The same physical order in both rows
Abstract
From intervals to actual prefix bounds
A consecutive local interval [lo,lo+len) in a positive chain has dyadic mass (2^len-1)2^lo times its head in either actual centered row. Its entries are nonnegative. A packet consists of a positive interval bag followed by its actual negative label. The doubled positive mass gives its peak; adding the doubled negative gives its next seam. The packet endpoint inequalities therefore imply bounds for every prefix by monotonicity on each positive bag. The interval identities and permutation use natural physical labels. Mapping them into Fin(k) is injective on this inventory; the marked-word identity converts a natural prefix length into one literal insertion of the fresh physical label k. Exact source totals give zero for both complete words.