Bernd von Mallinckrodt đŠProjection-Induced Observation...
Projection-Induced Observational Compression in Complex Systems: Robustness Across Independent Response Proxies and Observation Mechanisms
This preprint presents a systematic simulation-based analysis of projection-induced observational compression (PICD) as a source of diagnostic bias in complex systems. The study extends the CompressionâResponse Transition Index (CRTI) framework by explicitly modelling the observation process as a time-dependent, potentially rank-reducing projection operator acting on a higher-dimensional system state. Using a multivariate OrnsteinâUhlenbeck (OU) ground-truth system (n = 6) approaching critical slowing down, we investigate how different observation mechanisms alter the behaviour of composite diagnostics of the form T(t) = R(t) / Ί(t), where Ί(t) quantifies structural compression (via effective rank of the observed covariance matrix) and R(t) represents adaptive capacity. We implement three qualitatively distinct projection classes: (1) smooth sigmoid rank collapse, (2) abrupt step collapse, and (3) noisy projection (negative control). To address concerns about proxy dependence, we evaluate five conceptually independent response proxies: Râ: AR(1)-based recovery proxy (reference), Râ: multi-lag autocorrelation structure deviation, Râ: spectral centroid (frequency-domain proxy), Râ: variance fluctuation index (second-moment dynamics), Râ : eigenvalue concentration (multivariate proxy using all observed dimensions). Across N = 30 independent simulations per design cell and multiple projection strengths (Îł â {0.4, 0.8, 1.0}), we find: Structured rank-reducing projection mechanisms (sigmoid and abrupt) consistently induce strong collapse signals in the composite index T(t), with collapse probabilities P â„ 0.80 across all proxy families at Îł = 1.0. Unstructured noisy projection fails to reproduce the effect (P †0.20 across all proxies), establishing a clear negative control. Non-AR-based proxies (spectral, variance, and multivariate) produce equal or stronger signals than the AR(1)-based reference, demonstrating that the effect is not an artefact of lag-1 autocorrelation. The qualitative ranking of projection classes (sigmoid â abrupt â« noisy) is preserved across all proxy families, indicating robustness of the underlying mechanism. These results show that projection-induced compression operates at the level of observable state-space geometry rather than at the level of specific recovery-rate estimators. The findings highlight a previously underexplored limitation of early warning signals: diagnostic indicators may reflect changes in the observation mechanism rather than changes in the underlying system dynamics. The presented framework provides a formal basis for analysing observation-induced bias in domains where measurement, aggregation, or categorisation dynamically constrain the observable state space, including ecological monitoring, financial systems, and institutional reporting. All simulation code (V2âV6) and figure generation scripts are provided to ensure full reproducibility. complex systems, early warning signals, critical transitions, critical slowing down, observational bias, dimensionality reduction, projection effects, state space compression, effective rank, eigenvalue entropy, OrnsteinâUhlenbeck process, spectral analysis, permutation entropy, multivariate dynamics, system diagnostics, CRTI, Projection-Induced Determinism, robustness analysis
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Weddingweiser
Milo | Ziel der Menschheit
Lesering.de
Michael Blume
Gerd_Brodowski
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