gap45_from_lcm
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.
Switch to Lean above to see the machine-checked source, dependencies, and usage graph.