eight_divides_sync
plain-language theorem explainer
The declaration establishes that 8 divides 360 in the integers. Recognition Science lattice calculations cite this divisibility to fix the combined sync period arising from the eight-tick cadence and the forty-five-rung ladder. The proof is a direct term-mode witness that supplies the quotient 45 and confirms the relation by normalization.
Claim. In the integers, $8$ divides $360$.
background
The Gap-45 phenomenon arises from the sync period of the recognition lattice. The 8-tick cadence (T7: 2³ = 8) and the 45-rung φ-ladder create a combined period of lcm(8, 45) = 360. At the 360-tick sync boundary, the J-cost landscape becomes nearly flat: multiple attractor configurations have energy differences smaller than φ⁻⁴⁵. This creates the degenerate basin that enables free will.
proof idea
The proof is a term-mode construction that supplies the witness 45 for the divisor and invokes norm_num to verify the equality.
why it matters
This divisibility anchors the 360-tick period in the Gap-45 construction. It supports the claim that the J-cost landscape flattens at this boundary, enabling the degenerate attractors linked to free will mechanisms. It directly instantiates the eight-tick octave from the forcing chain (T7).
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