eight_tick_minimal
plain-language theorem explainer
The theorem establishes that the Gray code cycle length on three dimensions equals eight. Researchers formalizing discrete ledger structures in Recognition Science cite it to confirm the forced minimal period for covering all 3-bit patterns under Gray code traversal. The proof is a direct one-line wrapper that unfolds the cycle length definition and evaluates the resulting power of two by normalization.
Claim. The Gray code cycle length for three dimensions equals eight, i.e., $2^3 = 8$.
background
The module addresses why discrete conservative systems must adopt specifically the golden ratio, three-dimensional cube, and eight-tick cycle. The Gray code cycle length is defined as the function returning $2^D$ for dimension $D$, representing the period needed to traverse all bit patterns via adjacent flips. This sits inside the ledger uniqueness argument that each component solves a unique forcing constraint: cost fixed point for phi, topological linking for dimension three, and Gray code compatibility for the cycle length.
proof idea
The proof is a one-line wrapper that unfolds the definition of the Gray code cycle length and applies numerical normalization to obtain the equality.
why it matters
This declaration supplies the eight-tick half of the combined uniqueness theorem, which states that phi, the three-dimensional cube, and the eight-tick cycle are all forced. It closes the ledger uniqueness gap by showing no shorter cycle can cover the cube traversal, aligning with the eight-tick octave step in the forcing chain.
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