Quantitative Detection of the Symmetry-Derived Bifurcation Threshold in the Photon Matrix Model

This paper presents a quantitative experimental proposal for detecting the symmetry-derived bifurcation threshold predicted by the Photon Matrix Model (PMM). The PMM unifies mathematics and physics within a deterministic collapse geometry, predicting an exact, scale-invariant constant as the onset threshold for structured mode formation in coupled density–tension fields. This constant, derived from first principles and formalized in ZFC, has been indirectly observed in multiple prior experiments as unexplained anomalies. We review these existing results, reinterpret them through the PMM framework, and outline a high-precision coherent X-ray absorption study on vanadium oxide near its quantum critical point to directly detect the collapse threshold. The proposed experiment maps theoretical variables to measurable observables, specifies signal-to-noise targets, and provides falsifiable predictions to decisively confirm or refute the PMM bifurcation mechanism. This work is directly connected to the foundational PMM theoretical framework, extending its empirical validation.