averageGap_above_gap45
plain-language theorem explainer
The theorem shows that the average inter-style gap of 56 years in the Western canon exceeds the gap-45 threshold. Researchers applying the J-cost model to art-history periodization would cite this when confirming the predicted cycle length with phi-rational variation. The proof is a one-line wrapper that substitutes the pre-established equality for the average gap and normalizes the numerical comparison after unfolding the threshold definition.
Claim. The gap-45 threshold is at most the average inter-style gap: $45 ≤ 56$.
background
The module derives visual-style succession from the J-cost functional equation under Track I9. It enumerates eleven Western styles in the canon spanning 1400 to 1960. The average inter-style gap is defined as (1960 - 1400) divided by (canon length minus one), which equals 56 years. The gap-45 denotes the base 45-year period per major transition, compatible with the band [15, 90] years under phi-rational style-pair variation from the J-cost equation.
proof idea
The proof is a one-line wrapper. It rewrites the average inter-style gap via its equality to 56, unfolds the gap-45 definition, and applies norm_num to discharge the numerical inequality.
why it matters
This theorem supplies the final conjunct for the art-history one-statement, which packages canon length, average gap of 56 years, and membership in the gap-45 band. It also populates the style-succession certificate. In the Recognition framework it verifies the ~45-year cycle extracted from the J-cost trajectory and the phi-ladder, closing the numerical check for the consciousness-gap prediction.
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