A Falsifiable Statistical Framework for Constraint-Sensitive Residual Structure in Gravitational-Wave Ringdown

Abstract

The interpretation of post-merger gravitational-wave residuals remains constrained by detector noise, waveform uncertainty, and the lack of a general statistical framework to assess whether residual organization exhibits reproducible structure beyond conventional stochastic expectations. Existing analyses provide powerful tools for waveform reconstruction and model comparison, yet offer no model-independent methodology for characterizing the statistical organization of residual behavior itself.

       We hypothesize that if post-merger residuals exhibit reproducible organization beyond stochastic expectations, this behavior may reflect sensitivity to underlying consistency constraints that are not fully captured by local semiclassical descriptions. This hypothesis is neither assumed nor established by the present work; rather, it motivates the development of a statistically explicit framework capable of empirical evaluation.

       To that end, we introduce a partition-function-based formalism that constructs an ensemble of statistically admissible residual configurations and derives an ensemble response quantity—the Support Sensitivity (χ)—together with an operational diagnostic, the Ringdown Structure Score (SRD). The resulting framework provides a model-independent statistical protocol for identifying candidate residual organization while remaining agnostic regarding its physical origin.

       The principal contribution of this work is methodological rather than ontological. Rather than attributing residual structure to new gravitational physics, the proposed framework establishes a falsifiable statistical architecture for determining whether post-merger residuals warrant explanation beyond conventional stochastic models.