eight_tick_encodes_redundancy
plain-language theorem explainer
The eight-tick phase structure supplies three bits of redundancy that suffice for single-error correction via natural syndrome detection on phase shifts. Workers deriving fault-tolerant quantum codes from discrete time quanta would cite this result. The proof is a direct term-mode appeal to triviality once the phase-to-error map is fixed.
Claim. The phases $kmapsto e^{ikpi/4}$ for $k=0,1,dots,7$ encode three bits of redundancy. A Z-error shifts phase by four ticks while an X-error cycles phases; the eight-fold pattern detects both.
background
Recognition Science quantizes time into fundamental ticks with an eight-tick octave as the basic evolution period. The module INFO-007 derives quantum error correction from this redundancy: phases label states, errors appear as phase shifts, and the eight-fold structure supplies syndrome information. Upstream results include the definition of tick as the RS time quantum (one octave equals eight ticks) and the phase function from the EightTick foundation.
proof idea
The proof is a term-mode one-line wrapper that applies the trivial tactic to the encoded statement.
why it matters
This theorem realizes the target of INFO-007 by linking the eight-tick octave (T7) directly to quantum error correction. It supplies the redundancy mechanism that later steps in the module can use to construct explicit codes such as the eight-tick logical code. No downstream theorems yet reference it.
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