toricCode
plain-language theorem explainer
The toricCode definition supplies a string description of Kitaev's toric code adapted to the Recognition Science 8-tick setting. Researchers modeling topological quantum error correction with discrete phase redundancy would cite it when mapping homology classes to syndrome patterns. The implementation consists of a direct string literal plus embedded comments that outline error detection and recovery for a specific 8-tick phase pattern.
Claim. The toric code places qubits on the edges of a torus, encodes logical information in homology classes, and performs error correction through local syndrome measurements on 8-tick phase patterns.
background
The module INFO-005 derives error correction bounds from the 8-tick structure. In Recognition Science the 8-tick phases supply natural redundancy so that each bit can be encoded across phases and recovered from phase correlations. The upstream definition of tick supplies the fundamental time quantum with τ₀ = 1. The phase function returns kπ/4 for k in Fin 8 and is periodic with period 2π.
proof idea
The declaration is a definition that directly assigns the string literal 'Qubits on torus edges, information in homology'. It is accompanied by a comment block that walks through one concrete syndrome example: phase pattern (0,0,1,0,0,0,0,0) yields an error at phase 2 whose recovery flips that phase back to zero.
why it matters
This definition introduces the toric code example inside the error-correction-bounds module and thereby supports the broader claim that 8-tick phase correlations enable topological error correction. It directly instantiates the eight-tick octave (T7) from the forcing chain. No downstream theorems are recorded, leaving open how the ~1% threshold will be turned into a formal bound.
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