Recurrent Lifetimes in Self-Interacting Walkers: A Paired-Body Basin Study

This paper studies recurrent behavior in a deterministic self-interacting lattice-walker system with an accumulating integer wake. A preregistered 1,296-run third-walker injection sweep conditions on body-specific recurrent two-walker substrates formed autonomously. The sweep uses an exact integer realization policy, fixed integer turning costs, and a boundary-safe 3072 by 3072 register. The primary observable is the lifetime class of each exact recurrent episode. The companion affine-lifetime result makes each phase-resolved decision guard affine in completed packet count and distinguishes sectors whose fixed-policy continuation is indefinitely certified from finite episodes carrying a future policy-changing arithmetic root. Absolute three-walker recurrence occurs in 351 of 360 asymmetric-body runs and 803 of 936 symmetric-ring runs. Among the asymmetric runs, 300 contain at least one indefinitely certified episode. None of the ring runs do; all 2,118 registered ring episodes are finite-affine. Every finite-affine break predicted within the 1,500-comparison post-injection record occurs at the exact first mismatch index, 1,585 of 1,585 cases, with a further 22 of 22 exact matches in preregistered extension checks beyond that record. The same sweep shows that minimum reorientation payment is strongly selected but not universal: dynamically realized payment-six recurrent walkers occur under both body modes. A preregistered walker-local monotone “closure pre-shadow” statistic is not supported by its nonlocking controls. These are finite deterministic results on the stated parameter grid. The body-dependent separation in recurrent lifetime structure is therefore an empirical property of this experiment, not a universal theorem about deposition symmetry.