Spectral Vacuum Mechanism – Part XIX Gauss-Law Certificates and Audit Artifacts under SU(3) Truncation

Abstract Part XIX continues the SVM diagnostic line by making SU(3) Gauss-law enforcement audit-ready for truncated gauge-sector calculations. We study the penalty Hamiltonian H_μ = H + μC, μ > 0, where the Gauss constraint operator is C = Σ_x Σ_{a=1…8} (G_x^a)² (so C ≥ 0 and the physical sector satisfies C = 0). The paper provides certificates that can be attached to any computed spectrum. The core certificate is an unconditional energy-to-constraint bound: for each computed eigenpair of H_μ, the Gauss violation is bounded by measured energies, ⟨C⟩ ≤ (E(μ) − E_min)/μ, μ > 0, where E_min is a certified lower bound on the ground energy of the unpenalized Hamiltonian H in the same truncation (e.g., from analytic operator inequalities, strong‑coupling bounds, or blockwise exact diagonalization that yields a provable lower certificate). This converts μ-scans into quantitative upper bounds on constraint leakage without invoking additional assumptions. Improvements: Explicit characterization of γ_C(j_max) with empirical scaling analysis (Fig. 6.1) Quantitative μ_max guidelines that distinguish the theoretical floating‑point ceiling (≈ 1/ε_mach) from practical eigensolver conditioning targets (Table 6.1) Statistical validation: R² > 0.995 (energy), R² > 0.990 (plateau), with bootstrap p < 0.01 for rejecting the null that the selected μ‑window fails linearity/plateau under the resampling noise model Benchmark sanity checks: SU(2) 2×2 vs exact diagonalization; SU(3) 2×2 qualitative scale/order consistency check against the reference SU(3) glueball spectrum (Morningstar–Peardon) within fixed truncation assumptions Keywords Spectral Vacuum Mechanism; SU(3) lattice gauge theory; Gauss law; physical Hilbert space; penalty method; truncation diagnostics; epsilon_mix; reproducibility; audit protocol; numerical conditioning; constraint gap characterization. Other works by the author on this topic: Nemirovsky M., Spectral Vacuum Mechanism - Part XIV Spectral Confinement as a Necessary Condition for Quantum Field Theory Confinement Gate-Induced Spectral Localization and Dimensional Constraints, Zenodo. DOI: 10.5281/zenodo.18140235 (2026) Nemirovsky M., Spectral Vacuum Mechanism - Part XV Unification of the mass formula in SVM particles of the Standard Model, Zenodo. DOI: 10.5281/zenodo.18207487 (2026) Nemirovsky M., Spectral Vacuum Mechanism – Part XVI Spectral Confinement under Truncated SU(2) Gauge Embedding: Preservation of the Spectral Confinement Class, Zenodo. DOI: 10.5281/zenodo.18225421 (2026) Nemirovsky M., Spectral Vacuum Mechanism – Part XVII Spectral Confinement under Truncated SU(3) Gauge Embedding: Toward a Constructive QCD‑like Framework, Zenodo. DOI: 10.5281/zenodo.18280887 (2026) Nemirovsky M., Spectral Vacuum Mechanism – Part XVIII Continuum Trajectory and Low-Energy Self-Consistency under SU(3) Truncation, Zenodo. DOI: 10.5281/zenodo.18415826 (2026)