landscapeFlatness
plain-language theorem explainer
The landscape flatness parameter is defined as the reciprocal of the synchronization period. Researchers analyzing degenerate attractors in the recognition lattice cite this when bounding J-cost differences at the 360-tick boundary. The definition is a direct noncomputable assignment with no lemmas or reduction steps required.
Claim. For synchronization period $s$, the landscape flatness equals $1/s$.
background
The Gap-45 module examines near-degenerate attractors arising from the sync period of the recognition lattice. The 8-tick cadence and 45-rung phi-ladder combine via lcm(8,45)=360 to produce a J-cost landscape where attractor energy differences fall below phi^{-45}, creating a degenerate basin. The landscape flatness parameter is introduced here as the scaling factor that quantifies this flatness.
proof idea
The declaration is a direct definition that assigns the real reciprocal of the input natural number. No tactics, lemmas, or reductions are invoked.
why it matters
This definition supplies the flatness measure invoked by downstream results such as flatness_at_360 (which evaluates the parameter at 360) and gap45_creates_flat_landscape (which bounds it by 1/100). It operationalizes the flat-landscape claim within the Gap-45 section, linking the eight-tick octave (T7) and phi-ladder to the degenerate basin that enables free will. The construction remains open to refinement once explicit J-cost formulas from the simplicial ledger are substituted.
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