This note studies base-gcd splitting in deterministic three-walker shared-wake sectors. The walkers write integer wake fields and move according to local cost-normalized readouts of those fields. Earlier three-walker work showed that a recurrent route can have an arithmetic packet structure that is partially hidden by formation history. Here we test whether the observed base-gcd split depends on the asymmetric body-frame deposition stencil or on a particular tie-resolution convention. The main result is that base-gcd 2 survives both a symmetric-ring body control and alternative tie policies, but it is not attached to a fixed named pair of walkers. Across the tested sectors, every surviving pair with base-gcd 2 has a one-period pair packet that is entrywise even before passive audit convolution. Splitting that pair packet by walker shows the sharper mechanism: neither individual walker packet is entrywise even, but the two individual deposit maps coincide modulo 2. The doubled packet is therefore localized to a two-walker parity-registration condition. The result separates several possible explanations. The doubled base is not produced by the passive audit kernel, not tied to the original asymmetric body stencil, not fixed to a particular named pair, and not explained by collinearity alone. A relative mod-2 diagnostic distinguishes the registering base-2 cases from collinear primitive controls in the tested data. The note also identifies a next question: whether parity registration can be predicted from pair-relative word structure.
J.R. James (Wed,) studied this question.