Paper 175A Spatial Correlations, Spectral Oscillations, and Physical Scale

We distinguish three response constructions that should not be conflated: an inherited angularshell, a conditional phase-impulse inventory kernel, and the actual continuously reacting rotor sourceof Paper 175. For the latter, the finite-host population covariance is an exact double-mode sumincluding sum and difference frequencies and interference. Uniform finite-duration ages can preserveoscillatory structure. An initially displaced, resting source produces a quadratic rather than linearshort-time inventory signal; its outgoing continuum density is a compensated Laplacian of a retardedsource history. A stopping source does not remove already emitted waves. Independent weak-couplingintegration on the homogeneous FCC acoustic branch gives a low-frequency reaction spectral densityproportional to the cube of frequency. These calculations constrain possible source populations butdo not derive autonomous birth rates, a physical lifetime, baryon identity or an absolute BAO ruler.The source’s internal wavelength, its expanding front and its correlation peak are different lengths.An exact phase-preparation FCC density kernel and its conditional signed higher-order statisticssupplement the population calculation, without identifying baryons or deriving an astronomicaltracer response.