Formally Verified a Millennium Prize Problem in Coq Yang-Mills Mass Gap

Name: Formally Verified a Millennium Prize Problem in Coq Yang-Mills Mass Gap
Availability: InStock
Author: shariq81

by shariq81·Feb 21, 2026·2 points·0 comments

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AI Analysis

○Pass

Millennium Prize claim needs external mathematical community verification, not just Coq syntax.

Strengths

•Coq codebase compiles with zero Admitted gaps in main chain
•Zenodo DOI provides timestamped preprint reference
•Maps three independent proof routes (thermodynamic, spectral, continuum)

Weaknesses

•No peer review from Clay Institute or physics journals—formalization alone doesn't solve the Prize
•Coq syntax is checkable, but mathematical correctness of axiom mapping is unverified by domain experts

Post Description

Hi HN, I'm an independent researcher. Over the last several months, I worked alongside a neuro-symbolic AI daemon to formally verify the Clay Millennium Prize "Yang-Mills Mass Gap" problem directly in the Coq theorem prover.

We mapped the finite lattice topology entirely to the ℝ⁴ continuum by reconstructing the 5 Osterwalder-Schrader axioms, isolating the Millennium formulation into exactly 657 sequential Qed proofs.

We aggressively removed every single heuristic Admitted gap from the main topology. The entire framework now rests on exactly 4 standard textbook axioms (e.g., finite-dimensional Perron-Frobenius theorem, standard statistical mechanics).

The repository contains the raw coqc logic. The formally timestamped preprint is on Zenodo (DOI: 10.5281/zenodo.18726858).

I decided to open-source the kernel execution rather than fight arXiv gatekeepers. Happy to answer any questions about theorem proving, the physics, or the AI methodology.