A Saturation-Based Diagnostic for Evaluating Apparent Discretization in Gravitational-Wave Population Parameters

We introduce a saturation-based diagnostic framework for evaluating apparent discretization in gravitational-wave population parameters. Motivated by recent claims of clustering of compact-binary mass ratios near simple algebraic values, the framework adapts methods from constraint-saturation analysis in overdetermined integer systems to distinguish intrinsic population structure from selection- and inference-induced artifacts.

The central organizing principle is a baseline–excess decomposition: observed clustering is expressed as the sum of a baseline component generated by detection selection effects and parameter-estimation geometry, plus a residual component that may indicate intrinsic astrophysical structure. We define saturation as the persistence of excess clustering under catalog growth and introduce a concentration diagnostic to quantify proximity to proposed landmarks relative to population scatter.

The framework explicitly addresses metric dependence (mass ratio versus symmetric mass ratio), operator alignment between detection and inference pipelines, and the role of posterior width in generating spurious structure. Illustrative statistics from GWTC catalogs are presented descriptively, without claims of new physical constants or quantization.

This work does not assert the existence of intrinsic discretization in gravitational-wave populations. Instead, it provides a falsifiable, transferable diagnostic methodology for testing such claims rigorously. The approach is intended as a filter against over-interpretation and is applicable to any population analysis where apparent clustering may arise from measurement geometry rather than underlying physics.