Paper 175G Nonlinear Three-Point Predictions and Dynamical Response on the Holosphere Contact Lattice

We derive and test three-point density forecasts and phase-kick responses for the retained realHamiltonian on the fully occupied face-centered cubic Holosphere contact lattice. Sign pairing isolatesa fourth-order amplitude coefficient. An explicit initial-force kernel gives an evaluated ensemblecoefficient that depends on the preparation’s fourth cumulant despite equal initial covariance; itsnormalized reciprocal sum has a large-volume limit for the initial time-Taylor coefficient. A chain-ruledecomposition separates preparation, density readout and dynamical curvature. An inventory-preserving phase kick has an exact weighted-Laplacian initial slope, while its later response followsall native degrees of freedom.A 66-case extension compares three preparation laws at coordinate periods 32, 64 and 96, withfixed physical probe wavelengths and compact-kick radius. For its 27 weak-triad cases, three-blockaggregate errors of the supplemental two-component forecast span .0109–.0720% at amplitude .01and time 50, comparing forecasts and native sign pairs at the same integration step. Across 36evolved backgrounds and 72 global probes, 26.8–47.5% of squared density response lies outside theinput mode. Substantial mixing is already present in the initial current operator. Matching lowdensity projections, inventory and exact energy leaves small coupled native projections unmatched.At period 64, refining the step from .1 to .025 changes the raw-law forecasts by .85–1.75%, a separatesensitivity from the paired amplitude remainder. Full-history controls quantify trajectory sensitivity;an independent continuous uniform reference exposes substantial late periodic effects. One standalonereal polynomial core implements native, tangent and quadratic evolution. These are reproduciblefinite-lattice predictions; they do not establish a universal evolved medium, propagation speed,finite-time continuum limit or astronomical correlation ruler.