CAS I: A Geometric Coding Theorem
This paper establishes a direct analogue of the classical Coding Theorem in the setting of symmetry groups. We consider computable bijections on the set of binary strings and define the symmetry prior of a string x as the probability that a randomly chosen symmetry from a given group G has x as its unique fixed point. We show that for any fix-retractable symmetry group G, a group admitting a computable section that selects an isolating symmetry for every string, the symmetry prior is a universal lower semi-computable semi-measure. In this case, the Geometric Coding Theorem holds. This result is a coding-theoretic restatement of a theorem of Trejo, Kreinovich and Longpré, who showed that t...
| Authors | Romie Banerjee |
|---|---|
| Primary category | cs.IT |
| Published | 15 July 2026 |
| Last updated at source | 5 October 2026 |
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