Prime-Pattern Rank Rays in the 6-Wheel II / Finite State Bodies, LPF-Carrier Horizons, and Residual All-Prime Purity

Abstract

Prime-Pattern Rank Rays in the 6-Wheel II develops an exact finite State-body framework for fixed admissible even prime patterns, without assuming that the pattern occurs infinitely often. It embeds the PPRR-I All-Prime event leaf in the complete {P,C}ν{P,C}ν State space and establishes finite results for induced pair tables, CRT divisibility geometry, least-prime-factor ownership, Composite-Depth covariance, and pairwise maximum-entropy references. A registered decision study then filters the State body by LPF carrier horizons and residual All-Prime purity. Calibration selects a logarithmic 99%-purity exponent coordinate, which passes all primary gates on six gap-disjoint Holdout patterns, yielding the finite result A1A1. Because the protected execution contained fully disclosed protocol deviations, the final adjudication is A1 ACCEPT WITH DEVIATION. No universal carrier law, convergence to exponent 1/21/2, State-to-Ray theorem, or PPRR-III opening is claimed.