Structural Analysis and Non-Fundamental Nature of the LIGO--Caltech Statistical Framework for Gravitational-Wave Inference

This work presents a structural peer-style analysis of a set of recent contributions in gravitational-wave data analysis, including photon-counting inference, control optimization methods, the GWTC-4.0 series of general relativity tests, and black-hole spectroscopy studies. The aim is to examine the methodological and conceptual structure of these approaches. It is shown that all analyzed works rely on a common operational scheme: externally defined waveform models, empirically constructed noise representations, and likelihood-based statistical inference applied to data dominated by noise. The signal models are not derived from a closed mathematical or variational principle, but introduced through numerical simulations or phenomenological parametrizations. The probabilistic structure is explicitly assigned through the choice of likelihood, and the inference process operates within a predefined model space. It is further demonstrated that, in the low signal-to-noise regime, the statistical inference becomes weakly informative, and the resulting outputs are largely determined by model assumptions rather than by the data itself. A formal distinction is established between physical theories, which generate both admissible configurations and their statistical structure, and statistical pipelines, which perform model-dependent reconstruction. The analyzed works are shown to belong to the latter category. The main conclusion is that these frameworks do not constitute a generative physical theory, but rather a statistically consistent method for fitting externally defined models to observational data.