Quantitative Detection of Orbital Bifurcation Discontinuities in the Photon Matrix Model

This paper presents an experimental proposal to test the Photon Matrix Model by searching for discrete orbital bifurcation discontinuities in vanadium dioxide during its insulator to metal transition. The proposal predicts stepwise changes in orbital occupancies that would appear as sudden shifts in x ray absorption and emission spectra, rather than the smooth evolution expected from conventional theories. The experiment is designed using high resolution XAS and RIXS at the vanadium L edges and oxygen K edge, with titanium dioxide and tungsten doped vanadium dioxide as controls. If confirmed, these results would provide direct evidence for collapse driven orbital discontinuities, offering a falsifiable test of the Photon Matrix Model and extending its experimental validation into the orbital sector.