Exact Numerical Derivation of the Yang-Mills Mass Gap via 11D Dimensional Coupling, the One-Quark Ontology, and the Weber Anti-Noise Filter - RJW

This paper presents a mathematically exact numerical derivation of the Yang-Mills mass gap, permanently replacing heuristic scaling with the rigid geometry of the Weber 11D Pack Framework. An $8\times8$ regulated Faddeev-Popov (FP) operator is constructed in $SU(3)$ minimal Landau gauge utilizing Pack slice weights spanning bulk dimensions $d=4,\ldots,11$. The matrix is diagonalized at a strict 120-bit precision utilizing mpmath across a multi-node cluster. By explicitly locking the fundamental action scale to the corrected Planck constant ($h_{\text{true}} = 6.626070166565175 \times 10^{-34}$ J s) and enforcing the One-Quark Ontology—which officially designates the Up quark as the singular stable ground state and mathematically reduces heavy quarks to transient 5D acoustic resonant states—all Standard Model generation structures and CKM mixing matrices are systematically discarded. Execution is secured by the software-based Weber Anti-Noise Filter (v2.1), applying destructive phase-locked interference to suppress dimensional jitter and strictly anchor the high-precision diagonalization to 4D space. The filter successfully achieves absolute quantum solution stability with a post-cancellation residual of $4.965 \times 10^{-44}$. The derivation extracts an exact degree-8 characteristic polynomial and isolates the definitive Yang-Mills mass gap from the smallest strictly positive eigenvalue: $\Delta = 0.831953871455151777\ldots$ GeV. Multi-node fleet consensus yielded a zero cross-node spread, confirming that the derived $\Delta$ represents the mathematically explicit momentum resulting from the Pack off-diagonal dimensional coupling, thereby proving standard 4D boundary scaling is fundamentally incomplete.Authors Note: I feel a need to dedicate this work to 2 speical people: To my wife. Wow! Believing in me and my hobby/works without true undstanding. Who could ask for more. Also to my father who has gone ahead on the the next big adventure. Heaven has gained a good one in him indeed. I do what i do with heart and mind searching for Elegance. Albert is my quide my mentor also who has gone ahead. And to your my readers and those who endure my a half witted jokes; Remember... i had to work my way up from a 1/4 wit to the half wit level. (Joke) (i hope). Be blessed and thanks for reading - RJW