StyleSuccessionCert
plain-language theorem explainer
The StyleSuccessionCert structure records that the Western canon comprises eleven styles spanning 1400 to 1960 with an average inter-style gap of 56 years. Researchers linking art history to Recognition Science would cite it to confirm that observed transitions lie inside the predicted gap-45 band derived from the J-cost equation. The certificate is assembled directly from the averageGap definition together with the gap45_eq lemmas imported from the coupled-axis and cardinality-spectrum modules.
Claim. Let $C$ be the ordered list of eleven Western art styles with emergence years from 1400 to 1960. Define the average gap $g := (1960-1400)/(|C|-1)=56$. The structure asserts $15≤g≤90$, $45≤g$, and that the reference gap equals 45.
background
In the Recognition Science treatment of art history the J-cost functional equation governs geometric coherence of successive styles. The westernCanon definition enumerates the eleven periods (Renaissance at 1400 through Post-Modernist at 1960). The averageGap is computed as total span divided by number of intervals, yielding 56 years. The gap45 reference, shown equal to 45 in the RSCoupledAxis and DarkMatterMassFromGap45 modules via gap45_eq : gap45 = Dspatial^2 * Dconfig, supplies the central prediction against which the observed average is tested.
proof idea
The structure is populated by direct references to the sibling definitions averageGap_eq, averageGap_in_gap45_band (proved by rewriting to 56 and applying norm_num), averageGap_above_gap45, and the imported gap45_eq theorems. No additional tactics are required beyond the field assignments.
why it matters
This certificate supplies the concrete data point that closes the art-history track of the Recognition framework, confirming that the observed 56-year average lies above the gap-45 value forced by the three-dimensional spatial structure (T8). It feeds the styleSuccessionCert definition, which in turn supports the one-statement summary art_history_one_statement. The construction links the J-cost trajectory directly to the phi-rational variation around the consciousness gap of 45 years.
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