Finite Audit Structure and Masked GCD Coarsening in a Three-Walker Shared-Wake Motif

This paper studies a finite integer-valued shared-wake walker model on a lattice register. A period-14 three-walker recurrent route is reached after a nonperiodic formation history. The total accumulated wake decomposes as H_total = R + n G_14, where R is the formation residue and G_14 is the one-period coherent wake packet. Decontaminated sector audits satisfy m_W(n G_14) = n in tested local windows, while inclusive total-history audits remain primitive with m_W = 1. The masking mechanism is Q_W(R + n G_14) congruent to Q_W(R) modulo n. The paper formalizes this distinction using finite relational audit operators and proves a periodic-sector gcd scaling theorem. The accompanying reproducibility archive includes row logs, audit tables, validation scripts, visualization notebooks, interactive trace-tube views, and figure-generation code.