Orbit-Induced Redundancy in Finite Symbolic Systems
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| Formato: | Recurso digital |
| Lenguaje: | portugués |
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2026
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| _version_ | 1866901289797943296 |
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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 |