Persistent Chirality and Local Write-Once Memory in a Three-Dimensional Outer-Totalistic Cellular Automaton
Year: 2026
Type: preprint
Abstract: We study the three-dimensional binary outer-totalistic cellular automaton with a 26-site Mooreneighborhood, birth counts 5–7, and survival counts 5–9, on the infinite lattice Z3 with finite-support initialdata. We give exact constructions of separated fixed modules and infinitely many geometrically chiralfixed configurations. An integer-valued moment pseudoscalar certifies their handedness; a second, chiralfixed configuration has every radial-weighted vector moment equal to zero but is distinguished from itsmirror by a third-order directional moment. For the dynamics, we exhibit a five-cell receiver for which onetransient exterior cell changes the eventual state from extinction to a permanent eight-cell block within twosynchronous updates. An exhaustive, locality-reduced classification establishes exactly 480 successfulreceiver/signal pairs among all five-cell subsets of the block and all exterior singleton positions, groupedinto 12 cubic-symmetry orbits. Separated receivers store arbitrary finite bit strings, and a mirror-related pairof receivers writes one of three indefinitely stable chirality readings. We also prove finite-speed influencepropagation and monotonic inclusion of the lattice point-symmetry stabilizer. The claims establish explicitlocal information writing and persistent handed geometry for the specified automaton; they do not establisha traveling signal, reversible gates, computational universality, or a universal physical coherence principle.Proofs, exact integer computations, and executable checks accompany the manuscript.
Author: Poole, Rooke
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7225809600
Cites:
Cited by:
Related to: