coq

A GitHub repository presenting machine-checked Coq proofs of new Busy Beaver champions, including a 10-state machine whose score exceeds Graham's number (f_{ω+1} level in the fast-growing hierarchy), beating the previous BB(8), BB(9) and BB(10) champions with exact scores verified without axioms.

This paper applies the VGPT-RSI AI system to produce formally verified partial results related to the Riemann Hypothesis, including boundary certificates and finite Lagarias inequalities, while explicitly identifying remaining mathematical obstructions.

OpenAI introduces GamePad, a learning environment for applying machine learning to theorem proving in the Coq proof assistant, enabling proof synthesis and training baseline models for tactic prediction and position evaluation tasks.