Paper 175D Conserved Inventory Waves and Phase-Sensitive Probe Propagation

A conserved density disturbance and a probing signal can be calculated within one interactinglattice without assigning a refractive-index curve after the fact. The original part of this paperderives scalar probe propagation from Paper 175’s positive inventory–storage Hamiltonian, includingphase-sensitive sidebands and reciprocal energy transfer. A new, explicitly proposed gauge-covariantcompletion then retains that entire model as an exact neutral invariant sector while adding edgefields and oppositely signed source channels. On the occupied FCC triangular complex its exactfield spectrum has two low-frequency transverse polarizations. The coherent medium produces acalculated plasma-like cutoff; a live density wave modulates the transverse electric-like probe, andindependent full nonlinear trajectories recover the linear response. A prepared source counterflowalso launches transverse field from zero, with a balanced energy transfer. Charge balance, gaugecovariance, total energy, and the second-order recipient are checked. Finally, a number-conservingobservation map connects density, selection and inferred positions, and a conditional two-wavelengthcombination separates common clustering from the leading dispersive contamination. These resultsmake the electromagnetic-type and observational interfaces concrete. Physical field normalization,baryonic-tracer identification, a source population and an independent astronomical scale are notsupplied by the mathematical construction.