averageGap_eq
plain-language theorem explainer
The theorem establishes that the average inter-style gap across the eleven Western art styles from 1400 to 1960 equals exactly 56 years. Recognition theorists applying J-cost dynamics to cultural periods would cite it to anchor the gap-45 band prediction. The proof is a direct term reduction that unfolds the averageGap definition and rewrites with the canon length theorem.
Claim. The average inter-style gap equals $56$ years, computed as $(1960-1400)/(11-1)$ where the eleven styles span the Western canon.
background
In the Visual-Style Succession module the J-cost trajectory is applied to geometric coherence of artistic periods. The westernCanon is the ordered list of eleven named styles (Renaissance through Post-Modernist) with emergence years from 1400 to 1960. averageGap is defined as the total span divided by the number of intervals, i.e., (1960-1400)/(westernCanon.length-1). The upstream westernCanon_length theorem fixes the length at 11, while gap45 supplies the reference value 45 drawn from the forcing chain T7 octave and consciousness-gap scaling.
proof idea
The proof is a one-line term wrapper. It unfolds the averageGap definition then rewrites with the westernCanon_length theorem to obtain the numerical equality 56.
why it matters
This equality is packaged directly into the art_history_one_statement theorem and the styleSuccessionCert structure, which also invoke averageGap_above_gap45 and averageGap_in_gap45_band. It supplies the concrete numerical anchor for the gap-45 prediction in the art-history track of the Recognition framework, consistent with the phi-ladder mass formula and the eight-tick octave. The result touches the open question of whether additional cultural parameters are required beyond J-cost to fix exact transition dates.
Switch to Lean above to see the machine-checked source, dependencies, and usage graph.