Zsa-G Active Spectral Coercivity Framework: Infrared Stabilization and Numerical Evidence for Spectral Gap Structure in Lattice Yang–Mills Theory

This record contains Version 8 of the Zsa-G framework, a research project introducing active spectral coercivity as a mechanism for infrared stabilization in lattice Yang–Mills theory. The package includes: - Main manuscript (ZsaG_Framework_V8.pdf)- Supplementary technical notes detailing lattice setup, finite-size scaling, and diagnostic procedures- Technical report with benchmark results and performance analysis- Minimal reproducibility code demonstrating spectral diagnostics and Krylov-subspace methods The framework introduces a spectral projector acting on infrared modes of the Faddeev–Popov operator, stabilizing configurations near the Gribov horizon. Numerical investigations indicate:- persistent infrared spectral scale under finite-size scaling- strong reduction in autocorrelation times- efficient computation using Krylov-subspace methods Additional analysis addresses:- locality via exponential decay behavior- consistency with reflection positivity at the diagnostic level- ultraviolet irrelevance of the stabilization term This version consolidates previous iterations (V6/V7/V8) into a refined and submission-ready research package. Keywords:Yang-Mills, Lattice Gauge Theory, Mass Gap, Spectral Methods, Gribov Problem, Langevin Dynamics, Numerical Physics,Quantum Field Theory, Krylov Methods, Infrared Physics Commercial Use Notice:This work is licensed under CC BY-NC-ND 4.0. Commercial use, redistribution, or implementation in proprietary systems is not permitted without explicit permission from the author. Code Availability:A minimal diagnostic implementation is provided for reproducibility and conceptual validation. This code does not include full SU(3) simulation pipelines or production-level implementations.