Autonomous Branching from Hidden Wake Payloads in an Oriented Self-Interacting Walker

We study autonomous release from forced-history preparations in an oriented self-interacting lattice walker with anisotropic wake deposition. Each forced transport word prepares an endpoint pose and an accumulated integer wake field. Endpoint projection, however, forgets part of the wake-writing history. We ask whether that hidden history can become branch-active when the walker is released under a cost-normalized deterministic decision rule. For each forced word, we compute the decision-frontier wake spectrum, its OGT/ICL arithmetic signature, and the corresponding cost-normalized score spectrum. Exhaustive scans over forced words of lengths 3 through 6 reveal strict activation classes: endpoint-equivalent preparations with identical global wake mass and global gcd, but different local readout spectra and different first autonomous moves with positive score margins. Strict arithmetic activation grows sharply by length 6, showing that the effect is not an isolated specimen. A length-6 endpoint-pose filtration visualizes the full forced-word landscape, its heading fibers, branch-active classes, and strict arithmetic activation subset. Matched-motion controls further show that release splitting persists even when word length, endpoint displacement, path excess, left/right turn counts, signed turn accumulator, absolute turn load, and word cost are fixed. Thus the active payload is not reducible to endpoint kinematics, global wake invariants, or simple path summaries. It is encoded in the ordered wake-deposition history and becomes actionable through the local decision frontier.