Report on Ringdown Structural Realizability Tests

This technical report documents a focused methodological and Monte-Carlo–calibrated analysis of black-hole ringdown realizability in gravitational-wave data. The purpose of the report is not to introduce new theoretical claims, but to provide a transparent and reproducible diagnostic of whether additional (subdominant) ringdown modes introduce genuinely realizable information, or whether they remain confined to near-kernel directions dominated by noise and parameter degeneracy. Using coherent H1+L1 ringdown fits, Bayesian Information Criterion (ΔBIC), effective Fisher information rank, and explicit Monte-Carlo noise injection (N = 200 realizations), the analysis demonstrates that apparent two-mode preference frequently arises under noise alone and is often unaccompanied by an increase in realizable information dimensionality. When properly calibrated, the data favor a low-dimensional, single-mode ringdown structure consistent with observational closure. This report serves as a supporting methodological record for the empirical conclusions presented in: Black Holes as Realization Boundaries Absence of Realizable Subdominant Ringdown Modes in Gravitational-Wave Black Hole Mergers Black Holes as Structural Residues of Completed Realization The document is intended as a technical reference and reproducibility aid for readers interested in the robustness, limitations, and calibration of ringdown model selection in near-kernel regimes, rather than as a standalone conceptual or interpretive work.