sync_factorization
plain-language theorem explainer
The equality 360 equals 8 times 45 is recorded as a foundational arithmetic identity within the Gap-45 degeneracy module. Physicists modeling the recognition lattice would cite it to anchor the combined sync period arising from the eight-tick cadence and the 45-rung phi-ladder. Its proof proceeds via direct numerical normalization with no additional lemmas required.
Claim. $360 = 8 × 45$
background
The Gap-45 module examines near-degenerate attractors generated by the least common multiple of the 8-tick cadence and the 45-rung phi-ladder, yielding a 360-tick sync boundary. At this boundary the J-cost landscape flattens, with energy differences below phi to the minus 45, enabling the degenerate basin associated with free will. The upstream result in DimensionForcing establishes the sync period as 360 via unfolding the definitions of sync_period, eight_tick, and gap_45, confirming that lcm(8,45) equals 360 since their gcd is 1.
proof idea
The proof is a one-line term that applies numerical normalization to verify the arithmetic equality directly.
why it matters
This identity supplies the numerical anchor for the sync period used in the DimensionForcing module's corresponding theorem. It connects directly to the T7 eight-tick octave in the forcing chain and supports the flatness results such as landscapeFlatness and gap45_creates_flat_landscape that enable the free-will mechanism. No open questions are resolved here, but it closes the arithmetic prerequisite for the degeneracy analysis.
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