Correlation estimates are not unique fingerprints of physical systems: an example of non-uniqueness in model identification

Correlation estimates are not necessarily unique fingerprints of physical systems. This paper presents an explicit coherent-detection model showing that the normalised correlation function -cos(a-b) can arise from a deterministic local classical system, while the corresponding raw correlations remain fully Bell compliant. The increase from |S| = √2 to |S| = 2√2 is shown to originate entirely from Pearson variance normalisation applied to the measured observables, with no change in the underlying physical mechanism. The work does not claim a violation of Bell's theorem. Instead, it addresses a model-identification problem: different physical mechanisms may generate identical reported correlation functions. The observation of a cosine correlation or a CHSH value of 2√2 is therefore not, by itself, sufficient for unique identification of the underlying mechanism when only the reported correlation statistics are available.