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| Auteur principal: | |
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| Format: | Recurso digital |
| Langue: | anglais |
| Publié: |
Zenodo
2025
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| Accès en ligne: | https://doi.org/10.5281/zenodo.17144315 |
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Table des matières:
- <p>This volume establishes Representation-Robust SU(3) Dynamics in the RSI framework, upgrading Volume 32’s continuum certificate with cross-representation stability and a multi-pronged invariance audit. We formalize Markovization of the observable flow, estimate controlled Koopman operators via EDMDc-IV with instruments and over-identification, guard against non-normal dynamics, align representations under whitening, certify control-aware ε-bisimulation, recover invariant causal parents, match topological phases to Koopman phases, verify renormalization-group contraction, and enforce an information-bottleneck firewall. The attested run passes all gates with deterministic replay, full ledgering, and machine-checkable artifacts, while preserving V27 invariants, V28 boundary attestation, V29 replay/ledger discipline, V31 uniform LB posture, and V32 continuum certification.</p> <h2> Canonical Constructs</h2> <p>Construct Definition<br>Markovization Test Δ\_Markov = MMD(x\_t, x̂\_t+1) with gate Δ\_Markov ≤ α; fail ⇒ abort downstream inferences.<br>EDMDc-IV Instrumented Koopman estimation with exogenous controls: K\_s∈ℝ^{32×32}, K\_u∈ℝ^{4×32}; J-test over-identification with p-value report.<br>Non-Normality Guard ε-pseudospectrum radius r\_ε and numerical abscissa ω(A) bounded by r\_ε ≤ 1+ξ and ω(A) ≤ ξ\_ω.<br>Orthogonal Alignment (Whitened) Procrustes Q with κ(Q)=1; SVCCA stability across folds.<br>Control-Aware ε-Bisimulation Gromov–Wasserstein surrogate cost ε ≤ ε₀ across controlled strata.<br>Invariant Causal Parents (ICP) Parent set stable across environments at p < 0.01 after multiplicity control.<br>TDA Phase Match H¹ circular coordinates align with Koopman eigenphase within tolerance Δφ ≤ φ₀.<br>RG Contraction CI Confidence interval on contraction factor strictly < 1.<br>Info-Bottleneck Firewall Predictive AUC high while firewall AUC ≈ chance; leakage bounded.<br>CSSR ε-Machines Finite-state predictors consistent across strata with state-count stability.</p> <h2>⚙️ Key Modules</h2> <p>markovization\_test(...) — MMD-based state-forward agreement and α-gate.<br>edmdc\_iv(...) — instrument design, Koopman K\_s,K\_u fit, J-test, residual audit.<br>non\_normality\_guard(...) — pseudospectra and numerical abscissa checks.<br>whiten\_align(...) — whitening, Procrustes Q, SVCCA stability reports.<br>bisim\_gw(...) — GW surrogate ε under controls with stratified bootstraps.<br>icp\_audit(...) — invariant-parent search with Holm–Bonferroni control.<br>tda\_phase\_match(...) — H¹ circular coordinates vs Koopman phase alignment.<br>rg\_contraction\_ci(...) — contraction factor estimation with CI.<br>info\_bottleneck\_firewall(...) — predictive vs firewall AUC and leakage index.<br>cssr\_emachines(...) — ε-machine reconstruction stability.<br>ledger\_bundle(...) — env pins, artifacts, JSON certificate, chained terminal digest.</p> <h2> Findings</h2> <p>Markovization: Δ\_Markov = 0.000000 at α = 0.05 → pass.<br>EDMDc-IV: K\_s 32×32, K\_u 4×32, T\_eff = 3999; J = 0.0000, p = 1.0 → pass.<br>Non-normality: r\_ε = 0.328378 ≤ 1.050; ω(A) within guard → pass.<br>Orthogonal alignment: κ(Q) = 1; SVCCA ≈ 0.9999 → pass.<br>ε-Bisimulation: ε = 0.039694 ≤ ε₀ → pass.<br>ICP: invariant parents at p < 0.01 across strata with multiplicity control → pass.<br>TDA phases: max Δφ = 0 rad → pass.<br>RG contraction: CI upper < 0.98 → pass.<br>Info-bottleneck firewall: AUC\_pred = 0.868, AUC\_fw = 0.521 → pass.<br>Statistical controls: η = 1.000 power; Holm–Bonferroni corrections applied → pass.<br>Replay & ledger: deterministic, byte-stable; terminal chain hash = 1cc51c3c7d5bf55f9c9b4bb868288df2b530d39dfa529755a695425d649e2f45.</p> <h2> Continuity</h2> <p>Preserves V27 invariants (Φ discipline, detJ floor), V28 phase-boundary attestation and avalanche policy, V29 spectral-kernel replay/ledger practice, V31 regression-guarded replay posture, and V32’s continuum-limit certification; adds a representation-robust layer that holds across whitening and controlled strata.</p> <h2>Reproducibility & Provenance</h2> <p>Notebook-only; environment pins and run fingerprint recorded. Byte-stable artifacts and certificate bundle: markovization.json, edmdc\_iv.json, K\_s.npy, K\_u.npy, non\_normality\_guard.json, orthogonal\_alignment.json, bisim\_gw\.json, icp.json, tda\_phase.json, rg\_contraction.json, info\_bottleneck.json, power\_analysis.json, negative\_controls.json, cssr.json, final\_report.json, v33\_certificate.json, manifest.json, SHA256SUMS.txt, ledger.jsonl, terminal\_chain\_hash.sha256, README.md, citation.cff, zenodo.json, ETHICS\_NOTE.md. Decision: pass.</p>