Geometric Curvature Susceptibility in Large-scale Structure

We report the identification and characterization of a scale-selective, configuration-dependent gravitational response in large-scale structure that cannot be reduced to local matter density, galaxy properties, or simple cosmic-web morphology. Building on a sequence of prior empirical studies, we show that this response activates sharply only when curvature modes of the galaxy overdensity field organize into a specific large-scale configuration and disappears outside that regime.

The response exhibits several defining properties: it is localized to a narrow band of angular scales, turns on over a small range of curvature percentiles, relaxes rather than persists across redshift slices, and remains robust under extensive null, rotation, and randomization tests.

Curvature-based proxies dominate the response, while galaxy morphology and cosmic-web geometry tests yield null results, eliminating explanations tied to baryonic physics, galaxy type, or static structural classification.

We interpret these findings as evidence for a geometric curvature susceptibility (GCS) of spacetime—an effective, emergent response that becomes active only under specific geometric conditions. This susceptibility does not modify local gravitational dynamics, introduce new sources, or alter the Einstein field equations. Instead, it represents a conditional, large-scale behavior that operates within the framework of General Relativity.

The present work is deliberately empirical and phenomenological in scope. It establishes the existence, properties, and constraints of the susceptibility while deferring questions of microphysical origin to future investigation. By consolidating detection, falsification, universality, and morphology tests into a coherent framework, this study provides a well-defined target for subsequent theoretical and observational work on collective geometric behavior in gravity.