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 Hₜotal = R + n G₁4, where R is the formation residue and G₁4 is the one-period coherent wake packet. Decontaminated sector audits satisfy mW (n G₁4) = n in tested local windows, while inclusive total-history audits remain primitive with mW = 1. The masking mechanism is QW (R + n G₁4) congruent to QW (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.