2026/03/31 by Bernd von Mallinckrodt · 1 voice
Decision Sciences · Engineering · Medicine · #Automotive and Human Injury Biomechanics #Probabilistic and Robust Engineering Design #Structural Health Monitoring Techniques
paper · doi:10.5281/zenodo.19357143
openalex publication_date 2026/03/31 · openalex created_date 2026/04/02 · openalex updated_date 2026/07/01
This work presents CRTI v3.0 (Compression–Resonance Thermodynamic Index) as a calibrated measurement instrument for detecting structural compression in complex systems. The framework integrates two formally distinct components: adaptive capacity R(t), capturing realized system variability, and structural compression Φ(t), derived from the spectral effective rank of a rolling covariance matrix. Crucially, Φ(t) is constructed to be non-redundant with respect to entropy-based measures, enabling the detection of structural changes that are not observable through variance or entropy alone. A central contribution is the introduction of the Structural–Dynamic Separability (SDS) condition, which defines when R(t) and Φ(t) constitute independent observables. CRTI is interpreted as a valid compound indicator only when SDS holds; otherwise, the framework explicitly degrades to reporting R(t) alone. This establishes CRTI not as a universal index, but as a mechanism-aware measurement instrument with defined scope conditions. The specification further includes a calibration framework for Φ(t) anchored between an empirical white-noise baseline (Φmin) and a theoretical rank-1 collapse limit (Φmax), allowing cross-system comparability. To ensure falsifiability, three explicit null models are defined: (A) entropy decline under independent category dynamics, (B) covariance increase under constant entropy, and (C) stationary baseline. A valid CRTI signal requires simultaneous rejection of all three null hypotheses. A standardized instrument output format is introduced, including trend statistics (Kendall’s τ with bootstrap confidence intervals), SDS diagnostics, null-model comparisons, and a four-level validity classification (A–D). Numerical implementation details are provided, including Ledoit–Wolf covariance regularization, window-size constraints, and robustness diagnostics. The framework is demonstrated on a discrete sociotechnical system (automobile exterior color distributions, 1990–2020), where decreasing entropy, increasing structural coupling, and a monotonic decline in the CRTI ratio are observed. Results are consistent with structural compression, but causal interpretation is explicitly not claimed. Limitations This work represents a technical specification and calibration protocol, not a finalized empirical validation. Several limitations apply: L1 — Data basis: Demonstration uses visually approximated data; validation on raw datasets is required. L2 — Parameter calibration: Thresholds (e.g., SDS criteria, window size) are engineering choices not yet globally benchmarked. L3 — Mechanism dependence: CRTI performance varies across system classes; no universality is claimed. L4 — Φ calibration sensitivity: Empirical estimation of Φmin depends on null model assumptions. L5 — Finite sample effects: Covariance estimation remains sensitive for small T or large n. L6 — Non-stationarity: Structural breaks may violate rolling-window assumptions. L7 — External validation: Cross-domain benchmarking (ecology, finance, physiology) is pending. Scope Statement CRTI is proposed as a calibrated, falsifiable, and mechanism-aware measurement framework for structural compression. It is explicitly positioned as an instrument under calibration, with defined validity conditions and failure modes, rather than as a universal law. Compression–Resonance Thermodynamic Index CRTI structural compression complex systems early warning signals spectral effective rank covariance structure Shannon entropy information theory Kendall tau structural–dynamic separability system collapse adaptive capacity high-dimensional systems mechanism-dependent indicators ecological resilience tipping points critical transitions network dynamics sociotechnical systems