Correlation Degradation, Rank Collapse, and Operational Horizons in Observational Physics

Arc II — Observation Paper 4 Title Correlation Degradation, Rank Collapse, and Operational Horizons in Observational Physics Zenodo DOI 10.5281/zenodo.18188547 Description This paper develops a general operational theory of correlation loss in physical observation, showing how finite accessibility leads to systematic degradation of correlation rank across measurement channels. Rather than treating decoherence, noise, or irreversibility as dynamical effects, the analysis reframes them as consequences of constrained inference under finite observational capacity. Using rank as a protocol-independent measure of accessible correlation, the paper demonstrates that successive observations generically induce rank collapse: a reduction in the dimensionality of distinguishable joint states accessible to observers. When rank collapse becomes irreversible, an operational horizon forms, beyond which no experimental refinement can recover lost correlations. The framework applies uniformly to quantum measurement, classical signal processing, and cosmological observation. It clarifies why certain observational limits appear absolute despite differing experimental designs, and why increased resolution or repeated measurement cannot bypass fundamental accessibility constraints. By identifying horizons with rank collapse rather than spacetime boundaries, the paper unifies measurement limits, decoherence, and observational irreversibility within a single operational structure. Keywords correlation rank; decoherence; measurement limits; operational horizons; information loss; observational physics Notes Arc II — Observation (core synthesis paper) Introduces rank collapse as a universal operational phenomenon Horizons defined by irrecoverable correlation loss Applies to quantum, classical, and cosmological observations Bridges measurement theory and horizon physics