Noesion Radarnoesion.ai
Research2026-08-03

OpenAI published a public repository, openai/ten-proofs, containing Lean 4 formalizations of ten results in mathematics and theoretical computer science described in its paper "Ten advances in mathematics and theoretical computer science," alongside a set of reasoning walkthroughs. The results include improved asymptotic upper bounds on sphere-packing density reaching the Cohn–Elkies threshold, exponentially stronger upper bounds for binary codes, a construction of a non-sofic group, a counterexample to Connes's rigidity conjecture, an n^4/log n formula lower bound for the permanent, exponential parallel repetition for two-player quantum games, polynomial-factor hardness for the closest vector problem, Ehrhart's volume conjecture, and resolutions of Erdős problems 183, 146 and 180. The project builds with Lean 4.32.0, mathlib and Lake, is Apache-2.0 licensed, and includes instructions for independent checking with Comparator.

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