This paper develops a formal theory from a single admissibility constraint: observational distinction may not be annihilated at zero residual and zero cost. This workorganizes that constraint into a chain of levels: observational representation, obstructiongeometry, continuum bridge, action, coupled dynamics, internal channels, matter lifting,spectral rigidity, low-energy reduction, phenomenology, and confrontation. Within thestated assumptions, the bridge layer realizes obstruction as cocycle failure, sigma as acompensator, and the low-energy branch as a screened effective theory. The main claimis conditional and structural rather than absolute: the framework yields a coherentroute to U(1)×SU(2)×SU(3), Spinc matter, discrete branch selection, a residual tower,and a pre-registered branch-consistency test connecting cosmological and mass-ratiodata through one sigma parameter. The quantitative part is treated as a diagnostic withexplicit degrees of freedom, covariance control, and out-of-sample checks, not as a freeglobal fit. The theory is falsifiable in two independent ways: by a demonstrated zero-costerasure of distinction, or by failure of the correlated sigma-branch windows (Hubbletension + family hierarchies + gauge running) in the pre-registered branch-consistencytest.
Pavel Dzeraviaha (Sun,) studied this question.