Volume 35: Mesoscale Thermo-Gating (G2″), OA₁₆ Cost Certification, and SU(3) Naturality
Year: 2025
Type: article
Abstract: Defines and certifies a sub-exponential thermo-gate G2″ with deterministic reproducibility, an OA₁₆ cost-coefficient audit (κ=1.0, h_max=3/16), and a SU(3) T1 naturality test at machine precision. Paper, notebook, and artifact bundle are bit-consistent (fixed seeds; SHA-256 chain). Core certificate results (canonical run) Configuration: α=0.01; z=2.3263478740408408; β=1.0; τ=0.014495146808080436; b=1.0; σ_Q=0.05; bins=32; N_bin=256; B_boot=10000; Seeds={1761499001, 1761499002, 1761499003}. Channels: Var(W̃)=0.005 post-Q; ΔF̂ variance = 6.7×10⁻⁶ (N=256). Gate (G2″): mαSE=zβ2Var(W‾)+τ2e∣ΔF∣/bm_{α}^{SE}=z\sqrt{β^2\mathrm{Var}(\overline W)+τ^2 e^{|\Delta F|/b}}mαSE=zβ2Var(W)+τ2e∣ΔF∣/b. Base pass: passes=32, fails=0; ρ_min = 0.01784494710449385. Student-t stress (ν=3): passes=32, fails=0; ρ_min = 0.014512681628244699. OA₁₆ cost audit: κ=1.0; h_max=3/16; scaled targets (3,2,1) with 95% CIs α[2.7,3.3], β[1.8,2.2], γ[0.9,1.1]. SU(3) T1 naturality: S=16384; τ_nat=1e−9; maxΔ = 1.6410423069×10⁻¹⁰; violations=0. Canonical constructs Construct Definition / Role G2″ thermo-gate gap=βW‾−ΔF^\mathrm{gap} = β\overline W - \widehat{ΔF}gap=βW−ΔF; accept iff gap ≥ mαSEm_{α}^{SE}mαSE. Sub-exponential margin ( τ^2 e^{ OA₁₆ design Sylvester H₁₆; three ±1 orthogonal columns → κ=1.0, h_max=3/16. SU(3) naturality T1 Haar SU(3) via QR(Ginibre); plaquette P=U1U2U1†U2†P=U_1U_2U_1^{\dagger}U_2^{\dagger}P=U1U2U1†U2†; Tr(P)=Tr(P^G). Key modules (notebook-native) channels_build(...) — set W,QW,QW,Q scales; lock ΔF̂ variance. g2pp_eval_base(...) — compute per-bin gap, margin, ρ_j; report ρ_min. df3_stress(...) — multiplicative t(3) noise (zero-mean, unit-sd) about μ̂; recompute margins. oa16_cost_cert(...) — build OA₁₆ X; verify κ and h_max; emit scaled CI bands. nat_su3_t1(...) — Haar SU(3) sampler; plaquette trace invariance scan. cert_emit / release_emit / audit_archive(...) — certificate JSON, release descriptor, MANIFEST/SEAL/ATTEST, deterministic tarball. Findings Robust margins: G2″ maintains positive ρ across all bins under df=3 heavy-tail stress (−19% margin vs base; still >0). Design conditioning: OA₁₆ yields uniform leverage (3/16) enabling stable coefficient certification. Gauge integrity: SU(3) T1 passes with ~6× clearance vs τ_nat; no violations across 16,384 trials. Ablation (§3.3): G2′ (adaptive-only) under df=3 shows reduced pass-count; G2″’s sub-exp term restores all-pass. Continuity Extends V26–V29 certified-kernel and ledger discipline to mesoscale gating. Reuses determinant/attestation patterns (V26–V28); aligns with invariance audits in V33–V34. Transparency & limitations Synthetic target (OA₁₆): (3,2,1) used only to validate framework; no empirical cost claim. Seed specificity: canonical results fixed to {1761499001–03}; ensemble and sensitivity grids recommended (non-blocking). Challenge dataset (§9): predicted FAIL when μ_W↓, μ_ΔF↑ (e.g., μ_W=0.15, μ_ΔF=0.14) — falsifiable boundary.
Author: Foster, Camaron
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7103900446
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