eight_tick_redundancy
plain-language theorem explainer
The eight-tick redundancy result confirms that the fundamental period of eight ticks establishes an 8-fold repetition code for information encoding in Recognition Science. Researchers deriving error correction capabilities from the eight-tick octave would cite this when bounding the number of correctable errors via majority voting. The proof proceeds by direct numerical normalization of the division identity.
Claim. In the eight-tick framework the redundancy factor satisfies $8/1=8$, providing the basis for encoding one bit across eight phases with majority-vote decoding that corrects up to three errors.
background
The module INFO-005 derives error correction bounds from the 8-tick structure. Upstream, the tick is defined as the fundamental RS time quantum τ₀ = 1, with one octave equal to eight ticks. The local setting invokes Shannon's channel capacity theorem and notes that 8-tick phases supply natural redundancy: each bit encoded across phases allows recovery from single-phase errors by majority vote among the eight phases. From the upstream result: 'The fundamental RS time quantum (RS-native). τ₀ = 1 tick.' and 'One octave = 8 ticks: the fundamental evolution period.'
proof idea
The proof is a one-line wrapper that applies the norm_num tactic to verify the arithmetic identity 8 divided by 1 equals 8.
why it matters
This declaration marks the 8-fold redundancy inherent in the eight-tick octave (T7 in the forcing chain), feeding into subsequent bounds such as the Hamming bound for 8-tick codes in the same module. It connects the Recognition Composition Law and phi-ladder structures to practical error correction, though no downstream theorems yet reference it directly. It touches the open question of how the 8-tick code integrates with quantum error correction schemes listed in the module.
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