adjacencyGap
plain-language theorem explainer
adjacencyGap defines the separation between successive pottery styles as the J-cost evaluated at the golden ratio. Archaeologists modeling Petrie-style serial succession would cite it to fix the numerical gap in popularity curves. The definition is a direct one-line application of the J-cost function at phi.
Claim. The gap between adjacent styles is $J(φ) = φ - 3/2$, where $J(x) = (x + x^{-1})/2 - 1$.
background
The module models style popularity as a function of scaled time via popularity(t) = 1 / (1 + Cost.Jcost(t/τ)), where τ is the style half-life; neighbouring minima on the design graph are separated by the adjacency gap. Cost is the recognition cost quantity, introduced upstream as the abbrev Cost := Quantity CostUnit. The local setting is the derivation of Petrie's 1899 sequence dating as a J-cost trajectory on a one-dimensional family of styles.
proof idea
One-line definition that applies the J-cost function from Cost at the golden ratio phi.
why it matters
This definition supplies the concrete gap value used by PotterySerialCert and pottery_serial_one_statement to certify the full serial curve properties, including the band (0.11, 0.13). It realises the I2 track of Plan v5 by connecting J-uniqueness and the phi fixed point to archaeological serialisation. The gap value ≈ 0.118 anchors the frustration period between overlapping styles.
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