Paper 175F Persistence, Isotropy, and Predictive Tests of the Holosphere Correlation Scale

We test the predictive content of a real Hamiltonian on the occupied face-centered-cubic contactlattice. Relaxed source reactions generate a finite instability band without an imposed spatialcorrelation kernel. The same interaction determines a cubic density forecast and a complete fourth-order power expansion, including linear–cubic interference. At n0 = .9, initial amplitude 10−4, nativetime 500 and step .025, the cubic forecast reduces the matched-step density residual approximately1530-fold at period 32 and 1385-fold at period 64. Tests on twelve reserved preparations retain strongconditional improvement, while a fixed forty-reference versus twelve-native population comparisondoes not distinguish the linear, strict fourth-order and squared-cubic candidates. Their permutationp-values are .9690, .9705 and .9704.For eight fixed primary preparations, halving the step from .1 to .05 changes the maximum of thenormalized mean raw covariance from 25.647229a to 25.655428a. Individual peak displacements andunaligned field changes are reported separately. A further three-window comparison at steps .025and .0125 retains the radial dip and outer maximum, but the late centered angular patterns haveoverlap .475186 despite nearly equal angular norms. Radial persistence therefore does not establishtrajectory or directional-pattern convergence.Exact angular decompositions, bounded-mark ensemble identities and field-to-observable errorbounds connect these measurements. The continuous linear volume limit at fixed spacing cannot beisotropic throughout a positive radial interval. An explicit coefficient family instead links a collapsinginstability band to wavelength scaling σ−1a and growth-time scaling σ−3a ; its prepared initial forcehas a controlled limit at inventory amplitude ∆n = σ4aw. The results establish conditional forecastsand finite numerical correlation properties of the stated model, not an independently calibratedastronomical baryon-acoustic-oscillation scale.