Gaussian Pair Geometry and Physical Radiative Response

The preceding papers construct a three-parameter family of completed Gaussian current-zero states, identify the faithful quadratic pair geometry generating their all-orders Fock structure, and establish the Bose/Fock, analytic, and Poincaré structure of the generated degree-two sector. This fourth paper determines exactly which Gaussian parameters remain distinguishable after variational and radiative maps are applied.

The Gaussian covariance remains faithful to all three positive moduli. For the connection-quadratic Taylor sector, the realized density is independent of the ambient metric and its variational stress vanishes identically. A separate radiative branch probes the distinguished hypercharge diagonal, retaining exactly the hypercharge scale before normalization.

The physical-helicity adjoint bridge carries the nonzero source into a radiative one-particle state. Normalization removes the remaining positive amplitude, producing a nonzero unit Bose pair with exchange symmetry, diagonal Poincaré covariance, and exact degree-two Fock support. The equality kernels therefore form an exact information-compression hierarchy from faithful three-parameter covariance to one-parameter radiative response and finally to scale-independent normalized pair data.