partial": false, "source": "jayyhk", "state": "complete", "url": "https://github.com/Jayyhk/erdos-lean/blob/main/problems/862/Erdos862.lean" } ], "recommended_action": "Write the FC statement and link the matching hosted proof.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "Aristotle" ], "wiki_claims_lean": true, "wiki_claims_solved": false, "wiki_color": "green", "wiki_humans": [], "wiki_outcome": "Formalization" }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "proved", "erdos_url": "https://www.erdosproblems.com/863", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 863, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "GPT-5.4 Pro" ], "wiki_claims_lean": false, "wiki_claims_solved": true, "wiki_color": "green", "wiki_humans": [ "Boon Suan Ho" ], "wiki_outcome": "Full solution" }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/864", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": "subtle_error", "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 864, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/865", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos865.erdos_865", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos865.erdos_865", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 865, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "GPT-5.5 Pro" ], "wiki_claims_lean": false, "wiki_claims_solved": true, "wiki_color": "green", "wiki_humans": [ "Ricky Cipollini" ], "wiki_outcome": "Full solution" }, { "bucket": "partial", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/866", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": "hidden_constraints", "held_for_review": false, "machine_source": "plby", "machine_verdict": "unconditional", "named_assumptions": [], "non_kernel_axioms": [], "problem": 866, "proof_link": null, "proof_links": [ { "complete": false, "conditional": false, "label": "plby/lean-proofs", "partial": true, "source": "plby", "state": "partial", "url": "https://github.com/plby/lean-proofs/blob/main/src/v4.29.1/ErdosProblems/Erdos866.lean" } ], "recommended_action": "Only link a correctly stated variant after a per-problem review.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "Aristotle", "GPT-5.3 Instant" ], "wiki_claims_lean": true, "wiki_claims_solved": false, "wiki_color": "yellow", "wiki_humans": [ "Wouter van Doorn" ], "wiki_outcome": "Partial result (Lean)" }, { "bucket": "statement", "discrepancy": false, "erdos_state": "disproved (Lean)", "erdos_url": "https://www.erdosproblems.com/867", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": "plby", "machine_verdict": "unconditional", "named_assumptions": [], "non_kernel_axioms": [], "problem": 867, "proof_link": null, "proof_links": [ { "complete": true, "conditional": false, "label": "plby/lean-proofs", "partial": false, "source": "plby", "state": "complete", "url": "https://github.com/plby/lean-proofs/blob/main/src/v4.29.1/ErdosProblems/Erdos867.lean" }, { "complete": true, "conditional": false, "label": "Jayyhk/erdos-lean", "partial": false, "source": "jayyhk", "state": "complete", "url": "https://github.com/Jayyhk/erdos-lean/blob/main/problems/867/Erdos867.lean" } ], "recommended_action": "Write the FC statement and link the matching hosted proof.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "Aristotle" ], "wiki_claims_lean": true, "wiki_claims_solved": false, "wiki_color": "green", "wiki_humans": [], "wiki_outcome": "Formalization" }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "solved", "erdos_url": "https://www.erdosproblems.com/868", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos868.erdos_868.variants.Hartter_Nathanson", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos868.erdos_868.variants.Hartter_Nathanson", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 868, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "GPT-5.2 multi-agent system" ], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": "yellow", "wiki_humans": [], "wiki_outcome": "New partial result" }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "disproved", "erdos_url": "https://www.erdosproblems.com/869", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 869, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/870", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 870, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "GPT-5.4 Pro", "GPT-5.5 Pro" ], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": "white", "wiki_humans": [ "David Turturean" ], "wiki_outcome": "Candidate full solution" }, { "bucket": "done", "discrepancy": false, "erdos_state": "disproved (Lean)", "erdos_url": "https://www.erdosproblems.com/871", "fc_has_proof": true, "fc_linked": true, "fc_theorem": "Erdos871.erdos_871", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos871.erdos_871", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": "plby", "machine_verdict": "unconditional", "named_assumptions": [], "non_kernel_axioms": [], "problem": 871, "proof_link": "https://github.com/plby/lean-proofs/blob/main/src/v4.29.1/ErdosProblems/Erdos871.lean", "proof_links": [ { "complete": true, "conditional": false, "label": "plby/lean-proofs", "partial": false, "source": "plby", "state": "complete", "url": "https://github.com/plby/lean-proofs/blob/main/src/v4.29.1/ErdosProblems/Erdos871.lean" }, { "complete": true, "conditional": false, "label": "Jayyhk/erdos-lean", "partial": false, "source": "jayyhk", "state": "complete", "url": "https://github.com/Jayyhk/erdos-lean/blob/main/problems/871/Erdos871.lean" } ], "recommended_action": "No action.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "Claude Opus 4.5", "Gemini 3 Pro" ], "wiki_claims_lean": true, "wiki_claims_solved": true, "wiki_color": "green", "wiki_humans": [], "wiki_outcome": "Existing partial result upgraded to full solution (Lean)" }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/872", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 872, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "GPT-5.2 Pro", "GPT-5.4 Pro", "GPT-5.5 Pro" ], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": "yellow", "wiki_humans": [ "Jonas Silva", "Om_Buddhdev_sensho" ], "wiki_outcome": "Partial result" }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/873", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos873.erdos_873", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos873.erdos_873", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 873, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "GPT-5.4 Thinking", "GPT-5.5 Thinking" ], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": "white", "wiki_humans": [ "Ingo Alth\u00f6fer", "Ritvik Nayak" ], "wiki_outcome": "Candidate partial result" }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "proved", "erdos_url": "https://www.erdosproblems.com/874", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 874, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/875", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 875, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "Codex", "GPT-5.5 Pro" ], "wiki_claims_lean": true, "wiki_claims_solved": false, "wiki_color": "yellow", "wiki_humans": [ "Lech Mazur" ], "wiki_outcome": "Partial result (Lean)" }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/876", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 876, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "proved", "erdos_url": "https://www.erdosproblems.com/877", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 877, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/878", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 878, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/879", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 879, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "proved", "erdos_url": "https://www.erdosproblems.com/880", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 880, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/881", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos881.erdos_881", "fc_url": 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false, "fc_theorem": "Erdos885.erdos_885", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos885.erdos_885", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 885, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/886", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos886.erdos_886", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos886.erdos_886", "fidelity_note": null, "fidelity_source": null, 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887, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "solved", "erdos_url": "https://www.erdosproblems.com/888", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos888.erdos_888", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos888.erdos_888", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": "subtle_error", "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 888, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "Aristotle", "Claude Opus 4.5", "GPT-5.2 Thinking", "GPT-5.5 Pro", "Gemini 3 Pro" ], "wiki_claims_lean": false, "wiki_claims_solved": true, "wiki_color": "green", "wiki_humans": [ "Przemek Chojecki" ], "wiki_outcome": "Full solution" }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/889", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos889.erdos_889", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos889.erdos_889", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 889, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/890", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos890.erdos_890.variants.liminf_lower_bound", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos890.erdos_890.variants.liminf_lower_bound", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 890, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/891", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos891.erdos_891", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos891.erdos_891", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 891, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/892", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 892, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/893", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos893.erdos_893", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos893.erdos_893", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": "non_improving", "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 893, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "proved", "erdos_url": "https://www.erdosproblems.com/894", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 894, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "proved", "erdos_url": "https://www.erdosproblems.com/895", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 895, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "solved", "erdos_url": "https://www.erdosproblems.com/896", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 896, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "GPT-5.5 Pro" ], "wiki_claims_lean": false, "wiki_claims_solved": true, "wiki_color": "green", "wiki_humans": [ "Przemek Chojecki" ], "wiki_outcome": "Full solution" }, { "bucket": "done", "discrepancy": false, "erdos_state": "disproved (Lean)", "erdos_url": "https://www.erdosproblems.com/897", "fc_has_proof": true, "fc_linked": true, "fc_theorem": "Erdos897.erdos_897.parts.ii", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos897.erdos_897.parts.ii", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 897, "proof_link": 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"fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": "plby", "machine_verdict": "unconditional", "named_assumptions": [], "non_kernel_axioms": [], "problem": 898, "proof_link": null, "proof_links": [ { "complete": true, "conditional": false, "label": "plby/lean-proofs", "partial": false, "source": "plby", "state": "complete", "url": "https://github.com/plby/lean-proofs/blob/main/src/v4.29.1/ErdosProblems/Erdos898.lean" }, { "complete": true, "conditional": false, "label": "Jayyhk/erdos-lean", "partial": false, "source": "jayyhk", "state": "complete", "url": "https://github.com/Jayyhk/erdos-lean/blob/main/problems/898/Erdos898.lean" } ], "recommended_action": "Write the FC statement and link the matching hosted proof.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "Aristotle", "Gemini 3 Flash" ], "wiki_claims_lean": true, "wiki_claims_solved": false, "wiki_color": 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"proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/902", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 902, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "proved", "erdos_url": "https://www.erdosproblems.com/903", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 903, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "done", "discrepancy": false, "erdos_state": "proved (Lean)", "erdos_url": "https://www.erdosproblems.com/904", "fc_has_proof": true, "fc_linked": true, "fc_theorem": "Erdos904.erdos_904", "fc_url": 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null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "disproved", "erdos_url": "https://www.erdosproblems.com/910", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 910, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/911", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 911, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/912", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos912.erdos_912", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos912.erdos_912", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 912, "proof_link": null, 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"machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 928, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/929", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 929, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/930", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos930.erdos_930", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos930.erdos_930", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 930, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/931", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos931.erdos_931", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos931.erdos_931", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 931, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "Claude", "GPT-5.4" ], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": "yellow", "wiki_humans": [ "Adenwalla", "Malek Zribi" ], "wiki_outcome": "Partial result" }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/932", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos932.erdos_932", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos932.erdos_932", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 932, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/933", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 933, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/934", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 934, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/935", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 935, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "Aletheia" ], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": "yellow", "wiki_humans": [], "wiki_outcome": "Solution to one part of problem" }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/936", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos936.erdos_936.variants.factorial_sub_one", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos936.erdos_936.variants.factorial_sub_one", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 936, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "proved", "erdos_url": "https://www.erdosproblems.com/937", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos937.erdos_937", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos937.erdos_937", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 937, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/938", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos938.erdos_938", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos938.erdos_938", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 938, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/939", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos939.erdos_939", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos939.erdos_939", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 939, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/940", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos940.erdos_940", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos940.erdos_940", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 940, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "proved", "erdos_url": "https://www.erdosproblems.com/941", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 941, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/942", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos942.erdos_942", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos942.erdos_942", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 942, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "Aristotle", "Claude Opus 4.8", "Codex", "GPT-5.5", "Gemini" ], "wiki_claims_lean": true, "wiki_claims_solved": false, "wiki_color": "yellow", "wiki_humans": [ "Scott Hughes" ], "wiki_outcome": "New proof found" }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/943", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos943.erdos_943", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos943.erdos_943", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": "hidden_constraints", "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 943, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "GPT-5.4 Pro" ], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": "yellow", "wiki_humans": [ "Przemek Chojecki" ], "wiki_outcome": "Partial result" }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/944", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos944.erdos_944", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos944.erdos_944", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 944, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/945", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos945.erdos_945", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos945.erdos_945", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 945, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "proved", "erdos_url": "https://www.erdosproblems.com/946", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos946.erdos_946", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos946.erdos_946", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 946, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "statement", "discrepancy": false, "erdos_state": "proved (Lean)", "erdos_url": "https://www.erdosproblems.com/947", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": "plby", "machine_verdict": "unconditional", "named_assumptions": [], "non_kernel_axioms": [], "problem": 947, "proof_link": null, "proof_links": [ { "complete": true, "conditional": false, "label": "plby/lean-proofs", "partial": false, "source": "plby", "state": "complete", "url": "https://github.com/plby/lean-proofs/blob/main/src/v4.29.1/ErdosProblems/Erdos947.lean" }, { "complete": true, "conditional": false, "label": "Jayyhk/erdos-lean", "partial": false, "source": "jayyhk", "state": "complete", "url": "https://github.com/Jayyhk/erdos-lean/blob/main/problems/947/Erdos947.lean" } ], "recommended_action": "Write the FC statement and link the matching hosted proof.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "Aristotle", "GPT" ], "wiki_claims_lean": true, "wiki_claims_solved": false, "wiki_color": "green", "wiki_humans": [], "wiki_outcome": "Formalization" }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/948", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 948, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "Aristotle", "GPT-5.5 Pro" ], "wiki_claims_lean": true, "wiki_claims_solved": true, "wiki_color": "green", "wiki_humans": [], "wiki_outcome": "Full solution (Lean)" }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/949", "fc_has_proof": true, "fc_linked": false, "fc_theorem": "Erdos949.erdos_949.variants.sidon", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos949.erdos_949.variants.sidon", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 949, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "AlphaProof" ], "wiki_claims_lean": true, "wiki_claims_solved": false, "wiki_color": "yellow", "wiki_humans": [], "wiki_outcome": "Solution to variant problem (Lean)" }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/950", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos950.erdos_950.parts.ii", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos950.erdos_950.parts.ii", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 950, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/951", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos951.erdos_951", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos951.erdos_951", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 951, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "AlphaEvolve", "GPT-5.2 Pro", "GPT-5.2 Thinking" ], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": "yellow", "wiki_humans": [ "Nat Sothanaphan" ], "wiki_outcome": "Solution to variant problem" }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/952", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos952.erdos_952", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos952.erdos_952", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 952, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/953", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 953, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "GPT-5.5 Pro" ], "wiki_claims_lean": false, "wiki_claims_solved": true, "wiki_color": "green", "wiki_humans": [ "Przemek Chojecki" ], "wiki_outcome": "Full solution" }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/954", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": "hidden_constraints", "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 954, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/955", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 955, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/956", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 956, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "Aristotle", "GPT-5.5 Pro" ], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": "white", "wiki_humans": [ "Przemek Chojecki" ], "wiki_outcome": "Candidate full solution" }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "proved", "erdos_url": "https://www.erdosproblems.com/957", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 957, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "statement", "discrepancy": false, "erdos_state": "disproved (Lean)", "erdos_url": "https://www.erdosproblems.com/958", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": "plby", "machine_verdict": "unconditional", "named_assumptions": [], "non_kernel_axioms": [], "problem": 958, "proof_link": null, "proof_links": [ { "complete": true, "conditional": false, "label": "plby/lean-proofs", "partial": false, "source": "plby", "state": "complete", "url": "https://github.com/plby/lean-proofs/blob/main/src/v4.29.1/ErdosProblems/Erdos958.lean" }, { "complete": true, "conditional": false, "label": "Jayyhk/erdos-lean", "partial": false, "source": "jayyhk", "state": "complete", "url": "https://github.com/Jayyhk/erdos-lean/blob/main/problems/958/Erdos958.lean" } ], "recommended_action": "Write the FC statement and link the matching hosted proof.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "Aristotle", "Seed Prover 1.5" ], "wiki_claims_lean": true, "wiki_claims_solved": false, "wiki_color": "green", "wiki_humans": [], "wiki_outcome": "New proof found (Lean)" }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/959", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 959, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "disproved", "erdos_url": "https://www.erdosproblems.com/960", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 960, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "OpenAI internal model" ], "wiki_claims_lean": false, "wiki_claims_solved": true, "wiki_color": "green", "wiki_humans": [], "wiki_outcome": "Full solution" }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/961", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos961.erdos_961", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos961.erdos_961", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 961, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/962", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos962.erdos_962", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos962.erdos_962", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 962, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/963", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 963, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "Gemini 3 Pro" ], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "hypothesis-conditional", "discrepancy": false, "erdos_state": "proved (Lean)", "erdos_url": "https://www.erdosproblems.com/964", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": "plby", "machine_verdict": "conditional", "named_assumptions": [ "hGPY : Erdos964.GoldstonGrahamPintzYildirimStatement" ], "non_kernel_axioms": [], "problem": 964, "proof_link": null, "proof_links": [ { "complete": false, "conditional": true, "label": "plby/lean-proofs", "partial": false, "source": "plby", "state": "conditional", "url": "https://github.com/plby/lean-proofs/blob/main/src/v4.29.1/ErdosProblems/Erdos964.lean" }, { "complete": false, "conditional": true, "label": "Jayyhk/erdos-lean", "partial": false, "source": "jayyhk", "state": "axiomatic", "url": "https://github.com/Jayyhk/erdos-lean/blob/main/problems/964/Erdos964.lean" } ], "recommended_action": "Do not add a formal_proof link; document or wait for an unconditional theorem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "Antigravity", "Aristotle", "Gemini" ], "wiki_claims_lean": true, "wiki_claims_solved": false, "wiki_color": "green", "wiki_humans": [], "wiki_outcome": "Formalization" }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "disproved", "erdos_url": "https://www.erdosproblems.com/965", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos965.erdos_965", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos965.erdos_965", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 965, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "statement", "discrepancy": false, "erdos_state": "proved (Lean)", "erdos_url": "https://www.erdosproblems.com/966", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": "plby", "machine_verdict": "unconditional", "named_assumptions": [], "non_kernel_axioms": [], "problem": 966, "proof_link": null, "proof_links": [ { "complete": true, "conditional": false, "label": "plby/lean-proofs", "partial": false, "source": "plby", "state": "complete", "url": "https://github.com/plby/lean-proofs/blob/main/src/v4.29.1/ErdosProblems/Erdos966.lean" }, { "complete": true, "conditional": false, "label": "Jayyhk/erdos-lean", "partial": false, "source": "jayyhk", "state": "complete", "url": "https://github.com/Jayyhk/erdos-lean/blob/main/problems/966/Erdos966.lean" } ], "recommended_action": "Write the FC statement and link the matching hosted proof.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "Aristotle" ], "wiki_claims_lean": true, "wiki_claims_solved": true, "wiki_color": "green", "wiki_humans": [], "wiki_outcome": "Full solution (Lean)" }, { "bucket": "statement", "discrepancy": false, "erdos_state": "disproved (Lean)", "erdos_url": "https://www.erdosproblems.com/967", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": "plby", "machine_verdict": "unconditional", "named_assumptions": [], "non_kernel_axioms": [], "problem": 967, "proof_link": null, "proof_links": [ { "complete": true, "conditional": false, "label": "plby/lean-proofs", "partial": false, "source": "plby", "state": "complete", "url": "https://github.com/plby/lean-proofs/blob/main/src/v4.29.1/ErdosProblems/Erdos967.lean" }, { "complete": true, "conditional": false, "label": "Jayyhk/erdos-lean", "partial": false, "source": "jayyhk", "state": "complete", "url": "https://github.com/Jayyhk/erdos-lean/blob/main/problems/967/Erdos967.lean" } ], "recommended_action": "Write the FC statement and link the matching hosted proof.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "Aristotle" ], "wiki_claims_lean": true, "wiki_claims_solved": false, "wiki_color": "green", "wiki_humans": [], "wiki_outcome": "Formalization" }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/968", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos968.erdos_968", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos968.erdos_968", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 968, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/969", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": "non_improving", "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 969, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/970", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 970, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/971", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos971.erdos_971", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos971.erdos_971", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 971, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/972", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos972.erdos_972", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos972.erdos_972", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 972, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/973", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos973.erdos_973", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos973.erdos_973", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 973, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "statement", "discrepancy": false, "erdos_state": "proved (Lean)", "erdos_url": "https://www.erdosproblems.com/974", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 974, "proof_link": null, "proof_links": [ { "complete": true, "conditional": false, "label": "plby/lean-proofs", "partial": false, "source": "plby", "state": "complete", "url": "https://github.com/plby/lean-proofs/blob/main/src/v4.29.1/ErdosProblems/Erdos974.lean" }, { "complete": true, "conditional": false, "label": "Jayyhk/erdos-lean", "partial": false, "source": "jayyhk", "state": "complete", "url": "https://github.com/Jayyhk/erdos-lean/blob/main/problems/974/Erdos974.lean" } ], "recommended_action": "Write the FC statement and link the matching hosted proof.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "Aristotle" ], "wiki_claims_lean": true, "wiki_claims_solved": false, "wiki_color": "green", "wiki_humans": [], "wiki_outcome": "Formalization" }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/975", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos975.erdos_975", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos975.erdos_975", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 975, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/976", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 976, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "GPT-5.4" ], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": "yellow", "wiki_humans": [ "Aron Bhalla" ], "wiki_outcome": "Conditional partial result" }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "proved", "erdos_url": "https://www.erdosproblems.com/977", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 977, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "done", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/978", "fc_has_proof": true, "fc_linked": true, "fc_theorem": "Erdos978.erdos_978.variants.allow_fixed_divisors", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos978.erdos_978.variants.allow_fixed_divisors", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 978, "proof_link": "https://github.com/mo271/formal-conjectures/blob/3b5d6ac2555cd63b83d418c29ff040876be9dee0/FormalConjectures/ErdosProblems/978.lean#L64", "proof_links": [], "recommended_action": "No action.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/979", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos979.erdos_979", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos979.erdos_979", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 979, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "proved", "erdos_url": "https://www.erdosproblems.com/980", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 980, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "proved", "erdos_url": "https://www.erdosproblems.com/981", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 981, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "falsifiable", "erdos_url": "https://www.erdosproblems.com/982", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos982.erdos_982", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos982.erdos_982", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 982, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/983", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 983, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "GPT-5.5 Pro" ], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": "yellow", "wiki_humans": [], "wiki_outcome": "Partial result (solution to first part)" }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "proved", "erdos_url": "https://www.erdosproblems.com/984", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 984, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/985", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos985.erdos_985", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos985.erdos_985", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 985, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "proved", "erdos_url": "https://www.erdosproblems.com/986", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 986, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "Claude", "OpenAI internal model", "Trellis" ], "wiki_claims_lean": true, "wiki_claims_solved": true, "wiki_color": "green", "wiki_humans": [ "Domagoj Brada\u010d" ], "wiki_outcome": "Full solution" }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "proved", "erdos_url": "https://www.erdosproblems.com/987", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 987, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "OpenAI internal model" ], "wiki_claims_lean": false, "wiki_claims_solved": true, "wiki_color": "green", "wiki_humans": [], "wiki_outcome": "Full solution" }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "solved", "erdos_url": "https://www.erdosproblems.com/988", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 988, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "solved", "erdos_url": "https://www.erdosproblems.com/989", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 989, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "statement", "discrepancy": false, "erdos_state": "disproved (Lean)", "erdos_url": "https://www.erdosproblems.com/990", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": "plby", "machine_verdict": "unconditional", "named_assumptions": [], "non_kernel_axioms": [], "problem": 990, "proof_link": null, "proof_links": [ { "complete": true, "conditional": false, "label": "plby/lean-proofs", "partial": false, "source": "plby", "state": "complete", "url": "https://github.com/plby/lean-proofs/blob/main/src/v4.29.1/ErdosProblems/Erdos990.lean" }, { "complete": true, "conditional": false, "label": "Jayyhk/erdos-lean", "partial": false, "source": "jayyhk", "state": "complete", "url": "https://github.com/Jayyhk/erdos-lean/blob/main/problems/990/Erdos990.lean" } ], "recommended_action": "Write the FC statement and link the matching hosted proof.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "GPT-5.4 Pro", "OpenAI internal model" ], "wiki_claims_lean": true, "wiki_claims_solved": true, "wiki_color": "green", "wiki_humans": [], "wiki_outcome": "Full solution" }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "proved", "erdos_url": "https://www.erdosproblems.com/991", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 991, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "disproved", "erdos_url": "https://www.erdosproblems.com/992", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 992, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "falsifiable", "erdos_url": "https://www.erdosproblems.com/993", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 993, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "disproved", "erdos_url": "https://www.erdosproblems.com/994", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 994, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/995", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 995, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "GPT-5.4 Pro" ], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": "yellow", "wiki_humans": [ "Boon Suan Ho" ], "wiki_outcome": "Partial result" }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/996", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos996.erdos_996", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos996.erdos_996", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 996, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "GPT-5.4 Pro" ], "wiki_claims_lean": false, "wiki_claims_solved": true, "wiki_color": "green", "wiki_humans": [ "Boon Suan Ho" ], "wiki_outcome": "Full solution" }, { "bucket": "done", "discrepancy": true, "erdos_state": "proved (Lean)", "erdos_url": "https://www.erdosproblems.com/997", "fc_has_proof": true, "fc_linked": true, "fc_theorem": "Erdos997.erdos_997", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos997.erdos_997", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": "plby", "machine_verdict": "conditional", "named_assumptions": [], "non_kernel_axioms": [ "maynardTaoBFT" ], "problem": 997, "proof_link": "https://live.lean-lang.org/#project=mathlib-v4.28.0&url=https://gist.githubusercontent.com/pitmonticone/016f2ed66b4cd1c4c4b9998095170e60/raw/b7dfc05c525ae385b5835f89f1ada721443e4305/Erdos997.lean", "proof_links": [ { "complete": false, "conditional": true, "label": "plby/lean-proofs", "partial": false, "source": "plby", "state": "conditional", "url": "https://github.com/plby/lean-proofs/blob/main/src/v4.29.1/ErdosProblems/Erdos997.lean" }, { "complete": false, "conditional": true, "label": "Jayyhk/erdos-lean", "partial": false, "source": "jayyhk", "state": "axiomatic", "url": "https://github.com/Jayyhk/erdos-lean/blob/main/problems/997/Erdos997.lean" } ], "recommended_action": "No action.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "Aristotle", "OpenAI internal model" ], "wiki_claims_lean": true, "wiki_claims_solved": true, "wiki_color": "green", "wiki_humans": [], "wiki_outcome": "Full solution" }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "proved", "erdos_url": "https://www.erdosproblems.com/998", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 998, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "proved", "erdos_url": "https://www.erdosproblems.com/999", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 999, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "proved (Lean)", "erdos_url": "https://www.erdosproblems.com/1000", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": "plby", "machine_verdict": "unconditional", "named_assumptions": [], "non_kernel_axioms": [], "problem": 1000, "proof_link": null, "proof_links": [ { "complete": true, "conditional": false, "label": "plby/lean-proofs", "partial": false, "source": "plby", "state": "complete", "url": "https://github.com/plby/lean-proofs/blob/main/src/v4.29.1/ErdosProblems/Erdos1000.lean" }, { "complete": true, "conditional": false, "label": "Jayyhk/erdos-lean", "partial": false, "source": "jayyhk", "state": "complete", "url": "https://github.com/Jayyhk/erdos-lean/blob/main/problems/1000/Erdos1000.lean" } ], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "Aristotle", "GPT" ], "wiki_claims_lean": true, "wiki_claims_solved": false, "wiki_color": "green", "wiki_humans": [], "wiki_outcome": "Formalization" }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "solved", "erdos_url": "https://www.erdosproblems.com/1001", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 1001, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/1002", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos1002.erdos_1002", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos1002.erdos_1002", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 1002, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/1003", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos1003.erdos_1003", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos1003.erdos_1003", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 1003, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/1004", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos1004.erdos_1004", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos1004.erdos_1004", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 1004, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "GPT-5.5 Pro" ], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": "yellow", "wiki_humans": [], "wiki_outcome": "Partial result (implicit in literature)" }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/1005", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 1005, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "disproved", "erdos_url": "https://www.erdosproblems.com/1006", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 1006, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "solved (Lean)", "erdos_url": "https://www.erdosproblems.com/1007", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": "plby", "machine_verdict": "unconditional", "named_assumptions": [], "non_kernel_axioms": [], "problem": 1007, "proof_link": null, "proof_links": [ { "complete": true, "conditional": false, "label": "plby/lean-proofs", "partial": false, "source": "plby", "state": "complete", "url": "https://github.com/plby/lean-proofs/blob/main/src/v4.29.1/ErdosProblems/Erdos1007.lean" }, { "complete": true, "conditional": false, "label": "Jayyhk/erdos-lean", "partial": false, "source": "jayyhk", "state": "complete", "url": "https://github.com/Jayyhk/erdos-lean/blob/main/problems/1007/Erdos1007.lean" } ], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "Aristotle" ], "wiki_claims_lean": true, "wiki_claims_solved": false, "wiki_color": "green", "wiki_humans": [], "wiki_outcome": "New proof found (Lean)" }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "proved (Lean)", "erdos_url": "https://www.erdosproblems.com/1008", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": "plby", "machine_verdict": "unconditional", "named_assumptions": [], "non_kernel_axioms": [], "problem": 1008, "proof_link": null, "proof_links": [ { "complete": true, "conditional": false, "label": "plby/lean-proofs", "partial": false, "source": "plby", "state": "complete", "url": "https://github.com/plby/lean-proofs/blob/main/src/v4.29.1/ErdosProblems/Erdos1008.lean" }, { "complete": true, "conditional": false, "label": "Jayyhk/erdos-lean", "partial": false, "source": "jayyhk", "state": "complete", "url": "https://github.com/Jayyhk/erdos-lean/blob/main/problems/1008/Erdos1008.lean" } ], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "Aristotle" ], "wiki_claims_lean": true, "wiki_claims_solved": false, "wiki_color": "green", "wiki_humans": [], "wiki_outcome": "Formalization" }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "proved", "erdos_url": "https://www.erdosproblems.com/1009", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 1009, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "proved", "erdos_url": "https://www.erdosproblems.com/1010", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 1010, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/1011", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 1011, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "solved", "erdos_url": "https://www.erdosproblems.com/1012", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 1012, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/1013", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 1013, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "proved (Lean)", "erdos_url": "https://www.erdosproblems.com/1014", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": "conditional_conjecture", "held_for_review": false, "machine_source": "plby", "machine_verdict": "unconditional", "named_assumptions": [], "non_kernel_axioms": [], "problem": 1014, "proof_link": null, "proof_links": [ { "complete": true, "conditional": false, "label": "plby/lean-proofs", "partial": false, "source": "plby", "state": "complete", "url": "https://github.com/plby/lean-proofs/blob/main/src/v4.29.1/ErdosProblems/Erdos1014.lean" }, { "complete": true, "conditional": false, "label": "Jayyhk/erdos-lean", "partial": false, "source": "jayyhk", "state": "complete", "url": "https://github.com/Jayyhk/erdos-lean/blob/main/problems/1014/Erdos1014.lean" } ], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "OpenAI internal model" ], "wiki_claims_lean": false, "wiki_claims_solved": true, "wiki_color": "green", "wiki_humans": [], "wiki_outcome": "Full solution" }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "solved", "erdos_url": "https://www.erdosproblems.com/1015", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 1015, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/1016", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 1016, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/1017", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 1017, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "solved", "erdos_url": "https://www.erdosproblems.com/1018", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 1018, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "proved", "erdos_url": "https://www.erdosproblems.com/1019", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 1019, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "falsifiable", "erdos_url": "https://www.erdosproblems.com/1020", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 1020, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "proved", "erdos_url": "https://www.erdosproblems.com/1021", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": "hidden_constraints", "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 1021, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "proved (Lean)", "erdos_url": "https://www.erdosproblems.com/1022", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": "typo", "held_for_review": false, "machine_source": "plby", "machine_verdict": "unconditional", "named_assumptions": [], "non_kernel_axioms": [], "problem": 1022, "proof_link": null, "proof_links": [ { "complete": true, "conditional": false, "label": "plby/lean-proofs", "partial": false, "source": "plby", "state": "complete", "url": "https://github.com/plby/lean-proofs/blob/main/src/v4.29.1/ErdosProblems/Erdos1022.lean" }, { "complete": true, "conditional": false, "label": "Jayyhk/erdos-lean", "partial": false, "source": "jayyhk", "state": "complete", "url": "https://github.com/Jayyhk/erdos-lean/blob/main/problems/1022/Erdos1022.lean" } ], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "Aristotle" ], "wiki_claims_lean": true, "wiki_claims_solved": false, "wiki_color": "green", "wiki_humans": [], "wiki_outcome": "Formalization" }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "solved (Lean)", "erdos_url": "https://www.erdosproblems.com/1023", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": "plby", "machine_verdict": "unconditional", "named_assumptions": [], "non_kernel_axioms": [], "problem": 1023, "proof_link": null, "proof_links": [ { "complete": true, "conditional": false, "label": "plby/lean-proofs", "partial": false, "source": "plby", "state": "complete", "url": "https://github.com/plby/lean-proofs/blob/main/src/v4.29.1/ErdosProblems/Erdos1023.lean" }, { "complete": true, "conditional": false, "label": "Jayyhk/erdos-lean", "partial": false, "source": "jayyhk", "state": "complete", "url": "https://github.com/Jayyhk/erdos-lean/blob/main/problems/1023/Erdos1023.lean" } ], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "Aristotle" ], "wiki_claims_lean": true, "wiki_claims_solved": false, "wiki_color": "green", "wiki_humans": [], "wiki_outcome": "Formalization" }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "solved", "erdos_url": "https://www.erdosproblems.com/1024", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 1024, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "solved", "erdos_url": "https://www.erdosproblems.com/1025", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 1025, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "solved (Lean)", "erdos_url": "https://www.erdosproblems.com/1026", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": "plby", "machine_verdict": "unconditional", "named_assumptions": [], "non_kernel_axioms": [], "problem": 1026, "proof_link": null, "proof_links": [ { "complete": true, "conditional": false, "label": "plby/lean-proofs", "partial": false, "source": "plby", "state": "complete", "url": "https://github.com/plby/lean-proofs/blob/main/src/v4.29.1/ErdosProblems/Erdos1026.lean" }, { "complete": true, "conditional": false, "label": "Jayyhk/erdos-lean", "partial": false, "source": "jayyhk", "state": "complete", "url": "https://github.com/Jayyhk/erdos-lean/blob/main/problems/1026/Erdos1026.lean" } ], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "AlphaEvolve", "Aristotle", "GPT", "Gemini" ], "wiki_claims_lean": true, "wiki_claims_solved": true, "wiki_color": "green", "wiki_humans": [ "Boris Alexeev", "Lawrence Wu", "Stijn Cambie", "Terence Tao" ], "wiki_outcome": "Full solution (Lean)" }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "proved", "erdos_url": "https://www.erdosproblems.com/1027", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 1027, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "solved (Lean)", "erdos_url": "https://www.erdosproblems.com/1028", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": "plby", "machine_verdict": "unconditional", "named_assumptions": [], "non_kernel_axioms": [], "problem": 1028, "proof_link": null, "proof_links": [ { "complete": true, "conditional": false, "label": "plby/lean-proofs", "partial": false, "source": "plby", "state": "complete", "url": "https://github.com/plby/lean-proofs/blob/main/src/v4.29.1/ErdosProblems/Erdos1028.lean" }, { "complete": true, "conditional": false, "label": "Jayyhk/erdos-lean", "partial": false, "source": "jayyhk", "state": "complete", "url": "https://github.com/Jayyhk/erdos-lean/blob/main/problems/1028/Erdos1028.lean" } ], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "Aristotle" ], "wiki_claims_lean": true, "wiki_claims_solved": false, "wiki_color": "green", "wiki_humans": [], "wiki_outcome": "Formalization" }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/1029", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 1029, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/1030", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 1030, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "proved", "erdos_url": "https://www.erdosproblems.com/1031", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 1031, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/1032", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 1032, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "Codex", "GPT-5.5 Pro" ], "wiki_claims_lean": true, "wiki_claims_solved": false, "wiki_color": "yellow", "wiki_humans": [], "wiki_outcome": "Improved partial result (Lean)" }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/1033", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 1033, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "GPT-5.5 Pro" ], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": "white", "wiki_humans": [], "wiki_outcome": "Candidate partial result" }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "disproved (Lean)", "erdos_url": "https://www.erdosproblems.com/1034", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": "plby", "machine_verdict": "unconditional", "named_assumptions": [], "non_kernel_axioms": [], "problem": 1034, "proof_link": null, "proof_links": [ { "complete": true, "conditional": false, "label": "plby/lean-proofs", "partial": false, "source": "plby", "state": "complete", "url": "https://github.com/plby/lean-proofs/blob/main/src/v4.29.1/ErdosProblems/Erdos1034.lean" }, { "complete": true, "conditional": false, "label": "Jayyhk/erdos-lean", "partial": false, "source": "jayyhk", "state": "complete", "url": "https://github.com/Jayyhk/erdos-lean/blob/main/problems/1034/Erdos1034.lean" } ], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "Aristotle" ], "wiki_claims_lean": true, "wiki_claims_solved": false, "wiki_color": "green", "wiki_humans": [], "wiki_outcome": "Formalization" }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/1035", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 1035, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "proved (Lean)", "erdos_url": "https://www.erdosproblems.com/1036", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": "plby", "machine_verdict": "unconditional", "named_assumptions": [], "non_kernel_axioms": [], "problem": 1036, "proof_link": null, "proof_links": [ { "complete": true, "conditional": false, "label": "plby/lean-proofs", "partial": false, "source": "plby", "state": "complete", "url": "https://github.com/plby/lean-proofs/blob/main/src/v4.29.1/ErdosProblems/Erdos1036.lean" }, { "complete": true, "conditional": false, "label": "Jayyhk/erdos-lean", "partial": false, "source": "jayyhk", "state": "complete", "url": "https://github.com/Jayyhk/erdos-lean/blob/main/problems/1036/Erdos1036.lean" } ], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "Aristotle" ], "wiki_claims_lean": true, "wiki_claims_solved": false, "wiki_color": "green", "wiki_humans": [], "wiki_outcome": "Formalization" }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "disproved (Lean)", "erdos_url": "https://www.erdosproblems.com/1037", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": "plby", "machine_verdict": "unconditional", "named_assumptions": [], "non_kernel_axioms": [], "problem": 1037, "proof_link": null, "proof_links": [ { "complete": true, "conditional": false, "label": "plby/lean-proofs", "partial": false, "source": "plby", "state": "complete", "url": "https://github.com/plby/lean-proofs/blob/main/src/v4.29.1/ErdosProblems/Erdos1037.lean" }, { "complete": true, "conditional": false, "label": "Jayyhk/erdos-lean", "partial": false, "source": "jayyhk", "state": "complete", "url": "https://github.com/Jayyhk/erdos-lean/blob/main/problems/1037/Erdos1037.lean" } ], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "Aristotle" ], "wiki_claims_lean": true, "wiki_claims_solved": false, "wiki_color": "green", "wiki_humans": [], "wiki_outcome": "Formalization" }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/1038", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos1038.erdos_1038.variants.inf_upperBound", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos1038.erdos_1038.variants.inf_upperBound", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 1038, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "AlphaEvolve", "Claude Fable 5", "Codex", "GPT-5.2 Thinking", "GPT-5.4 Thinking", "GPT-5.5" ], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": "yellow", "wiki_humans": [ "Hua Xu", "Junnosuke Koizumi", "Kenneth Mendoza", "Nat Sothanaphan", "Terence Tao", "catsflowers5544", "jspier" ], "wiki_outcome": "Partial result" }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/1039", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 1039, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "Aristotle", "Claude Opus 4.6", "Codex", "GPT-5.5", "GPT-5.5 Pro" ], "wiki_claims_lean": true, "wiki_claims_solved": false, "wiki_color": "yellow", "wiki_humans": [ "Houi" ], "wiki_outcome": "Partial result" }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/1040", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 1040, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "Aletheia" ], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": "yellow", "wiki_humans": [], "wiki_outcome": "Solution to one part of problem; incorrect solution to other part" }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "falsifiable", "erdos_url": "https://www.erdosproblems.com/1041", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos1041.erdos_1041", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos1041.erdos_1041", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 1041, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "Claude Opus 4.6", "GPT-5.4", "GPT-5.4 Thinking", "Gemini 3.1 Pro" ], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [ "shtuka" ], "wiki_outcome": null }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "proved", "erdos_url": "https://www.erdosproblems.com/1042", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 1042, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "done", "discrepancy": false, "erdos_state": "disproved (Lean)", "erdos_url": "https://www.erdosproblems.com/1043", "fc_has_proof": true, "fc_linked": true, "fc_theorem": "Erdos1043.erdos_1043", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos1043.erdos_1043", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": "plby", "machine_verdict": "unconditional", "named_assumptions": [], "non_kernel_axioms": [], "problem": 1043, "proof_link": "https://github.com/plby/lean-proofs/blob/main/src/v4.24.0/ErdosProblems/Erdos1043.lean", "proof_links": [ { "complete": true, "conditional": false, "label": "plby/lean-proofs", "partial": false, "source": "plby", "state": "complete", "url": "https://github.com/plby/lean-proofs/blob/main/src/v4.29.1/ErdosProblems/Erdos1043.lean" }, { "complete": true, "conditional": false, "label": "Jayyhk/erdos-lean", "partial": false, "source": "jayyhk", "state": "complete", "url": "https://github.com/Jayyhk/erdos-lean/blob/main/problems/1043/Erdos1043.lean" } ], "recommended_action": "No action.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "Aristotle", "GPT" ], "wiki_claims_lean": true, "wiki_claims_solved": false, "wiki_color": "green", "wiki_humans": [], "wiki_outcome": "New proof found (Lean)" }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "solved (Lean)", "erdos_url": "https://www.erdosproblems.com/1044", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": "plby", "machine_verdict": "unconditional", "named_assumptions": [], "non_kernel_axioms": [], "problem": 1044, "proof_link": null, "proof_links": [ { "complete": true, "conditional": false, "label": "plby/lean-proofs", "partial": false, "source": "plby", "state": "complete", "url": "https://github.com/plby/lean-proofs/blob/main/src/v4.29.1/ErdosProblems/Erdos1044.lean" }, { "complete": true, "conditional": false, "label": "Jayyhk/erdos-lean", "partial": false, "source": "jayyhk", "state": "complete", "url": "https://github.com/Jayyhk/erdos-lean/blob/main/problems/1044/Erdos1044.lean" } ], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "Aristotle", "GPT-5.2 Pro" ], "wiki_claims_lean": true, "wiki_claims_solved": false, "wiki_color": "green", "wiki_humans": [], "wiki_outcome": "Formalization" }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/1045", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 1045, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "disproved", "erdos_url": "https://www.erdosproblems.com/1046", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 1046, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "disproved (Lean)", "erdos_url": "https://www.erdosproblems.com/1047", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": "plby", "machine_verdict": "unconditional", "named_assumptions": [], "non_kernel_axioms": [], "problem": 1047, "proof_link": null, "proof_links": [ { "complete": true, "conditional": false, "label": "plby/lean-proofs", "partial": false, "source": "plby", "state": "complete", "url": "https://github.com/plby/lean-proofs/blob/main/src/v4.29.1/ErdosProblems/Erdos1047.lean" }, { "complete": true, "conditional": false, "label": "Jayyhk/erdos-lean", "partial": false, "source": "jayyhk", "state": "complete", "url": "https://github.com/Jayyhk/erdos-lean/blob/main/problems/1047/Erdos1047.lean" } ], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "Aristotle" ], "wiki_claims_lean": true, "wiki_claims_solved": false, "wiki_color": "green", "wiki_humans": [], "wiki_outcome": "New proof found (Lean)" }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "disproved (Lean)", "erdos_url": "https://www.erdosproblems.com/1048", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": "plby", "machine_verdict": "unconditional", "named_assumptions": [], "non_kernel_axioms": [], "problem": 1048, "proof_link": null, "proof_links": [ { "complete": true, "conditional": false, "label": "plby/lean-proofs", "partial": false, "source": "plby", "state": "complete", "url": "https://github.com/plby/lean-proofs/blob/main/src/v4.29.1/ErdosProblems/Erdos1048.lean" }, { "complete": true, "conditional": false, "label": "Jayyhk/erdos-lean", "partial": false, "source": "jayyhk", "state": "complete", "url": "https://github.com/Jayyhk/erdos-lean/blob/main/problems/1048/Erdos1048.lean" } ], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "Aristotle" ], "wiki_claims_lean": true, "wiki_claims_solved": false, "wiki_color": "green", "wiki_humans": [], "wiki_outcome": "Proof found (Lean), which is a specific case of Pommerenke" }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/1049", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos1049.erdos_1049", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos1049.erdos_1049", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 1049, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "proved", "erdos_url": "https://www.erdosproblems.com/1050", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 1050, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "done", "discrepancy": false, "erdos_state": "proved (Lean)", "erdos_url": "https://www.erdosproblems.com/1051", "fc_has_proof": true, "fc_linked": true, "fc_theorem": "Erdos1051.erdos_1051", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos1051.erdos_1051", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": "plby", "machine_verdict": "unconditional", "named_assumptions": [], "non_kernel_axioms": [], "problem": 1051, "proof_link": "https://www.erdosproblems.com/forum/thread/1051", "proof_links": [ { "complete": true, "conditional": false, "label": "plby/lean-proofs", "partial": false, "source": "plby", "state": "complete", "url": "https://github.com/plby/lean-proofs/blob/main/src/v4.29.1/ErdosProblems/Erdos1051.lean" }, { "complete": true, "conditional": false, "label": "Jayyhk/erdos-lean", "partial": false, "source": "jayyhk", "state": "complete", "url": "https://github.com/Jayyhk/erdos-lean/blob/main/problems/1051/Erdos1051.lean" } ], "recommended_action": "No action.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "Aletheia" ], "wiki_claims_lean": true, "wiki_claims_solved": true, "wiki_color": "green", "wiki_humans": [], "wiki_outcome": "Full solution (Lean)" }, { "bucket": "done", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/1052", "fc_has_proof": true, "fc_linked": true, "fc_theorem": "Erdos1052.even_of_isUnitaryPerfect", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos1052.even_of_isUnitaryPerfect", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 1052, "proof_link": "https://github.com/mzhorvath1/formal-conjectures/blob/b70a2ddf5e55f743aac9d4f4a907786b39bc9807/FormalConjectures/ErdosProblems/1052.lean#L46", "proof_links": [], "recommended_action": "No action.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/1053", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 1053, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/1054", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos1054.f_undefined_at_2", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos1054.f_undefined_at_2", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 1054, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "Claude Opus 4.8", "GPT-5.5 Pro", "Principia Math" ], "wiki_claims_lean": true, "wiki_claims_solved": false, "wiki_color": "yellow", "wiki_humans": [], "wiki_outcome": "Partial result (Lean)" }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/1055", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos1055.erdos_1055", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos1055.erdos_1055", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 1055, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "partial", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/1056", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos1056.erdos_1056", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos1056.erdos_1056", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": "plby", "machine_verdict": "unconditional", "named_assumptions": [], "non_kernel_axioms": [], "problem": 1056, "proof_link": null, "proof_links": [ { "complete": false, "conditional": false, "label": "plby/lean-proofs", "partial": true, "source": "plby", "state": "partial", "url": "https://github.com/plby/lean-proofs/blob/main/src/v4.29.1/ErdosProblems/Erdos1056.lean" } ], "recommended_action": "Only link a correctly stated variant after a per-problem review.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/1057", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos1057.erdos_1057", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos1057.erdos_1057", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 1057, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "proved", "erdos_url": "https://www.erdosproblems.com/1058", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 1058, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/1059", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos1059.erdos_1059", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos1059.erdos_1059", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 1059, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/1060", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos1060.erdos_1060.parts.ii", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos1060.erdos_1060.parts.ii", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 1060, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/1061", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos1061.erdos_1061", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos1061.erdos_1061", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 1061, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "GPT" ], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": "white", "wiki_humans": [ "Eric Li" ], "wiki_outcome": "Candidate full solution" }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/1062", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos1062.erdos_1062.variants.lower_bound", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos1062.erdos_1062.variants.lower_bound", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 1062, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "GPT-5.4 Pro" ], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": "yellow", "wiki_humans": [ "Damek Davis" ], "wiki_outcome": "Partial result" }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/1063", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos1063.erdos_1063.variants.cambie_upper_bound", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos1063.erdos_1063.variants.cambie_upper_bound", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": "subtle_error", "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 1063, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "proved", "erdos_url": "https://www.erdosproblems.com/1064", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos1064.erdos_1064", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos1064.erdos_1064", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 1064, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/1065", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos1065.erdos_1065.parts.ii", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos1065.erdos_1065.parts.ii", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 1065, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/1066", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 1066, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "done", "discrepancy": false, "erdos_state": "disproved (Lean)", "erdos_url": "https://www.erdosproblems.com/1067", "fc_has_proof": true, "fc_linked": true, "fc_theorem": "Erdos1067.erdos_1067", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos1067.erdos_1067", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": "plby", "machine_verdict": "unconditional", "named_assumptions": [], "non_kernel_axioms": [], "problem": 1067, "proof_link": 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"fc_theorem": "Erdos1068.erdos_1068", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos1068.erdos_1068", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 1068, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "solved", "erdos_url": "https://www.erdosproblems.com/1069", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 1069, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/1070", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 1070, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "Codex", "GPT-5.5" ], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": "yellow", "wiki_humans": [ "D\u00e1niel Varga", "\u00c1kos D\u00facz" ], "wiki_outcome": "Partial result" }, { "bucket": "done", "discrepancy": false, "erdos_state": "proved (Lean)", "erdos_url": "https://www.erdosproblems.com/1071", "fc_has_proof": true, "fc_linked": true, "fc_theorem": "Erdos1071.erdos_1071.parts.ii", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos1071.erdos_1071.parts.ii", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 1071, "proof_link": "https://github.com/plby/lean-proofs/blob/main/src/v4.24.0/ErdosProblems/Erdos1071b.lean", "proof_links": [ { "complete": true, "conditional": false, "label": "plby/lean-proofs", "partial": false, "source": "plby", "state": "complete", "url": "https://github.com/plby/lean-proofs/blob/main/src/v4.29.1/ErdosProblems/Erdos1071.lean" }, { "complete": true, "conditional": false, "label": "Jayyhk/erdos-lean", "partial": false, "source": "jayyhk", "state": "complete", "url": "https://github.com/Jayyhk/erdos-lean/blob/main/problems/1071/Erdos1071.lean" } ], "recommended_action": "No action.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "Aleph Prover", "Aristotle", "GPT" ], "wiki_claims_lean": true, "wiki_claims_solved": false, "wiki_color": "green", "wiki_humans": [], "wiki_outcome": "Formalization" }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/1072", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos1072.erdos_1072.parts.i", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos1072.erdos_1072.parts.i", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 1072, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/1073", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos1073.erdos_1073", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos1073.erdos_1073", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 1073, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "done", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/1074", "fc_has_proof": true, "fc_linked": true, "fc_theorem": "Erdos1074.erdos_1074.variants.EHSNumbers_infinite", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos1074.erdos_1074.variants.EHSNumbers_infinite", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 1074, "proof_link": "https://github.com/mzhorvath1/formal-conjectures/blob/3dec597bd1a73778760b761712a1fc5fb24bc5d7/FormalConjectures/ErdosProblems/1074.lean#L99", "proof_links": [], "recommended_action": "No action.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/1075", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 1075, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "proved", "erdos_url": "https://www.erdosproblems.com/1076", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 1076, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "disproved", "erdos_url": "https://www.erdosproblems.com/1077", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos1077.erdos_1077", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos1077.erdos_1077", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 1077, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "proved", "erdos_url": "https://www.erdosproblems.com/1078", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 1078, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "solved", "erdos_url": "https://www.erdosproblems.com/1079", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 1079, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "done", "discrepancy": false, "erdos_state": "disproved (Lean)", "erdos_url": "https://www.erdosproblems.com/1080", "fc_has_proof": true, "fc_linked": true, "fc_theorem": "Erdos1080.erdos_1080", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos1080.erdos_1080", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": "plby", "machine_verdict": "conditional", "named_assumptions": [ "h_adj1 : Erdos1080.is_adjacent F q (Erdos1080.zero_Point hq) l1", "h_adj2 : Erdos1080.is_adjacent F q p1 l1", "h_adj3 : Erdos1080.is_adjacent F q p1 l2" ], "non_kernel_axioms": [], "problem": 1080, "proof_link": "https://github.com/plby/lean-proofs/blob/main/src/v4.24.0/ErdosProblems/Erdos1080.lean", "proof_links": [ { "complete": true, "conditional": false, "label": "plby/lean-proofs", "partial": false, "source": "plby", "state": "complete", "url": "https://github.com/plby/lean-proofs/blob/main/src/v4.29.1/ErdosProblems/Erdos1080.lean" }, { "complete": true, "conditional": false, "label": "Jayyhk/erdos-lean", "partial": false, "source": "jayyhk", "state": "complete", "url": "https://github.com/Jayyhk/erdos-lean/blob/main/problems/1080/Erdos1080.lean" } ], "recommended_action": "No action.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "Aristotle" ], "wiki_claims_lean": true, "wiki_claims_solved": false, "wiki_color": "green", "wiki_humans": [], "wiki_outcome": "Formalization" }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "disproved", "erdos_url": "https://www.erdosproblems.com/1081", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 1081, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "done", "discrepancy": false, "erdos_state": "falsifiable", "erdos_url": "https://www.erdosproblems.com/1082", "fc_has_proof": true, "fc_linked": true, "fc_theorem": "Erdos1082.erdos_1082.parts.ii", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos1082.erdos_1082.parts.ii", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 1082, "proof_link": "https://github.com/google-deepmind/formal-conjectures/blob/0aca4d71095301c0fd2dca32611b7addb2ea735c/FormalConjectures/ErdosProblems/1082.lean", "proof_links": [], "recommended_action": "No action.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "DeepMind prover agent" ], "wiki_claims_lean": true, "wiki_claims_solved": false, "wiki_color": "yellow", "wiki_humans": [], "wiki_outcome": "Counterexample to one part (Lean)" }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/1083", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 1083, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "done", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/1084", "fc_has_proof": true, "fc_linked": true, "fc_theorem": "Erdos1084.erdos_1084.variants.upper_d1", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos1084.erdos_1084.variants.upper_d1", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": "partial_literature", "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 1084, "proof_link": "https://github.com/Sanexxxx777/formal-conjectures/blob/9e4f3845be122a8fa3190d38543ebdd0a6f25605/FormalConjectures/ErdosProblems/1084.lean#L232", "proof_links": [], "recommended_action": "No action.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/1085", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos1085.erdos_1085.variants.upper_d2", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos1085.erdos_1085.variants.upper_d2", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 1085, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/1086", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 1086, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/1087", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 1087, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/1088", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 1088, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "solved", "erdos_url": "https://www.erdosproblems.com/1089", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 1089, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "Aletheia" ], "wiki_claims_lean": false, "wiki_claims_solved": true, "wiki_color": "green", "wiki_humans": [], "wiki_outcome": "Full solution found" }, { "bucket": "done", "discrepancy": false, "erdos_state": "proved (Lean)", "erdos_url": "https://www.erdosproblems.com/1090", "fc_has_proof": true, "fc_linked": true, "fc_theorem": "Erdos1090.erdos_1090", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos1090.erdos_1090", 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"wiki_color": "green", "wiki_humans": [], "wiki_outcome": "Proof found (Lean)" }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "solved", "erdos_url": "https://www.erdosproblems.com/1091", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 1091, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "OpenAI internal model" ], "wiki_claims_lean": false, "wiki_claims_solved": true, "wiki_color": "green", "wiki_humans": [], "wiki_outcome": "Full solution" }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "disproved", "erdos_url": "https://www.erdosproblems.com/1092", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos1092.f_asymptotic_general", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos1092.f_asymptotic_general", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": "hidden_constraints", "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 1092, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "GPT-5.5 Pro" ], "wiki_claims_lean": false, "wiki_claims_solved": true, "wiki_color": "green", "wiki_humans": [ "Przemek Chojecki" ], "wiki_outcome": "Full solution" }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/1093", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos1093.erdos_1093.parts.i", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos1093.erdos_1093.parts.i", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 1093, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/1094", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos1094.erdos_1094", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos1094.erdos_1094", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 1094, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "partial", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/1095", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos1095.erdos_1095.variants.log_equivalent", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos1095.erdos_1095.variants.log_equivalent", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": "plby", "machine_verdict": "unconditional", "named_assumptions": [], "non_kernel_axioms": [], "problem": 1095, "proof_link": null, "proof_links": [ { "complete": false, "conditional": false, "label": "plby/lean-proofs", "partial": true, "source": "plby", "state": "partial", "url": "https://github.com/plby/lean-proofs/blob/main/src/v4.29.1/ErdosProblems/Erdos1095.lean" } ], "recommended_action": "Only link a correctly stated variant after a per-problem review.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "Aristotle", "Claude Opus 4.6", "GPT-5.4 Pro", "Gemini 3.1 Pro" ], "wiki_claims_lean": true, "wiki_claims_solved": false, "wiki_color": "yellow", "wiki_humans": [ "shtuka" ], "wiki_outcome": "New proof of (slightly weaker) partial result (Lean)" }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "proved", "erdos_url": "https://www.erdosproblems.com/1096", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos1096.erdos_1096", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos1096.erdos_1096", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 1096, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "done", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/1097", "fc_has_proof": true, "fc_linked": true, "fc_theorem": "Erdos1097.erdos_1097", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos1097.erdos_1097", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 1097, "proof_link": "https://github.com/mo271/formal-conjectures/blob/f13dd54b520cdf2136fdd3a04f0f9fa50e311358/FormalConjectures/ErdosProblems/1097.lean#L306", "proof_links": [], "recommended_action": "No action.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "AlphaEvolve" ], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": "yellow", "wiki_humans": [], "wiki_outcome": "Slight improvement to past construction" }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "proved (Lean)", "erdos_url": "https://www.erdosproblems.com/1098", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": "plby", "machine_verdict": "unconditional", "named_assumptions": [], "non_kernel_axioms": [], "problem": 1098, "proof_link": null, "proof_links": [ { "complete": true, "conditional": false, "label": "plby/lean-proofs", "partial": false, "source": "plby", "state": "complete", "url": "https://github.com/plby/lean-proofs/blob/main/src/v4.29.1/ErdosProblems/Erdos1098.lean" }, { "complete": true, "conditional": false, "label": "Jayyhk/erdos-lean", "partial": false, "source": "jayyhk", "state": "complete", "url": "https://github.com/Jayyhk/erdos-lean/blob/main/problems/1098/Erdos1098.lean" } ], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "Aristotle" ], "wiki_claims_lean": true, "wiki_claims_solved": false, "wiki_color": "green", "wiki_humans": [], "wiki_outcome": "Formalization" }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "proved", "erdos_url": "https://www.erdosproblems.com/1099", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 1099, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/1100", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": "plby", "machine_verdict": "conditional", "named_assumptions": [ "hPNT : Erdos1100b.PNT_statement" ], "non_kernel_axioms": [], "problem": 1100, "proof_link": null, "proof_links": [ { "complete": false, "conditional": false, "label": "plby/lean-proofs", "partial": true, "source": "plby", "state": "partial", "url": "https://github.com/plby/lean-proofs/blob/main/src/v4.29.1/ErdosProblems/Erdos1100.lean" } ], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/1101", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos1101.erdos_1101.parts.ii", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos1101.erdos_1101.parts.ii", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 1101, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "GPT-5.5 Pro" ], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": "white", "wiki_humans": [], "wiki_outcome": "Candidate partial result (solution to second part)" }, { "bucket": "done", "discrepancy": false, "erdos_state": "solved (Lean)", "erdos_url": "https://www.erdosproblems.com/1102", "fc_has_proof": true, "fc_linked": true, "fc_theorem": "Erdos1102.erdos_1102.density_zero_of_P", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos1102.erdos_1102.density_zero_of_P", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 1102, "proof_link": "https://github.com/Woett/Lean-files/blob/1e075c4f6e8a907b924647fa88238f978e941742/ErdosProblem1102PropertyP.lean", "proof_links": [ { "complete": true, "conditional": false, "label": "plby/lean-proofs", "partial": false, "source": "plby", "state": "complete", "url": "https://github.com/plby/lean-proofs/blob/main/src/v4.29.1/ErdosProblems/Erdos1102.lean" }, { "complete": true, "conditional": false, "label": "Jayyhk/erdos-lean", "partial": false, "source": "jayyhk", "state": "complete", "url": "https://github.com/Jayyhk/erdos-lean/blob/main/problems/1102/Erdos1102.lean" } ], "recommended_action": "No action.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "Aristotle" ], "wiki_claims_lean": true, "wiki_claims_solved": false, "wiki_color": "green", "wiki_humans": [], "wiki_outcome": "Formalization" }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/1103", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 1103, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/1104", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos1104.erdos_1104.variants.upper", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos1104.erdos_1104.variants.upper", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 1104, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "proved", "erdos_url": "https://www.erdosproblems.com/1105", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos1105.erdos_1105.parts.i", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos1105.erdos_1105.parts.i", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": "partial_literature", "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 1105, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/1106", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos1106.erdos_1106.parts.i", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos1106.erdos_1106.parts.i", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 1106, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/1107", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos1107.erdos_1107", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos1107.erdos_1107", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 1107, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/1108", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos1108.erdos_1108.parts.ii", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos1108.erdos_1108.parts.ii", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 1108, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/1109", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 1109, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/1110", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 1110, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/1111", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 1111, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/1112", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 1112, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/1113", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos1113.erdos_1113", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos1113.erdos_1113", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 1113, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "proved", "erdos_url": "https://www.erdosproblems.com/1114", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 1114, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "solved", "erdos_url": "https://www.erdosproblems.com/1115", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 1115, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "solved", "erdos_url": "https://www.erdosproblems.com/1116", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 1116, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/1117", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 1117, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "solved", "erdos_url": "https://www.erdosproblems.com/1118", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 1118, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "independent", "erdos_url": "https://www.erdosproblems.com/1119", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos1119.erdos_1119", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos1119.erdos_1119", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 1119, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/1120", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 1120, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "proved (Lean)", "erdos_url": "https://www.erdosproblems.com/1121", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": "plby", "machine_verdict": "conditional", "named_assumptions": [ "hns : Erdos1121.CirclesNonseparable circles" ], "non_kernel_axioms": [], "problem": 1121, "proof_link": null, "proof_links": [ { "complete": true, "conditional": false, "label": "plby/lean-proofs", "partial": false, "source": "plby", "state": "complete", "url": "https://github.com/plby/lean-proofs/blob/main/src/v4.29.1/ErdosProblems/Erdos1121.lean" }, { "complete": true, "conditional": false, "label": "Jayyhk/erdos-lean", "partial": false, "source": "jayyhk", "state": "complete", "url": "https://github.com/Jayyhk/erdos-lean/blob/main/problems/1121/Erdos1121.lean" } ], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "Aristotle" ], "wiki_claims_lean": true, "wiki_claims_solved": false, "wiki_color": "green", "wiki_humans": [], "wiki_outcome": "Formalization" }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/1122", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 1122, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "independent", "erdos_url": "https://www.erdosproblems.com/1123", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 1123, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "proved", "erdos_url": "https://www.erdosproblems.com/1124", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 1124, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "done", "discrepancy": false, "erdos_state": "proved (Lean)", "erdos_url": "https://www.erdosproblems.com/1125", "fc_has_proof": true, "fc_linked": true, "fc_theorem": "Erdos1125.erdos_1125", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos1125.erdos_1125", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": "plby", "machine_verdict": "unconditional", "named_assumptions": [], "non_kernel_axioms": [], "problem": 1125, "proof_link": "https://github.com/plby/lean-proofs/blob/main/src/v4.29.1/ErdosProblems/Erdos1125.lean", "proof_links": [ { "complete": true, "conditional": false, "label": "plby/lean-proofs", "partial": false, "source": "plby", "state": "complete", "url": "https://github.com/plby/lean-proofs/blob/main/src/v4.29.1/ErdosProblems/Erdos1125.lean" }, { "complete": true, "conditional": false, "label": "Jayyhk/erdos-lean", "partial": false, "source": "jayyhk", "state": "complete", "url": "https://github.com/Jayyhk/erdos-lean/blob/main/problems/1125/Erdos1125.lean" } ], "recommended_action": "No action.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "Aristotle" ], "wiki_claims_lean": true, "wiki_claims_solved": false, "wiki_color": "green", "wiki_humans": [], "wiki_outcome": "Formalization" }, { "bucket": "done", "discrepancy": false, "erdos_state": "proved (Lean)", "erdos_url": "https://www.erdosproblems.com/1126", "fc_has_proof": true, "fc_linked": true, "fc_theorem": "Erdos1126.erdos_1126", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos1126.erdos_1126", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": "plby", "machine_verdict": "unconditional", "named_assumptions": [], "non_kernel_axioms": [], "problem": 1126, "proof_link": "https://github.com/plby/lean-proofs/blob/main/src/v4.29.1/ErdosProblems/Erdos1126.lean", "proof_links": [ { "complete": true, "conditional": false, "label": "plby/lean-proofs", "partial": false, "source": "plby", "state": "complete", "url": "https://github.com/plby/lean-proofs/blob/main/src/v4.29.1/ErdosProblems/Erdos1126.lean" }, { "complete": true, "conditional": false, "label": "Jayyhk/erdos-lean", "partial": false, "source": "jayyhk", "state": "complete", "url": "https://github.com/Jayyhk/erdos-lean/blob/main/problems/1126/Erdos1126.lean" } ], "recommended_action": "No action.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "Aristotle" ], "wiki_claims_lean": true, "wiki_claims_solved": false, "wiki_color": "green", "wiki_humans": [], "wiki_outcome": "Formalization" }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "independent", "erdos_url": "https://www.erdosproblems.com/1127", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 1127, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "disproved", "erdos_url": "https://www.erdosproblems.com/1128", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos1128.erdos_1128", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos1128.erdos_1128", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 1128, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "proved", "erdos_url": "https://www.erdosproblems.com/1129", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": "literature", "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 1129, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "proved", "erdos_url": "https://www.erdosproblems.com/1130", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": "literature", "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 1130, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/1131", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 1131, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "GPT-5.5 Pro" ], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": "white", "wiki_humans": [], "wiki_outcome": "Candidate partial result" }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/1132", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 1132, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "AlphaEvolve", "Claude", "GPT-5.4 Pro", "Gemini Pro" ], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": "yellow", "wiki_humans": [ "Terence Tao" ], "wiki_outcome": "Partial result" }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/1133", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos1133.erdos_1133", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos1133.erdos_1133", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 1133, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "GPT-5.5 Pro" ], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": "white", "wiki_humans": [ "Przemek Chojecki" ], "wiki_outcome": "Candidate full solution" }, { "bucket": "statement", "discrepancy": false, "erdos_state": "disproved (Lean)", "erdos_url": "https://www.erdosproblems.com/1134", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 1134, "proof_link": null, "proof_links": [ { "complete": true, "conditional": false, "label": "Jayyhk/erdos-lean", "partial": false, "source": "jayyhk", "state": "complete", "url": "https://github.com/Jayyhk/erdos-lean/blob/main/problems/1134/Erdos1134.lean" } ], "recommended_action": "Write the FC statement and link the matching hosted proof.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "AxiomProver" ], "wiki_claims_lean": true, "wiki_claims_solved": false, "wiki_color": "green", "wiki_humans": [], "wiki_outcome": "Formalization" }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/1135", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos1135.erdos_1135", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos1135.erdos_1135", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 1135, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "statement", "discrepancy": false, "erdos_state": "proved (Lean)", "erdos_url": "https://www.erdosproblems.com/1136", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": "plby", "machine_verdict": "unconditional", "named_assumptions": [], "non_kernel_axioms": [], "problem": 1136, "proof_link": null, "proof_links": [ { "complete": true, "conditional": false, "label": "plby/lean-proofs", "partial": false, "source": "plby", "state": "complete", "url": "https://github.com/plby/lean-proofs/blob/main/src/v4.29.1/ErdosProblems/Erdos1136.lean" }, { "complete": true, "conditional": false, "label": "Jayyhk/erdos-lean", "partial": false, "source": "jayyhk", "state": "complete", "url": "https://github.com/Jayyhk/erdos-lean/blob/main/problems/1136/Erdos1136.lean" } ], "recommended_action": "Write the FC statement and link the matching hosted proof.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "Aristotle" ], "wiki_claims_lean": true, "wiki_claims_solved": false, "wiki_color": "green", "wiki_humans": [], "wiki_outcome": "Formalization" }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/1137", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos1137.erdos_1137", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos1137.erdos_1137", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 1137, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "done", "discrepancy": false, "erdos_state": "disproved (Lean)", "erdos_url": "https://www.erdosproblems.com/1138", "fc_has_proof": true, "fc_linked": true, "fc_theorem": "Erdos1138.erdos_1138", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos1138.erdos_1138", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": "plby", "machine_verdict": "unconditional", "named_assumptions": [], "non_kernel_axioms": [], "problem": 1138, "proof_link": "https://github.com/YanYablonovskiy/formal-conjectures/blob/7c134317104d3b98ecc751afbb79ec0adddf8e7c/FormalConjectures/ErdosProblems/1138a.lean#L496", "proof_links": [ { "complete": false, "conditional": false, "label": "plby/lean-proofs", "partial": true, "source": "plby", "state": "partial", "url": "https://github.com/plby/lean-proofs/blob/main/src/v4.29.1/ErdosProblems/Erdos1138.lean" }, { "complete": true, "conditional": false, "label": "Jayyhk/erdos-lean", "partial": false, "source": "jayyhk", "state": "complete", "url": "https://github.com/Jayyhk/erdos-lean/blob/main/problems/1138/Erdos1138.lean" } ], "recommended_action": "No action.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "Aristotle", "GPT-5.5 Pro", "GPT-5.5 Thinking" ], "wiki_claims_lean": true, "wiki_claims_solved": true, "wiki_color": "green", "wiki_humans": [ "Hrishi Sunder", "Kireet Cheri", "Sourish Kumrawat" ], "wiki_outcome": "Full solution" }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/1139", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos1139.erdos_1139", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos1139.erdos_1139", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 1139, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "GPT-5.2 Pro", "GPT-5.5 Pro" ], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": "white", "wiki_humans": [ "Liam Price", "Przemek Chojecki", "Terence Tao", "gavinsherry" ], "wiki_outcome": "Candidate full solution" }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "disproved", "erdos_url": "https://www.erdosproblems.com/1140", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 1140, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "done", "discrepancy": true, "erdos_state": "disproved (Lean)", "erdos_url": "https://www.erdosproblems.com/1141", "fc_has_proof": true, "fc_linked": true, "fc_theorem": "Erdos1141.erdos_1141", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos1141.erdos_1141", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": "plby", "machine_verdict": "conditional", "named_assumptions": [], "non_kernel_axioms": [ "Pollack17.theorem_1_3" ], "problem": 1141, "proof_link": "https://github.com/yuta0x89/ErdosProblems/blob/a1319f732cdee5140faf47d984e2c451c1184803/Erdos1141.lean", "proof_links": [ { "complete": false, "conditional": true, "label": "plby/lean-proofs", "partial": false, "source": "plby", "state": "conditional", "url": "https://github.com/plby/lean-proofs/blob/main/src/v4.29.1/ErdosProblems/Erdos1141.lean" }, { "complete": false, "conditional": true, "label": "Jayyhk/erdos-lean", "partial": false, "source": "jayyhk", "state": "axiomatic", "url": "https://github.com/Jayyhk/erdos-lean/blob/main/problems/1141/Erdos1141.lean" } ], "recommended_action": "No action.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "GPT-5.2 Pro", "GPT-5.2 Thinking", "GPT-5.4 Pro", "OpenAI internal model" ], "wiki_claims_lean": true, "wiki_claims_solved": true, "wiki_color": "green", "wiki_humans": [ "Quanyu Tang" ], "wiki_outcome": "Full solution" }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/1142", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos1142.erdos_1142", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos1142.erdos_1142", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 1142, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/1143", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 1143, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "GPT-5.5 Pro" ], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": "yellow", "wiki_humans": [ "Przemek Chojecki" ], "wiki_outcome": "Partial result (implicit in literature)" }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/1144", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 1144, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/1145", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos1145.erdos_1145", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos1145.erdos_1145", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 1145, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/1146", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos1146.erdos_1146", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos1146.erdos_1146", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 1146, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "disproved", "erdos_url": "https://www.erdosproblems.com/1147", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 1147, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "hypothesis-conditional", "discrepancy": true, "erdos_state": "proved (Lean)", "erdos_url": "https://www.erdosproblems.com/1148", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos1148.erdos_1148", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos1148.erdos_1148", "fidelity_note": "Hosted theorem takes Duke's theorem as a hypothesis; #print axioms alone would not catch this.", "fidelity_source": "local", "gpt_erdos": null, "held_for_review": false, "machine_source": "plby", "machine_verdict": "conditional", "named_assumptions": [ "h_duke : Erdos1148.DukeTheoremStatement" ], "non_kernel_axioms": [], "problem": 1148, "proof_link": null, "proof_links": [ { "complete": false, "conditional": true, "label": "plby/lean-proofs", "partial": false, "source": "plby", "state": "conditional", "url": "https://github.com/plby/lean-proofs/blob/main/src/v4.29.1/ErdosProblems/Erdos1148.lean" }, { "complete": false, "conditional": true, "label": "Jayyhk/erdos-lean", "partial": false, "source": "jayyhk", "state": "axiomatic", "url": "https://github.com/Jayyhk/erdos-lean/blob/main/problems/1148/Erdos1148.lean" } ], "recommended_action": "Do not add a formal_proof link; document or wait for an unconditional theorem.", "signed_by": "reviewer:will-blair", "signed_fidelity_verdict": "variant", "wiki_ai_systems": [ "Claude Opus 4.6", "GPT-5.2 Pro", "GPT-5.2 Thinking", "GPT-5.4", "GPT-5.4 Pro", "GPT-5.5 Pro", "Gemini 3 Pro", "Gemini 3.1", "Gemini 3.1 Pro", "UlamAI Prover" ], "wiki_claims_lean": true, "wiki_claims_solved": true, "wiki_color": "green", "wiki_humans": [ "Ingo Alth\u00f6fer", "Przemek Chojecki", "Wouter van Doorn" ], "wiki_outcome": "Full solution" }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "proved", "erdos_url": "https://www.erdosproblems.com/1149", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 1149, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/1150", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos1150.erdos_1150", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos1150.erdos_1150", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 1150, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/1151", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 1151, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "Codex", "GPT", "GPT-5.5 Pro" ], "wiki_claims_lean": true, "wiki_claims_solved": true, "wiki_color": "green", "wiki_humans": [ "Przemek Chojecki" ], "wiki_outcome": "Full solution" }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/1152", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 1152, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "proved", "erdos_url": "https://www.erdosproblems.com/1153", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 1153, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "AlphaEvolve", "Claude", "GPT-5.2 Thinking", "GPT-5.4 Pro", "Gemini Pro" ], "wiki_claims_lean": false, "wiki_claims_solved": true, "wiki_color": "green", "wiki_humans": [ "Aron Bhalla", "Nat Sothanaphan", "Terence Tao" ], "wiki_outcome": "Full solution" }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "not disprovable", "erdos_url": "https://www.erdosproblems.com/1154", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 1154, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/1155", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 1155, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/1156", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 1156, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/1157", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 1157, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/1158", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 1158, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/1159", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 1159, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/1160", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 1160, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "solved", "erdos_url": "https://www.erdosproblems.com/1161", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 1161, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/1162", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 1162, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/1163", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 1163, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "proved", "erdos_url": "https://www.erdosproblems.com/1164", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 1164, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "solved", "erdos_url": "https://www.erdosproblems.com/1165", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 1165, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "proved", "erdos_url": "https://www.erdosproblems.com/1166", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 1166, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/1167", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos1167.erdos_1167", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos1167.erdos_1167", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 1167, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/1168", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 1168, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "not disprovable", "erdos_url": "https://www.erdosproblems.com/1169", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 1169, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/1170", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 1170, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/1171", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 1171, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/1172", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 1172, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/1173", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 1173, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "not disprovable", "erdos_url": "https://www.erdosproblems.com/1174", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 1174, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/1175", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos1175.erdos_1175", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos1175.erdos_1175", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 1175, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "not disprovable", "erdos_url": "https://www.erdosproblems.com/1176", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos1176.erdos_1176", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos1176.erdos_1176", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 1176, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "in-pr", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/1177", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 1177, "proof_link": null, "proof_links": [], "recommended_action": "Skip because an open PR already touches this problem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "GPT" ], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": "white", "wiki_humans": [ "Eric Li" ], "wiki_outcome": "Candidate full solution" }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/1178", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 1178, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "proved", "erdos_url": "https://www.erdosproblems.com/1179", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 1179, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "proved", "erdos_url": "https://www.erdosproblems.com/1180", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 1180, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/1181", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 1181, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/1182", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 1182, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/1183", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 1183, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "GPT-5.4 Pro" ], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": "yellow", "wiki_humans": [ "Przemek Chojecki", "Quanyu Tang" ], "wiki_outcome": "Partial result" }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/1184", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 1184, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "solved", "erdos_url": "https://www.erdosproblems.com/1185", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 1185, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/1186", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 1186, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "hypothesis-conditional", "discrepancy": false, "erdos_state": "solved", "erdos_url": "https://www.erdosproblems.com/1187", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": "plby", "machine_verdict": "conditional", "named_assumptions": [ "hp : Erdos1187b.Prime p" ], "non_kernel_axioms": [], "problem": 1187, "proof_link": null, "proof_links": [ { "complete": false, "conditional": false, "label": "plby/lean-proofs", "partial": true, "source": "plby", "state": "partial", "url": "https://github.com/plby/lean-proofs/blob/main/src/v4.29.1/ErdosProblems/Erdos1187.lean" } ], "recommended_action": "Do not add a formal_proof link; document or wait for an unconditional theorem.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "Codex", "GPT-5.5" ], "wiki_claims_lean": true, "wiki_claims_solved": false, "wiki_color": "green", "wiki_humans": [], "wiki_outcome": "Formalization" }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/1188", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 1188, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/1189", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 1189, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "statement", "discrepancy": false, "erdos_state": "solved (Lean)", "erdos_url": "https://www.erdosproblems.com/1190", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": "plby", "machine_verdict": "unconditional", "named_assumptions": [], "non_kernel_axioms": [], "problem": 1190, "proof_link": null, "proof_links": [ { "complete": true, "conditional": false, "label": "plby/lean-proofs", "partial": false, "source": "plby", "state": "complete", "url": "https://github.com/plby/lean-proofs/blob/main/src/v4.29.1/ErdosProblems/Erdos1190.lean" }, { "complete": true, "conditional": false, "label": "Jayyhk/erdos-lean", "partial": false, "source": "jayyhk", "state": "complete", "url": "https://github.com/Jayyhk/erdos-lean/blob/main/problems/1190/Erdos1190.lean" } ], "recommended_action": "Write the FC statement and link the matching hosted proof.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "GPT-5.4 Pro", "GPT-5.5 Pro", "Unspecified" ], "wiki_claims_lean": true, "wiki_claims_solved": true, "wiki_color": "green", "wiki_humans": [ "Boon Suan Ho", "Przemek Chojecki" ], "wiki_outcome": "Full solution" }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/1191", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 1191, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/1192", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos1192.erdos_1192", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos1192.erdos_1192", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 1192, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "statement", "discrepancy": false, "erdos_state": "solved (Lean)", "erdos_url": "https://www.erdosproblems.com/1193", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": "plby", "machine_verdict": "unconditional", "named_assumptions": [], "non_kernel_axioms": [], "problem": 1193, "proof_link": null, "proof_links": [ { "complete": true, "conditional": false, "label": "plby/lean-proofs", "partial": false, "source": "plby", "state": "complete", "url": "https://github.com/plby/lean-proofs/blob/main/src/v4.29.1/ErdosProblems/Erdos1193.lean" }, { "complete": true, "conditional": false, "label": "Jayyhk/erdos-lean", "partial": false, "source": "jayyhk", "state": "complete", "url": "https://github.com/Jayyhk/erdos-lean/blob/main/problems/1193/Erdos1193.lean" } ], "recommended_action": "Write the FC statement and link the matching hosted proof.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "Aristotle" ], "wiki_claims_lean": true, "wiki_claims_solved": false, "wiki_color": "green", "wiki_humans": [], "wiki_outcome": "Formalization" }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/1194", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 1194, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "Codex", "GPT-5.4 Pro", "GPT-5.5 Pro" ], "wiki_claims_lean": true, "wiki_claims_solved": false, "wiki_color": "yellow", "wiki_humans": [ "Lech Mazur" ], "wiki_outcome": "Partial result" }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "solved", "erdos_url": "https://www.erdosproblems.com/1195", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 1195, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "GPT-5.4 Pro" ], "wiki_claims_lean": false, "wiki_claims_solved": true, "wiki_color": "green", "wiki_humans": [ "Boon Suan Ho" ], "wiki_outcome": "Full solution" }, { "bucket": "done", "discrepancy": false, "erdos_state": "proved (Lean)", "erdos_url": "https://www.erdosproblems.com/1196", "fc_has_proof": true, "fc_linked": true, "fc_theorem": "Erdos1196.erdos_1196", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos1196.erdos_1196", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": "plby", "machine_verdict": "unconditional", "named_assumptions": [], "non_kernel_axioms": [], "problem": 1196, "proof_link": "https://github.com/math-inc/Erdos1196/blob/02fba13be7487cc51315f68d8fa7ef277633d3c8/PrimitiveSetsAboveX/FormalConjecturesErdos1196.lean", "proof_links": [ { "complete": true, "conditional": false, "label": "plby/lean-proofs", "partial": false, "source": "plby", "state": "complete", "url": "https://github.com/plby/lean-proofs/blob/main/src/v4.29.1/ErdosProblems/Erdos1196.lean" }, { "complete": true, "conditional": false, "label": "Jayyhk/erdos-lean", "partial": false, "source": "jayyhk", "state": "complete", "url": "https://github.com/Jayyhk/erdos-lean/blob/main/problems/1196/Erdos1196.lean" } ], "recommended_action": "No action.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "GPT-5.4 Pro", "GPT-5.4 Thinking", "Gauss" ], "wiki_claims_lean": true, "wiki_claims_solved": true, "wiki_color": "green", "wiki_humans": [ "Nat Sothanaphan" ], "wiki_outcome": "Full solution" }, { "bucket": "docstring", "discrepancy": true, "erdos_state": "disproved (Lean)", "erdos_url": "https://www.erdosproblems.com/1197", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": "plby", "machine_verdict": "conditional", "named_assumptions": [], "non_kernel_axioms": [ "Erdos1197.bm_approx_data" ], "problem": 1197, "proof_link": null, "proof_links": [ { "complete": false, "conditional": true, "label": "plby/lean-proofs", "partial": false, "source": "plby", "state": "conditional", "url": "https://github.com/plby/lean-proofs/blob/main/src/v4.29.1/ErdosProblems/Erdos1197.lean" }, { "complete": true, "conditional": false, "label": "Jayyhk/erdos-lean", "partial": false, "source": "jayyhk", "state": "complete", "url": "https://github.com/Jayyhk/erdos-lean/blob/main/problems/1197/Erdos1197.lean" } ], "recommended_action": "Add only a docstring note if useful; do not add formal_proof.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "Aristotle", "Claude Opus 4.7", "GPT-5.4 Pro" ], "wiki_claims_lean": true, "wiki_claims_solved": true, "wiki_color": "green", "wiki_humans": [], "wiki_outcome": "Full solution (Lean)" }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "disproved", "erdos_url": "https://www.erdosproblems.com/1198", "fc_has_proof": false, "fc_linked": false, "fc_theorem": null, "fc_url": null, "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 1198, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/1199", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos1199.erdos_1199", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos1199.erdos_1199", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], 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"wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "open", "erdos_url": "https://www.erdosproblems.com/1201", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos1201.erdos_1201", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos1201.erdos_1201", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 1201, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [ "GPT-5.5 Pro" ], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": "white", "wiki_humans": [ "Przemek Chojecki" ], "wiki_outcome": "Candidate full solution" }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": 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null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": false, "erdos_state": "proved", "erdos_url": "https://www.erdosproblems.com/1214", "fc_has_proof": false, "fc_linked": false, "fc_theorem": "Erdos1214.erdos_1214", "fc_url": "https://google-deepmind.github.io/formal-conjectures/theorem/?name=Erdos1214.erdos_1214", "fidelity_note": null, "fidelity_source": null, "gpt_erdos": null, "held_for_review": false, "machine_source": null, "machine_verdict": null, "named_assumptions": [], "non_kernel_axioms": [], "problem": 1214, "proof_link": null, "proof_links": [], "recommended_action": "No action until a hosted proof appears.", "signed_by": null, "signed_fidelity_verdict": null, "wiki_ai_systems": [], "wiki_claims_lean": false, "wiki_claims_solved": false, "wiki_color": null, "wiki_humans": [], "wiki_outcome": null }, { "bucket": "no-proof", "discrepancy": 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