Pose-Ensemble Integer Convolution Locking in Self-Interacting Walker Wakes

This paper develops a pose-ensemble and readout-restricted arithmetic analysis of self-interacting lattice walker wakes. A walker pose deposits an oriented integer body stencil into an accumulated wake field. Although each deposit is local, the resulting integer overlap field can carry arithmetic structure not determined by endpoint kinematics alone. Using Occupied Grain Theorem / Integer Convolution Locking diagnostics, the paper analyzes both full wake fields and local walker-readable decision frontiers. The diagnostics include total mass, gcd grain, effective probability grain, residue coherence, symmetry defects, and support statistics. Static pose atlases show that equal deposited mass need not imply equal arithmetic structure: a fully heading-symmetrized pose orbit produces a parity-pure wake while a mass-matched loop does not. A D₄ covariance check verifies that the deposition rule commutes with the dihedral action on oriented poses, separating rule covariance from self-symmetry of individual wake fields. Forced-word scans over lengths 3–5 show that globally gcd-trivial wakes can exhibit gcd collapse or exact affine residue locking on local decision frontiers. Endpoint-equivalent words with identical global mass and gcd can differ in frontier gcd, and decorated transition matrices reveal hidden-channel splitting even when source pose, appended action, and target pose are fixed. Readout-geometry experiments show that local sampling acts as an arithmetic filter: the same wake can appear gcd-trivial, gcd-locked, or residue-locked depending on how it is sampled. The results establish a pre-dynamical algebra of word history, wake incidence, endpoint quotienting, and readout-restricted rational grain. Autonomous release experiments are left for future work. Keywords self-interacting walker; integer convolution locking; Occupied Grain Theorem; lattice walker; wake field; readout geometry; decision frontier; gcd grain; residue coherence; dihedral symmetry; pose ensemble; discrete spacetime; Relational Blockworld; Dual Incidence Graph