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

This work provides a structural peer-style analysis of a set of recent contributions in gravitational-wave data analysis, including photon-counting inference, control optimization methods, GWTC-4.0 general relativity tests, and black-hole spectroscopy studies. The objective is to examine the mathematical and methodological structure of these approaches. It is shown that all analyzed works rely on the same operational scheme: externally defined waveform models, empirically constructed noise representations, and likelihood-based statistical inference applied to data dominated by noise. The signal is not derived from a closed mathematical principle, but introduced through numerical simulations or fitted parametrizations. The probabilistic framework is explicitly assigned, 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. The main result is that the analyzed frameworks do not constitute a physical theory, but a statistically consistent data-processing pipeline. The distinction between physical theory and statistical inference is established through a formal generative criterion.