Private arithmetic of the strict physical chamber
Abstract
The complete far mask certificate
Write t=2sq and r=4th with s>=8,q>=1,h>=1 and s even. The U mask is (s-1)q and the W tail is floor((K_beta-u)/(2L-s-1)); their physical supports lie in distinct chains. The exact Euclidean remainder R satisfies 0<=R<lambda. With delta=H_beta-Lz, the proof establishes 0<2delta<u-1. After substitution by nonnegative gaps, the polynomial Delta is positive in the regions t>=4s and r>=8t. At r=4t,t=2s the exact floor is r/2-4 and 2delta=6s^2-s+6. Explicit old/new seam inequalities certify the alpha,gamma,beta order with the literal ear before T. The owning strict-chamber theorem consumes this certificate through the existing physical realizer; it introduces no new scheduler.