| |

A Source-to-Endpoint Construction for Compact-Simple Yang–Mills Existence and Mass Gap

Byadmin


Internal ID: CGI-RSR-000034
Author(s): Barry L. Petersen
Document Type: Research Paper
Publication Date: July 2026
Original Creation Date: July 6, 2026
Status: Public
Domains: Mathematics, Physics
Research Topics: Mathematical physics, Yang-Mills Theory, Clay Millennium Problems

Abstract

We give a source-to-endpoint construction of compact-simple Yang–Mills theory on \(\mathbb R^4\) with positive Hamiltonian mass gap. The construction begins with a finite-type Yang–Mills coherence source
$$
S_{\mathrm{YM}}(G)=\mathrm{Gen}(\Sigma_{G,4}),
$$
built from compact-simple channel data, local transport, curvature gates, obstruction closure, gauge quotient, strict source closure, and primitive terminal readout. The source-first formulation separates source-admissible terminal data from endpoint-visible artifacts: projected or continuum-visible features contribute to the physical spectrum only if they survive source generation, closure, quotienting, terminal readout, Euclidean reconstruction, and calibrated endpoint projection.
At the source level we prove a normalized no-accumulation theorem for non-vacuum primitive terminal laws. Together with relative-channel locking, soft-sequence reduction, compact-simple synchronized-residue exclusion, and strict source closure, this gives
$$
\Delta_{\mathrm{CG}}(G)>0.
$$
We then construct a reflection-positive Euclidean source functional, prove refinement convergence, recover Euclidean covariance and clustering, and project to the public Euclidean endpoint. Ordinary endpoint recovery identifies the projected source endpoint with the independently specified compact-simple Yang–Mills observable endpoint:
$$
\mathcal A_{\mathrm{YM,ord}}^{E}
=
\mathcal A_{\mathrm{YM,src}}^{E},
\qquad
\mathcal A_{\mathrm{YM,ord},+}^{E}
=
\mathcal A_{\mathrm{YM,src},+}^{E}.
$$
Osterwalder–Schrader reconstruction produces
$$
(\mathcal H_G,\Omega_G,\mathcal A_G,H_G),
$$
with nontrivial physical sector and unique vacuum. Finally, calibrated temporal bridge transfer,
$$
\rho_G(E)=\alpha_GE-\log B_t,
$$
converts the source terminal gap into physical Hamiltonian spectral exclusion:
$$
E_{H_G}\bigl((0,c_G\Delta_{\mathrm{CG}}(G))\bigr)
\mathcal H_G^{\mathrm{phys}}
={0},
\qquad
c_G\Delta_{\mathrm{CG}}(G)>0.
$$
Thus the source-first construction recovers the ordinary compact-simple Yang–Mills endpoint on \(\mathbb R^4\) and gives a positive mass gap.

Available Document

DOI: 10.5281/zenodo.21215771

Citation:
Petersen, B. L. (2026). A Source-to-Endpoint Construction for Compact-Simple Yang–Mills Existence and Mass Gap. Zenodo. 
https://doi.org/10.5281/zenodo.21215771

Source Code and Supporting Materials

N/A

Summary and Notes

This archival research paper presents a source-to-endpoint construction for compact-simple Yang–Mills theory on four-dimensional Euclidean spacetime. The manuscript develops a finite-type Yang–Mills coherence source, proves a normalized source-level terminal mass gap, constructs a reflection-positive Euclidean source functional, recovers the ordinary compact-simple Yang–Mills Euclidean observable endpoint, applies Osterwalder–Schrader reconstruction, and transfers the source gap to physical Hamiltonian spectral exclusion by calibrated temporal bridge transfer.

The central organizing principle is that endpoint-visible data are not counted as physical spectral data unless they survive source generation, closure, quotienting, primitive terminal readout, Euclidean reconstruction, ordinary endpoint recovery, and calibrated spectral transfer. The paper is released as a public archival preprint for independent inspection, verification, criticism, and refinement.

Related Work

Local coherence Hessians and a structural classification of spectral gaps paper:
Petersen, B. L. (2026). Local Coherence Hessians: A Structural Classification
of Spectral Gaps. Zenodo.
https://doi.org/10.5281/zenodo.19969141

Birch-Swinnerton-Dyer rank-equality source-closure paper:
Petersen, B. L. (2026). The Birch–Swinnerton-Dyer Rank Equality
from Source Closure and Endpoint Readout. Zenodo.
https://doi.org/10.5281/zenodo.20731232

Riemann Hypothesis zero-orbit source closure paper:
Petersen, B. L. (2026). The Riemann Hypothesis from Zero-Orbit
Source Closure and Rank-Area Exclusion. Zenodo.
https://doi.org/10.5281/zenodo.20758204

Coherence Geometry Foundations, Part I:
Petersen, B. L. (2026). Coherence Geometry Foundations, Part I:
Orientation, Closure, and Algebraic Foundations. Zenodo.
https://doi.org/10.5281/zenodo.20156532

Similar Posts