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

A conserved inventory wave changes weak-probe propagation through the same interaction thatdrives the wave. This paper derives that response from the positive inventory–storage Hamiltonian,including phase-sensitive sidebands and reciprocal energy transfer. A proposed gauge-covariantextension preserves the entire scalar model as an exact neutral invariant sector and adds twotransverse low-frequency field modes on the occupied face-centered-cubic triangular complex. Themoving inventory background modulates this field, and a prepared source counterflow launchesit from zero. The homogeneous field cutoff and the held-source electric energy depend on oneshared coefficient combination, giving an independent static–dynamic consistency relation. Twofield-frequency measurements identify the remaining spectral combination; a canonical rescaling stateswhich individual parameters still require field-unit calibration. A number-conserving observationmap then carries density, selection and inferred-position changes into tracer clustering. Two matchedfrequency bands separate a common component from an assumed inverse-square contribution, whilea reserved third band tests that frequency dependence. The real-number program verifies thecoupled dynamics, energy account and calibration relations. Physical field normalization, sourcedemographics, tracer identification and an absolute astronomical length remain inputs to an empiricalforecast.