eight_tick_is_2_cubed
plain-language theorem explainer
The theorem establishes that the eight-tick synchronization period equals two cubed. Researchers tracing the Recognition Science forcing chain cite it to connect the cycle length directly to three spatial dimensions. The proof is a one-line reflexivity step that holds once the period is defined as eight.
Claim. The eight-tick synchronization period satisfies $8 = 2^3$.
background
The Dimension Forcing module derives that spatial dimension equals three through four arguments, one of which is gap-45 synchronization. The eight-tick period is the cycle length 2^D required for ledger coverage; at D=3 this length is eight. Upstream definitions in PhiForcing, Gap45.PhysicalMotivation, RRF.Constants, and RecognitionThermodynamics each set the period to eight, with the Gap45 version noting that closure of an eight-tick cycle requires nine steps by the fence-post principle.
proof idea
The proof is a term-mode reflexivity step. It applies rfl directly to the definition of the eight-tick period as the numeral eight, which is identical to two cubed.
why it matters
The equality closes the link between the eight-tick octave (T7) and D=3 (T8) in the unified forcing chain. It supports the gap-45 argument that produces lcm(8,45)=360 and thereby identifies three dimensions via SO(3) periodicity. The result underpins the topological linking argument that only D=3 permits stable conservation in the ledger.
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