FORMAL DOCUMENTATION FOR THE YANG-MILLS MILLENNIUM PRIZE PROBLEM: THE MCEC-TOPOLOGICAL FRAMEWORK
- 1Independent Research
Abstract
This paper provides a rigorous, non-perturbative axiomatic construction of quantum Yang-Mills theory with a compact non-Abelian gauge group on , establishing a formal connection between structural elastodynamics and subatomic gauge interactions. By mapping the topological and rheological invariants of a self-organizing continuum onto the quantum vacuum, we demonstrate that the system undergoes an algebraic scale-invariance collapse, defined as the Inertial Cancellation Principle.
We rigorously prove three fundamental theorems of convergence and regularity: first, the weak convergence of the discrete lattice action to the continuous Yang-Mills action under strict reflection positivity, satisfying the Osterwalder-Schrader reconstruction axioms; second, the uniform stability and scale-invariance of the covariant Laplace-Beltrami operator spectrum via the conformal invariance of the Hodge star operator in four dimensions; third, the compactness of the quantum Hamiltonian resolvent, driven by an asymptotic fractal volume lens mechanism.
By feeding experimentally verified parameters of dense nuclear matter into this geometric-kinematic framework, we analytically derive the existence of a non-zero lower bound in the energy spectrum (the mass gap), quantized at the exact stable value of , alongside an emerging isotropic confinement pressure of which topologically resolves QCD color confinement.
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BibTeX
@misc{chianura2026formal,
title = {{FORMAL DOCUMENTATION FOR THE YANG-MILLS MILLENNIUM PRIZE PROBLEM: THE MCEC-TOPOLOGICAL FRAMEWORK}},
author = {Piergiuseppe Chianura},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.5281/zenodo.23480094},
url = {https://zenodo.org/records/23480094},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - FORMAL DOCUMENTATION FOR THE YANG-MILLS MILLENNIUM PRIZE PROBLEM: THE MCEC-TOPOLOGICAL FRAMEWORK
AU - Piergiuseppe Chianura
PY - 2026
DA - 2026/10/19
PB - Zenodo
DO - 10.5281/zenodo.23480094
UR - https://zenodo.org/records/23480094
AB - This paper provides a rigorous, non-perturbative axiomatic construction of quantum Yang-Mills theory with a compact non-Abelian gauge group on , establishing a formal connection between structural elastodynamics and subatomic gauge interactions. By mapping the topological and rheological invariants of a self-organizing continuum onto the quantum vacuum, we demonstrate that the system undergoes an algebraic scale-invariance collapse, defined as the Inertial Cancellation Principle. We rigorously prove three fundamental theorems of convergence and regularity: first, the weak convergence of the discrete lattice action to the continuous Yang-Mills action under strict reflection positivity, satisfying the Osterwalder-Schrader reconstruction axioms; second, the uniform stability and scale-invariance of the covariant Laplace-Beltrami operator spectrum via the conformal invariance of the Hodge star operator in four dimensions; third, the compactness of the quantum Hamiltonian resolvent, driven by an asymptotic fractal volume lens mechanism. By feeding experimentally verified parameters of dense nuclear matter into this geometric-kinematic framework, we analytically derive the existence of a non-zero lower bound in the energy spectrum (the mass gap), quantized at the exact stable value of , alongside an emerging isotropic confinement pressure of which topologically resolves QCD color confinement.
ER -