Interface Rigidity and the Limits of Descriptive Compression — A Diagnostic Analysis of Persistent Residuals in Geometry–Growth Inference

This technical note presents a diagnostic analysis of persistent residuals emerging in contemporary geometry–growth inference frameworks. Rather than proposing new physical models or extensions of established theories, the work examines the limits of descriptive compression that arise when heterogeneous observational domains are forced into a single globally closed representation. By applying a sequence of representational stress tests—including domain separation, relaxed comparability assumptions, and re-parametrization checks—the analysis shows that many reported tensions either collapse or migrate across domains once global point-like assumptions are weakened. However, a restricted class of residual effects remains stable under all admissible relaxations considered. These persistent effects are localized at the interface between geometric reconstruction and structure growth observables, and manifest empirically through lensing-related inconsistencies reconstructed along different inferential pathways. The note classifies these effects as interface-localized residuals, interpretable either as non-invertibility of current observational interfaces or as effective contributions confined to the interface itself. No new physical degrees of freedom, dynamical laws, or ontological commitments are introduced. The analysis is strictly diagnostic and aims to clarify where and why global descriptive compression fails, thereby constraining the space of viable interpretations of cosmological tensions before invoking new physics.