erdos-problems

An open, checkable map of AI-assisted discovery in mathematics, named in honor of Paul Erdős's problems. Every result of ours carries receipts: two independent checks, a control and a rerunnable certificate.

Connected bipartite graphs of degeneracy exactly r with ex(n,H) ≥ c·n^(2−1/r+1/(28r²)), refuting the Erdős–Simonovits degeneracy conjecture (Erdős problem #146) for every r ≥ 2, with the exact limits of the method. Machine-checked in Lean 4.

CLI toolkit for Erdős problem research: literature ingestion, RAG search, and Lean 4 formalization

Papers, proofs and research records for eight Erdős problems, including what is established and what remains open.

Lean 4 formalization of the corrected Erdős Problem 796, proving the second-order asymptotic and explicit kernel-checked bounds.

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.

Dafny proofs for 16 selected computations in an 88-component research-workflow prototype, with generated Python and coverage maps. Not verification of the complete system.

Lean 4 proof of the dimension-five variants of Erdős problem 1007: the least edge count of a graph of dimension five is 15, attained by K₆ and K₁,₃,₃.

Lean 4 proof of the extremal half of Erdős problem 1007: a graph of dimension four with nine edges and no isolated vertex is K₃,₃.

Stanford AI for Lean Club progress on Erdős problems: papers, frontier notes, visualizer data, and Lean formalization.

Lean 4 proof of Erdős Problem 181 (Erdos 181): the Ramsey number of the n-dimensional hypercube satisfies R(Q_n) = O(2^n), linear in its number of vertices; formalization with Mathlib

The official repository of the Nexus Resonance Codex (NRC)

Independent exact certification of machine-generated mathematics — exact arithmetic, no code shared with the claimant, refusal as a verdict.

AI-agent pipeline producing machine-verified Lean 4 proofs — four PRs merged into Google DeepMind's formal-conjectures

Lean 4 proof of the finite case of Erdős Problem 172 (Erdos 172, Hindman sums and products): every finite colouring of the positive integers has, for each m, an m-element set whose nonempty subset sums and products share one colour; formalization with Mathlib

Preprint series on fractional and integral clique partitions, chordal graphs and quantitative stability, with bilingual manuscripts, Lean 4 formalizations and audit evidence.

An observed prime-descent law for Erdos 710 with five primes held out as a live test, five sealed Hall theorems, and a closed form for the Erdos 1044 extremal family

A quantitative corollary of Bradač’s theorem resolving Erdős Problem 920

AlphaProof Nexus evolution on Erdős Problem #25 — does every congruence-avoiding set have a logarithmic density? Open problem, formalized in Lean 4.

Lean 4 proof of the higher-dimensional Erdős distinct-distances bound (Erdos distinct distances): n points in R^d, d ≥ 3, determine at least c_d n^(2/d) distinct distances, and this order is sharp; formalization with Mathlib