2026/03/29 by Bernd von Mallinckrodt · 1 voice
Earth and Planetary Sciences · Environmental Science · Physics and Astronomy · #Complex Systems and Dynamics #Earthquake Detection and Analysis #Ecosystem dynamics and resilience
paper · doi:10.5281/zenodo.19310858
openalex publication_date 2026/03/29 · openalex created_date 2026/03/30 · openalex updated_date 2026/07/01
This preprint introduces Projection-Induced Determinism (PID) as a formal epistemic mechanism affecting collapse detection in complex systems. Existing early warning signal (EWS) frameworks—particularly those based on Critical Slowing Down—implicitly assume that the observation process is neutral with respect to the underlying system dynamics. We demonstrate that this assumption may fail under a broad class of dimensionality reduction scenarios. PID arises when high-dimensional stochastic dynamics are observed through low-dimensional projections, such that covariance structure is distorted and the relationship between system state and observables is altered. Under specific structural conditions, this can lead to attenuation, amplification, or inversion of canonical EWS indicators such as variance and lag-1 autocorrelation. In the inversion regime, observed indicators may suggest increasing stability while the underlying system approaches collapse. We provide a formal characterization of PID using linear projection operators and covariance transformations, and define three qualitative distortion regimes: weak distortion, strong distortion, and sign inversion. The framework generates falsifiable predictions, including directional reversal of EWS indicators under controlled projection conditions and increasing discrepancy between observational subspaces with rising structural compression. PID is positioned as a complementary extension to existing collapse detection frameworks, including multivariate EWS approaches, information-theoretic indicators, and entropy-based collapse models. We further establish a connection to the Compression–Response Transition Index (CRTI), showing that structural compression may be systematically underestimated under projection, leading to biased assessments of system viability. Rather than replacing existing methods, PID defines the conditions under which their applicability requires explicit verification. This reframes collapse detection as a joint problem of system dynamics and observability, with implications for ecological monitoring, machine learning systems, and model-based inference. Primary Keywords: Projection-Induced Determinism Early Warning Signals Complex Systems Collapse Detection Critical Transitions Core Theoretical Anchors: Structural Compression Observability Dimensionality Reduction Covariance Structure High-Dimensional Systems Bridging / Discovery Keywords: Critical Slowing Down Fisher Information Multivariate Early Warning Signals Spectral Entropy Effective Rank Epistemic Constraints System Collapse Complexity Science