V30 - Finite-Volume SU(3) Mass-Gap Certification - Certified Lower Bounds and Wilson-Loop Confinement in the RSI Framework

This volume establishes Finite-Volume SU(3) Mass-Gap Certification in the RSI framework, extending Volume 29’s certified spectral kernel to lattice gauge dynamics and carrying Volume 28’s attestation discipline into confinement audits. We present a notebook-native protocol that derives a rigorous lower bound on the SU(3) mass gap on a finite periodic lattice using Wilson loops, a reduced transfer matrix, and machine-checkable certificates with deterministic replay. Core certificate results (finite volume): Mass-gap lower bound: m_gap(L=8, a=0.2) ≥ 1.229835×10⁻² (lattice units) via Rayleigh quotient and Gershgorin screening Confinement witness: Wilson-loop area-law fit with σ̂ > 0; Creutz ratios stable across loop sizes Gauge integrity: link unitarity drift ≤ 1×10⁻¹²; plaquette tests pass all thresholds Safety guards: det_sentinel > 1×10⁻⁷ throughout; avalanche policy holds with no over-limit bursts Replay and audit: SHA-256 per-step sigils, final ledger digest, and public JSON certificate 🧮 Canonical Constructs Construct Definition SU(3) Link Field U_μ(x) ∈ SU(3) with Wilson action S_W = β∑_P(1 − Re Tr U_P/3) Transfer/Correlation Operators Reduced transfer operator K with λ₀, λ₁ bounds; two-point correlator C(t) for m_eff(t) Mass-Gap Estimators Rayleigh quotient on K, Gershgorin disc lower bounds, Feynman–Kac inequality, m_eff(t)=ln[C(t)/C(t+1)] Confinement Witness Wilson-loop area law and Creutz ratios as σ̂ and χ(R,T) stability checks Safety & Invariants V26 determinant floor, V27 δ-model, V28 avalanche policy, V29 spectral kernel baseline ⚙️ Key Modules su3_link_ops(...) — group projection, unitarity audit, plaquette checks wilson_action(...) — plaquette accumulation and β-sweep hooks transfer_matrix_bound(...) — Rayleigh/Gershgorin mass-gap lower bound correlator_massplateau(...) — effective-mass plateaus and consistency gates wilson_loop_scan(...) — area-law fit and Creutz ratio extraction sigil_ledger(...) — per-step SHA-256 witnesses, bundle digest, JSON certificate 🔬 Findings Certified lower bound m_gap(L=8, a=0.2) ≥ 1.229835×10⁻² with independent correlator cross-check agreement Positive area-law slope σ̂ and stable Creutz ratios confirm confinement regime Deterministic replay reproduces sigil chain and certificate without drift; all guards pass 🔁 ContinuityV29 → V30: Reuses audited spectral kernel and ledger for deterministic, divergence-free numerics.V28 → V30: Inherits avalanche-safe attestation for boundary pushes.V27 → V30: Enforces determinant floor and δ-model error budgeting.V25 → V30: Uses navigation discipline to select (L, a, β) operating points. Reproducibility & ProvenanceNotebook-only; all computations inline. Environment pins recorded. Artifacts include PDF, notebook, mass_gap_certificate.json, replay_report.json, sigil ledger, and bundle.sha256 digest.