gap45
plain-language theorem explainer
The declaration supplies the integer 45 as the reference inter-style gap in years for Western visual styles ordered by J-cost coherence. Art historians or Recognition Science researchers testing cultural periodization against the phi-ladder would cite this anchor when checking observed transitions. The definition is a direct numeric assignment with no reduction steps or lemmas.
Claim. Define the reference gap constant $g_{45} := 45$ (in years) for successive visual-style emergences under the J-cost model.
background
The module derives visual-style succession from the J-cost functional $J(x) = (x + x^{-1})/2 - 1$, which quantifies geometric coherence of period styles. Styles alternate between low-J high-coherence phases and high-J high-variance phases along the phi-ladder; the consciousness gap of 45 years emerges as the expected interval between major transitions. The local setting is Track I9 of Plan v5, which tabulates eleven Western styles from Renaissance to Post-Modernist and predicts inter-style gaps compatible with phi-rational variation.
proof idea
The declaration is a direct definition that assigns the natural number 45. No lemmas, tactics, or upstream results are applied.
why it matters
This definition anchors the gap-45 reference in §3 of the module, enabling the band check in averageGap_in_gap45_band that places the observed average gap inside [15,90] years. It supplies the concrete numerical link between the J-cost equation and historical periodization, consistent with the eight-tick octave and T7-T8 forcing chain. The value remains an input rather than a derived output from the Recognition Composition Law.
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