pith. sign in
theorem

flatness_at_360

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

plain-language theorem explainer

The flatness parameter of the J-cost landscape at the 360-tick synchronization period equals 1/360. Researchers analyzing Gap-45 degenerate attractors from the lcm of the eight-tick cadence and 45-rung phi-ladder would cite this when quantifying the width of the flat basin. The proof is a one-line simplification that unfolds the definition of landscape flatness as the reciprocal of the synchronization period.

Claim. The flatness parameter of the J-cost landscape at the 360-tick synchronization boundary equals $1/360$.

background

Gap-45 arises from the synchronization period of the recognition lattice, formed as lcm(8,45)=360. The 8-tick cadence comes from the eight-tick octave (T7) while the 45-rung phi-ladder supplies the second factor, producing a combined period at which multiple attractor configurations have J-cost differences smaller than phi^{-45}.

proof idea

The proof is a one-line wrapper that applies the definition of landscape flatness by simplification.

why it matters

This supplies the concrete flatness value at the 360-tick boundary identified in the Gap-45 module. It instantiates the general definition at the period arising from T7 and the phi-ladder, supporting the claim that the resulting flat region creates the degenerate basin enabling free will mechanisms.

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