Spatial Coherence C_{ij} as a Substrate-Agnostic Information-Theoretic Primitive Volume II: Cross-Domain Validation of Collapse Signatures

Abstract

Volume I of this series defined spatial coherence C_{ij} as a candidate substrate-agnostic information-theoretic primitive for complex networked dynamical systems under stress. It supplied the formal definition, justified the hybrid L1/L2 normalization, established analytic bridges to mutual information and conditional independence, and placed the statistic hierarchically beneath the Standard Coherence Fidelity Layer (SCFL) as a measurement primitive. All claims concerning cross-domain behavior were stated as hypotheses, most centrally Hypothesis H1 (Substrate-Approximate Independence): once network topology and stress class are fixed and observations are placed under identical reference normalization, the qualitative shape of the coherence-collapse trajectory is approximately independent of substrate. Volume II tests that hypothesis under a single, locked computational pipeline. The identical formula was applied without case-specific tuning to seven independent stress events spanning two bulk-electric systems (ERCOT and PJM) and two independent telemetry substrates (zonal demand and locational marginal price). Season-matched reference baselines were selected prior to inspection of each event window to eliminate look-ahead contamination. Negative controls on both substrates confirmed that the measurement remains quiet under ordinary operating conditions and produces large excursions only during genuine multi-day stress. The central empirical result is a graded relationship between event severity and the depth of system-average coherence depression. Short-duration or demand-only peaks produce only repeating diurnal cycling. Multi-day high-severity events produce sustained multi-day depression whose magnitude tracks documented severity. The same qualitative ordering appears on both grids. Spectral entropy as originally defined in Volume I encounters a structural obstacle—real coherence matrices are frequently indefinite—and is handled via an operational rectification convention documented in the manuscript. Negative-eigenvalue mass is recorded as a quarantined secondary diagnostic only. Hypothesis H1 receives qualified empirical support inside the bulk-electric domain. The measurement discriminates stress from calm, tracks severity continuously rather than as a binary threshold, and is not ERCOT-specific. Extension beyond power-system telemetry remains untested. The Tier-1 coherence substrate is now sufficiently characterized to serve as a reliable input layer for SCFL operator development. Further work should extend the identical pipeline to at least one non-power domain, resolve the spectral-entropy convention through controlled comparison of candidate resolutions, and subject each remaining operator to the same multi-event, negative-control discipline that coherence has received. This volume is strictly validation-only. It does not introduce new theoretical claims beyond those defined in Volume I.