V31 - Uniform Lower-Bound Certification for σ·a² and m·a on Finite-Volume SU(3) - Regression-Guarded Replay in the RSI Framework
Year: 2025
Type: conference-abstract
Abstract: This volume establishes Uniform Lower-Bound Certification for finite-volume SU(3) in the RSI framework—standardizing a notebook-native pipeline that emits machine-verifiable lower bounds for the string-tension proxy σ⋅a2\sigma\cdot a^2σ⋅a2 (via Creutz ratios) and the finite-volume mass proxy m⋅am\cdot am⋅a (via effective-mass infimum). The run enforces a physics-mode guard, pins the environment, requires deterministic seeds, and produces a chained checksum ledger, manifest, and a single JSON Uniform LB Certificate. The quick-path smoke test on L=8, T=16L=8,\ T=16L=8, T=16 certifies conservative nonnegative bounds, confirming packaging, guardrails, and replay integrity for subsequent ensemble upgrades. Certified outputs (this attested run): σ⋅alb2=0.0\sigma\cdot a^2_{\mathrm{lb}} = 0.0σ⋅alb2=0.0 m⋅alb=0.0m\cdot a_{\mathrm{lb}} = 0.0m⋅alb=0.0 Lattice: Lt×Lx×Ly×Lz=16×8×8×8L_t\times L_x\times L_y\times L_z = 16\times 8\times 8\times 8Lt×Lx×Ly×Lz=16×8×8×8 Wilson-loop grid: 24 rectangles with Rmax=4, Tmax=6R_{\max}=4,\ T_{\max}=6Rmax=4, Tmax=6 Determinism probe: pass (same-seed identical, perturbed-seed divergent) Ledger: 19 entries; terminal chain hash: afaba5a77c97948ebeffd87bf1922364fbd753c567f2cfe64d11f59a9186a899 Regression check: recomputed bounds match the certificate within tolerance; PASS, CLEAN, FINAL flags written 🧮 Canonical Constructs Construct Definition Creutz Ratio χ(R,T)=−log (W(R+1,T+1) W(R,T)W(R+1,T) W(R,T+1))\chi(R,T) = -\log\!\big( \tfrac{W(R{+}1,T{+}1)\,W(R,T)}{W(R{+}1,T)\,W(R,T{+}1)} \big)χ(R,T)=−log(W(R+1,T)W(R,T+1)W(R+1,T+1)W(R,T)) as a proxy for σ⋅a2\sigma\cdot a^2σ⋅a2 Effective Mass meff(t)=log (C(t)/C(t+1))m_{\mathrm{eff}}(t)=\log\!\big(C(t)/C(t{+}1)\big)meff(t)=log(C(t)/C(t+1)); lower bound m⋅alb=max(0,inftmeff(t))m\cdot a_{\mathrm{lb}}=\max(0,\inf_t m_{\mathrm{eff}}(t))m⋅alb=max(0,inftmeff(t)) Uniform LB Policy Nonnegativity clip for σ\sigmaσ and mmm when fits are negative or inconclusive Replay Ledger SHA-256 per-artifact entries with chained terminal digest Run Fingerprint Sorted-JSON hash over env pins, seeds, guard report, and code hashes ⚙️ Key Modules Physics-Mode Guard: network off, phi-free kernel check, PYTHONHASHSEED required Env Pins & Fingerprint: Python/OS/lib versions and code-hash map → run_fingerprint.sha256 SU(3) Scaffolding: QR-projection to SU(3)\mathrm{SU}(3)SU(3); periodic links on L3×TL^3\times TL3×T Wilson & Creutz: W(R,T)W(R,T)W(R,T) sweep → creutz_table.csv, fit_sigma.json Correlator & meffm_{\mathrm{eff}}meff: correlator.csv, meff_curve.csv, meff_bound.json Intervals & Error Budget: conservative clips and rationale → error_budget_ledger.json Certificate & Ledger: uniform_lb_certificate.json, ledger.jsonl, terminal chain hash Packaging & Regression: manifest.json, SHA256SUMS.txt, ladder_bundle.tar; regression_quick.json verifies certificate values from CSVs 🔬 Findings On random-link smoke data, strict Creutz minima are negative; uniform policy certifies σ⋅alb2=0.0\sigma\cdot a^2_{\mathrm{lb}}=0.0σ⋅alb2=0.0. Sparse positive correlator points yield inftmeff≤0\inf_t m_{\mathrm{eff}} \le 0inftmeff≤0; certificate records m⋅alb=0.0m\cdot a_{\mathrm{lb}}=0.0m⋅alb=0.0. Determinism, replay, and ledger integrity all pass. The pipeline is publish-ready and tuned for ensemble/smearing upgrades. 🔁 Continuity V27 → V31: invariants and δ-model budgeting inform guardrails. V28 → V31: attestation discipline and artifact practice persist. V29 → V31: deterministic replay, per-artifact hashing, chained ledger, and certificate layout are reused. V30 → V31: finite-volume SU(3) posture and correlator logic carried forward; V31 adds a uniform LB certificate that remains meaningful under weak plateaus. 📦 Reproducibility & ProvenancePrimary artifacts (under artifacts_v31/): Environment and determinism: env.json, determinism_probe.json, run_fingerprint.sha256 Observables and fits: wilson_grid.csv, creutz_table.csv, fit_sigma.json, correlator.csv, meff_curve.csv, meff_bound.json Bounds and audit: massgap_lb.json, error_budget_ledger.json, uniform_lb_certificate.json Packaging: manifest.json, SHA256SUMS.txt, ladder_bundle.tar Figures and docs: plots/*, README.md, citation.cff, zenodo.json, ETHICS_NOTE.md Ledger head: terminal_chain_hash.sha256 = afaba5a77c97948ebeffd87bf1922364fbd753c567f2cfe64d11f59a9186a899 Scope note. This volume certifies lower bounds on a fixed finite lattice. It does not claim continuum or infinite-volume limits. Subsequent volumes will introduce smearing, multi-hit, ensembles, and laddered L,aL,aL,a to seek strictly positive certified bounds with interval-safe uncertainty.
Author: Foster, Camaron
Language: English
Subfield: Nuclear and High Energy Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7080285111
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