Topological Saturation and the Existence of the Yang-Mills Mass Gap in Sub-Planckian Matrix Spacetime
Abstract
We present a rigorous, non-perturbative proof for the existence of the Yang-Mills mass gap (Delta YM > 0) on a four-dimensional Euclidean manifold R^4. We postulate that the physical vacuum is a dense matrix of entangled one-dimensional gauge bundles characterized by a strict topological saturation bound Lambda_sat. By treating the bundle intersection density Omega(x) as a continuous scalar field coupled to the non-Abelian gauge fields, we formulate the invariant action. The saturation bound acts as a natural, non-perturbative ultraviolet (UV) regulator, preventing the divergence of the path integral and ensuring the existence of the quantum theory without counterterms. Furthermore, we demonstrate that the discrete nature of the internal algebraic Lie dimensions enforces a strictly positive, discrete energy spectrum. This geometrically locks the vacuum state away from the first excited state, mathematically proving that Delta YM = E1 - E0 > 0.
Framework Context: This paper presents the final mathematical proof for the Yang-Mills mass gap based on the SIT/GMPS framework. It resolves the Millennium Prize Problem by demonstrating that the topological saturation of the spacetime bundle matrix acts as a natural UV regulator and enforces a discrete energy spectrum.
Related
- Topological Bundle Restructuring in Sub-Planckian Matrix Spacetime: Absolute Muon Mass, Vacuum Interaction, and the g-2 Anomaly
- Sub-Planckian Matrix Spacetime (GMPS): Photon Time Delay, Landau Pole Resolution, and Gamma-Ray Burst Spectral Cutoff Analysis
- Facets of Gravity: A journey exploring spacetime from Planckian to cosmological scales
- Spacetime Existence Theory
- Spacetime Existence Theory——Fundamental equation
BibTeX
@misc{borda2026topological,
title = {{Topological Saturation and the Existence of the Yang-Mills Mass Gap in Sub-Planckian Matrix Spacetime}},
author = {Mohamed Abdel momen Abu Borda},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.5281/zenodo.23467134},
url = {https://zenodo.org/records/23467134},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Topological Saturation and the Existence of the Yang-Mills Mass Gap in Sub-Planckian Matrix Spacetime
AU - Mohamed Abdel momen Abu Borda
PY - 2026
DA - 2026/10/19
PB - Zenodo
DO - 10.5281/zenodo.23467134
UR - https://zenodo.org/records/23467134
AB - We present a rigorous, non-perturbative proof for the existence of the Yang-Mills mass gap (Delta YM > 0) on a four-dimensional Euclidean manifold R^4. We postulate that the physical vacuum is a dense matrix of entangled one-dimensional gauge bundles characterized by a strict topological saturation bound Lambda_sat. By treating the bundle intersection density Omega(x) as a continuous scalar field coupled to the non-Abelian gauge fields, we formulate the invariant action. The saturation bound acts as a natural, non-perturbative ultraviolet (UV) regulator, preventing the divergence of the path integral and ensuring the existence of the quantum theory without counterterms. Furthermore, we demonstrate that the discrete nature of the internal algebraic Lie dimensions enforces a strictly positive, discrete energy spectrum. This geometrically locks the vacuum state away from the first excited state, mathematically proving that Delta YM = E1 - E0 > 0. Framework Context: This paper presents the final mathematical proof for the Yang-Mills mass gap based on the SIT/GMPS framework. It resolves the Millennium Prize Problem by demonstrating that the topological saturation of the spacetime bundle matrix acts as a natural UV regulator and enforces a discrete energy spectrum.
ER -