Emergent Recurrence and Exact Lifetimes in Self-Interacting Walkers with Unbounded Integer Memory
Year: 2026
Type: preprint
Abstract: This preprint synthesizes and extends two previously archived studies by John R. James: Self-Generated Guarded Counter Loops and Exact Lifetimes of Recurrent Self-Interacting Walkers (doi:10.5281/zenodo.22310638) and Recurrent Lifetimes in Self-Interacting Walkers: A Paired-Body Basin Study (doi:10.5281/zenodo.22770917). The paper develops a unified theoretical and computational account of how deterministic self-interacting walkers with unbounded, integer-valued shared wake memory can autonomously enter registered recurrent conduct, and how the subsequent lifetime of an entered recurrent sector can be determined exactly. Once a recurrent word is identified, its repeated deposition defines an additive integer packet, allowing the policy-complete local dynamics to be reduced to a finite guarded counter system. This reduction provides certificates of indefinite continuation or the first output-changing recurrence failure. Beyond consolidating the formal lifetime result and the paired-body experimental population in common notation, the manuscript extends the analysis through a backward-admissibility audit of 2,580 registered episodes. This distinguishes the nonnegativity and policy boundaries of the recurrent sector and examines where observed recurrence onset lies relative to those boundaries. The synthesis also incorporates additional policy-incidence diagnostics, provenance controls, and explicitly bounded interpretations of recurrence formation and lifetime certification. The underlying source studies and their computational archives remain separately preserved. The formal lifetime reproducibility record is doi:10.5281/zenodo.22310652, and the sealed paired-body primary reproducibility record is doi:10.5281/zenodo.22770833. A separate versioned supplementary record (doi:10.5281/zenodo.23701009) contains the backward-admissibility calculations, policy-incidence audits, supplementary controls, and associated validation artifacts. This manuscript does not supersede those records. It provides an integrated presentation of their results, clarifies their common mathematical structure, and contributes the additional backward-admissibility analysis. Its lifetime conclusions apply to entered registered recurrent sectors under the specified deterministic realization policy; they do not establish generic recurrence formation.
Author: James, John Robert
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7225463140