Private arithmetic of the physical constructor
Abstract
Floor and ceiling bounds for the complete physical construction
Euclidean division supplies exact lower and upper bounds for every floor mask. The b=2 ratio-two family uses the nonzero remainder of a power of two modulo five. The c=2 ceiling mask is strictly below r/64, which separates its physical bit support from the tail mask 25r/64. The proofs establish capacities and all old/new seam inequalities on unbounded parameter ranges. The a=2 ordered family retains its s=8 boundary separately. These private certificates are consumed by the exhaustive constructor certificate in the minimum-two joint-lift theorem.