The same physical order in both rows
Abstract
Native physical order at a=s
When a=s, all four old chain heads equal A=q^3+q^2+q+1. Use the entire native physical word range(4s), with all 4s labels retained. Insert k immediately before the first U terminal, at cut s-1. Each old native packet has sum zero. The new packet increments on the old labels are -1,-q,-q^2,-q^3, and the ear adds A. The four new seams are A-1,A-1-q,q^3,0. The first new positive peak, including the ear, equals the new cap N. The remaining doubled peak slacks are q,q^2+q,A-1. This argument uses physical occurrences even when their numerical values repeat.