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We develop a reproducible diagnostic framework for modular phase transitions in RG-proxy flows of quantum states. The diagnostics are derived from the modular generator Kρ = −log ρ and include (i) spectral quantile coordinates kq = −log λq(ρ), (ii) a normalized commutator probe L(ρ;O) = ∥[Kρ,O]∥F /(∥Kρ∥F ∥O∥F ), and (iii) a running exponent ν extracted from sliding log–log fits of L(t). We introduce pre-registered stability rules using bootstrap over seeds and model-selection criteria (AICc/BIC/LOOCV), converting qualitative phase narratives into PASS/FAIL statements. Using a reference experiment (dim=64; Nvis = 5, Nhid = 1; Gibbs-chaotic family with mixing parameter p), we demonstrate robustness across observables (near vs far), normalization choices, and mild noise channels, and we identify explicit domain limitations (failure on extreme random-pure families). Finally, we explain how these diagnostics interface with phase/locality criteria through spectral-flow markers and provide a practical route to numerical phase mapping under modular RG-proxy dynamics.
Несен О. И. 2026. Reproducible Spectral Diagnostics for Modular Phase Transitions. PREPRINTS.RU. https://doi.org/10.24108/preprints-3114711
