Pairwise Reduction and Base-GCD Splitting in a Three-Walker Shared-Wake Sector

We study pairwise reductions of a previously identified three-walker shared-wake motif with distinct formation and locked sectors. At each of the 14 phases of the observed period-14 locked sector, one walker is removed from active evolution, and the surviving pair is continued for 140 comparison moves. Separate interventions distinguish removal of the active walker from removal of its accumulated wake. Five of the six reductions preserve the corresponding pair projection of the original three-walker route over the full tested horizon. The exception is the BC continuation after deletion of A's wake, which diverges after 0 to 8 index steps depending on removal phase. For the route-surviving phase continuations, actual deposited rows are grouped into 14-move packet increments and tested in 280 phase-kernel-center audit series, comprising 2, 800 cumulative packet audits. Every series satisfies mW (nG) = n mW (G) and preserves the gcd-reduced registered readout, but the one-period base gcd is reduction-dependent. The AB continuation and the wake-supported BC continuation have primitive base mW (G) = 1, whereas the AC continuation has base gcd 2 in every tested audit. This split aligns with the pair-relative geometry: C - A is the unique collinear, zero-area orbit, while B - A and C - B span two-dimensional loops. The result is not a binary reducibility verdict but a layered dependency structure separating route persistence, stored-wake support, packet scaling, primitive base, and relative geometry.