V33 - Representation-Robust SU(3) Dynamics - Markovization, EDMDc-IV, Non-Normality Guards, ε-Bisimulation, and Invariance Audit in the RSI Framework
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2025
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| author | Foster, Camaron |
| author_facet | Foster, Camaron |
| contents | <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> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_17144315 |
| institution | Zenodo |
| language | eng |
| publishDate | 2025 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | V33 - Representation-Robust SU(3) Dynamics - Markovization, EDMDc-IV, Non-Normality Guards, ε-Bisimulation, and Invariance Audit in the RSI Framework Foster, Camaron Algorithms Models, Theoretical Markov Chains Machine learning Machine Learning Information Theory Monte Carlo Method Fourier analysis Fourier Analysis Principal Component Analysis Graph theory Nonlinear Dynamics Artificial intelligence Artificial Intelligence <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> |
| title | V33 - Representation-Robust SU(3) Dynamics - Markovization, EDMDc-IV, Non-Normality Guards, ε-Bisimulation, and Invariance Audit in the RSI Framework |
| topic | Algorithms Models, Theoretical Markov Chains Machine learning Machine Learning Information Theory Monte Carlo Method Fourier analysis Fourier Analysis Principal Component Analysis Graph theory Nonlinear Dynamics Artificial intelligence Artificial Intelligence |
| url | https://doi.org/10.5281/zenodo.17144315 |