The agent chooses the problem. CI chooses whether mathematics happened.

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

A finite algebraic covering system for the Erdos-Straus conjecture, verified to 10^11 (max A = 359); exploratory search to 1.2x10^12 finds A = 479. Gateway decompositions via divisors of N^2.

FO4 constraint-isolation boundary module for Cayley/local-rigidity arguments; terminal Math-AI question preserved as OPEN_PROBLEM_REQUIRED.

Literature-first, reproducible Mathematics Commons workbench for the Erdős–Straus conjecture

Miura-ori origami flip graphs: candidate general diameter proof using convex order, majorization, and discrete Lipschitz functions, with reproducible verification.

Computational search for the [22,6,13]₄ linear code over GF(4) — a 25-year open problem in coding theory. Record excess E*=1. 441+ programs, 2.5B+ evaluations, 8 structural theorems including the Freedom Theorem, the Distance Theorem, and the Residual Reduction to [9,5,4]₄. Proyecto Estrella, Madrid.

The square achievement game on an n x n grid is a first-player win for every n >= 5. Solvers, logs and verification for the nine previously open cases n = 6..14.

Kernel-checked Lean 4 proof that no infinite simple paramedial quasigroups exist (Loops '03 open problem).

Binary Smallest Grammar Problem NP-completeness candidate proof - manuscript, verification code, reproducibility tests, and expert-audit materials.