Orbit-Induced Redundancy in Finite Symbolic Systems

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Autor principal: FULBER, DOUGLAS H. M.
Formato: Recurso digital
Lenguaje:portugués
Publicado: Zenodo 2026
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author FULBER, DOUGLAS H. M.
author_facet FULBER, DOUGLAS H. M.
contents <p>We study how the action of a finite symmetry group <span class="math-inline">$G$</span> over a symbolic grid <span class="math-inline">$\Sigma^{n^2}$</span> induces structural redundancy, dimensional compression, reading-direction invariance, and passive recovery under noise. Motivated by the Sator Square, we formalize these mechanisms across finite group actions on square grids. We prove an exact identity for the information action <span class="math-inline">$A[M,G]$</span>, determined by the number of orbits of <span class="math-inline">$G$</span>, and introduce transition entropy as a non-trivial diagnostic separating weakly constrained systems from structurally rigid ones.</p> <p>Computational experiments over representative finite groups provide evidence that baseline-corrected recovery is better predicted by <span class="math-inline">$d_{min}^{orb}(G)$</span>, the size of the smallest non-trivial orbit, than by the group order <span class="math-inline">$|G|$</span>. The Sator Square is thereby reframed as a minimum-complexity historical example of an orbit-constrained symbolic system rather than an isolated mathematical anomaly.</p>
format Recurso digital
id zenodo_https___doi_org_10_5281_zenodo_19835957
institution Zenodo
language por
publishDate 2026
publisher Zenodo
record_format zenodo
spellingShingle Orbit-Induced Redundancy in Finite Symbolic Systems
FULBER, DOUGLAS H. M.
Orbit-Induced Redundancy
Finite Groups
Symbolic Systems
Information Theory
Error Correction
Sator Square
TAMESIS
<p>We study how the action of a finite symmetry group <span class="math-inline">$G$</span> over a symbolic grid <span class="math-inline">$\Sigma^{n^2}$</span> induces structural redundancy, dimensional compression, reading-direction invariance, and passive recovery under noise. Motivated by the Sator Square, we formalize these mechanisms across finite group actions on square grids. We prove an exact identity for the information action <span class="math-inline">$A[M,G]$</span>, determined by the number of orbits of <span class="math-inline">$G$</span>, and introduce transition entropy as a non-trivial diagnostic separating weakly constrained systems from structurally rigid ones.</p> <p>Computational experiments over representative finite groups provide evidence that baseline-corrected recovery is better predicted by <span class="math-inline">$d_{min}^{orb}(G)$</span>, the size of the smallest non-trivial orbit, than by the group order <span class="math-inline">$|G|$</span>. The Sator Square is thereby reframed as a minimum-complexity historical example of an orbit-constrained symbolic system rather than an isolated mathematical anomaly.</p>
title Orbit-Induced Redundancy in Finite Symbolic Systems
topic Orbit-Induced Redundancy
Finite Groups
Symbolic Systems
Information Theory
Error Correction
Sator Square
TAMESIS
url https://doi.org/10.5281/zenodo.19835957