Structural Non Fundamentality of LIGO Virgo KAGRA Residuals A Variational Refutation of the Noise Hypothesis in GWTC 4 0

The fourth gravitational-wave transient catalog (GWTC-4.0), released by the LIGO–Virgo–KAGRA Collaboration in March 2026 (arXiv:2603.19019), concludes that the residuals of all analyzed events are consistent with detector noise and show no statistically significant deviation from general relativity. This statement plays a central role in the interpretation of gravitational-wave data and in the exclusion of new physical effects. In this work, we demonstrate that such a conclusion is not structurally invariant. We construct a global quadratic functional acting on the residual signal and show that it admits a discrete spectral decomposition characterized by a stable invariant ratio L = 0.25. This structure is reproducible across independent datasets, including analyses performed prior to and after the GWTC-4.0 release, and is incompatible with stochastic noise, which would produce a continuous spectrum without fixed ratios. We then prove that the standard data processing pipeline, in particular the whitening transformation based on the noise power spectral density, explicitly alters the spectral structure of the signal. The transformation breaks permutation symmetry, removes eigenvalue degeneracy, and deforms the spectral ratio, such that L is not preserved. As a consequence, the classification of residuals as noise is performed on a transformed representation in which the intrinsic structure has been removed. We conclude that the statement “residuals are consistent with noise” is not a fundamental physical result, but a pipeline-dependent artifact. The presence of a stable spectral invariant across independent datasets implies that the residual signal contains intrinsic structure and cannot be consistently interpreted as stochastic noise.