Volumes I–III
The complete mathematical argument and theorem dependency chain.
Core manuscript
Four-Dimensional Pure Yang–Mills Theory for Every Compact Simple Global Form
Existence, Wightman Reconstruction, and Mass Gap
Status
Available for expert review
Unconditional proof claimed in Volumes I–III. Independent expert review ongoing. The canonical three-volume set is linked below, with an exact release identifier, source snapshot, page counts, and checksums so reviewers can cite the version they inspected.
YM-I-III-R1 · 21 August 2026Abstract in brief
The paper constructs a nontrivial pure Yang–Mills Wightman theory on ℝ⁴ for every compact connected non-abelian gauge group with simple Lie algebra, including its distinct finite central quotients. The construction produces a unique invariant vacuum and a strictly positive Hamiltonian mass gap.
Its route is constructive and same-family: Wilson lattice measures, multiscale flow, continuum Euclidean limits, Osterwalder–Schrader reconstruction, Yang–Mills identification, and spectral coercivity are carried within one dependency chain.
Release set
Release manifest
The canonical route manifest and exact source snapshot for reproducible navigation.
Additional work
Lean formalisation of selected proof interfaces is in progress. Glueball spectrum project is in development.
Canonical manuscript release
Read the proof before deciding what to review.
This is the public release of the three-volume manuscript. The source snapshot is c89fa4157; the PDFs are unchanged copies of the repository volumes listed in papers/clay/VOLUMES.md.
Volume I · 341 pages
The All-Group Theorem and Finite-Prefix Wilson Renormalization
Download PDF SHA-256 121f9d96f071e81b654015e5e160eee2551c4d8a27d44359a97fb859e343aeda
Volume II · 205 pages
Global Forms, Asymptotic Freedom, and Dimensional Transmutation
Download PDF SHA-256 9b08d486c4ec60103bc686a498af922c43f4691d8fe6ac9f38edb5c8d948a6ca
Volume III · 231 pages
Reconstruction, Mass Gap, and Yang–Mills Identification
Download PDF SHA-256 5b68732d0ffc6b5148bc0ff3f0b366d42cddd4faf7335e920d63f6e1d25dc45b
Navigation aid
Main-route proof manifest
Download JSON SHA-256 582580035a840d90d5a7b28ddf0401901a435596fe2d725d0672004bb3095245
Reviewer materials
Expert-review talk package
Download package SHA-256 4080897509801dd9c5aa5fdd275de3348dcea96e078679687dc6ff5f30a81df8
Development provenance
Developed primarily with GPT‑5.
GPT‑5 performed much of the exploratory, drafting, integrative, and adversarial work under Leslie P. Polzer’s research direction. That role is disclosed because it is material to how the proof was produced.
The disclosure is not an argument for correctness. The manuscript makes no appeal to model authority: its claims must stand as mathematics and survive independent expert review.
Read the methodologyWhy review is visible here
A major claim should invite exacting scrutiny.
“Under review” describes the publication process, not the ambition of the result. The site states the theorem directly while keeping acceptance and independent validation distinct from authorship of the proof.
See the open reviewer call