The Zsa-G Framework: Active Spectral Control for High-Precision Mass Gap Extraction in SU(N) Gauge Theories

This repository contains the manuscript and supporting data for the Zsa-G Framework, a novel approach to stabilizing stochastic quantization in non-perturbative Yang–Mills theories. The Zsa-G framework introduces Active Spectral Control to address the long-standing challenges of mass plateau instabilities and topological freezing in lattice simulations. By leveraging Bakry–Émery theory and spectral coercivity, the framework enforces a volume-independent Log-Sobolev constant (p » 0.15), allowing for reliable mass gap extraction even as simulations approach the continuum limit (a ->0). Key features demonstrated in this work: Spectral stabilization of Langevin dynamics for SU(2) through SU(5) gauge groups. Systematic suppression of spurious mass plateaus and high-frequency stochastic noise. Significant reduction in integrated autocorrelation times (Tᵢₙₜ). Verification of the Wilson loop area law and linear confinement under the modified dynamics. This framework provides a robust foundation for high-precision spectroscopy in gauge theories and offers a computationally efficient methodology for large-N limits.