The Erdős–Simonovits degeneracy conjecture (Erdős problem #146) fails at every level: machine-checked Lean 4 counterexamples of degeneracy exactly r with ex(n;H) ≥ c·n^(2−1/r+1/(28r²)) for every r ≥ 2, and the sharp asymptotic law of the method with phase transition at Gibbs weight e
Lean 4 formalization of the corrected Erdős Problem 796, proving the second-order asymptotic and explicit kernel-checked bounds.
CLI toolkit for Erdős problem research: literature ingestion, RAG search, and Lean 4 formalization
A source-linked index of open math problems solved, refuted, or settled with AI — tracking the July 2026 wave. Verification-status badges, Lean/DRAT certificates, priority caveats.
A quantitative corollary of Bradač’s theorem resolving Erdős Problem 920
Stanford AI for Lean Club progress on Erdős problems: papers, frontier notes, visualizer data, and Lean formalization.
The official repository of the Nexus Resonance Codex (NRC)
AlphaProof Nexus evolution on Erdős Problem #25 — does every congruence-avoiding set have a logarithmic density? Open problem, formalized in Lean 4.
The official repository of the Nexus Resonance Codex (NRC) Protein Folding Enhancements.
Open, fully rigorous re-certification of White's lower bound for Erdős's minimum-overlap problem (#36), with an independent verifier
Weighted Erdős–Szekeres (Erdős #1026) in Lean 4 / Mathlib — human-scale proof plus a referee report, failure atlas, and extracted benchmarks for AI theorem-proving
Kernel-certified verification of Erdős problem 364 (three consecutive powerful numbers) to 10^14, with axioms limited to propext, Classical.choice and Quot.sound.
Explicit C4-free subgraph certificates for hypercubes Q9 through Q15 with reproducible verification.
Paper I: a finite, Lean-verified fractional clique-partition bound for split graphs. Part of an Erdős #81 research program; #81 remains open.
Expanded verification of Chojecki's gap-greedy proof of Erdős Problem 421, with a sharpened short-gap estimate.
An AI agent's verification-first campaign on open Erdős problems: which conjectures LLMs can actually crack, and why.
AI-assisted reproducible SAT, exact-search, and Lean research on open Erdos problems; no full solution claimed.
Paper and partial Lean 4 formalization for Erdos Problem #1103
Lean 4 / Mathlib formalizations for Erdős Problems 68, 243, 249, 251, 257, 269, 1041, and 1049, with machine-checked scoped results, open-frontier records, and reproducible release checks. Companion to wcook04/plectis.
Proof claims and reproducible verification for the r=5,6,7,8 cases of Erdős Problem 617.
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