pith. sign in
theorem

gap45_from_lcm

proved
show as:
module
IndisputableMonolith.Foundation.Gap45Degeneracy
domain
Foundation
line
31 · github
papers citing
none yet

plain-language theorem explainer

The least common multiple of the 8-tick octave period and the 45-rung phi-ladder equals 360. Recognition Science researchers cite this to fix the sync boundary where the J-cost landscape flattens. The proof reduces to a single native computation of the LCM.

Claim. $lcm(8,45)=360$

background

The Gap-45 phenomenon arises from the sync period of the recognition lattice. The 8-tick cadence comes from T7 where the period is 2^3 = 8, and 45 comes from the phi-ladder rung count. Their LCM is 360. At the 360-tick sync boundary, the J-cost landscape becomes nearly flat with energy differences smaller than phi^{-45}. This creates the degenerate basin that enables free will.

proof idea

The proof is a one-line wrapper that invokes native_decide to evaluate the LCM computation directly.

why it matters

This result establishes the 360-tick period that produces the near-degenerate attractors in the Gap-45 region. It feeds into theorems on flat landscapes and free will mechanisms. It directly implements the T7 eight-tick octave combined with the phi-ladder from the forcing chain.

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