acceptanceBandRatio_eq
plain-language theorem explainer
The acceptance band ratio in the Berlyne inverted-U model equals the golden ratio phi. Aesthetic theorists and Recognition Science researchers cite this to fix the exact half-width of the pleasure acceptance interval. The proof is a direct reflexivity on the definition of the ratio.
Claim. The ratio defining the half-width of the aesthetic acceptance band equals the golden ratio $phi$.
background
The module derives the Berlyne inverted-U from J-cost reciprocal symmetry. Pleasure(r) equals 1 minus J(r) over its maximum at phi, where r is observed complexity over optimal complexity. The acceptance band is the interval where pleasure exceeds 0.5, spanning from 1/phi to phi with width factor phi, consistent with observed complexity-preference windows of 1.5 to 1.7.
proof idea
The proof is a one-line term that applies reflexivity to match the definition of the acceptance band ratio directly to phi.
why it matters
This equality anchors the aesthetic acceptance band to the golden ratio, supporting the module derivation from J-cost symmetry. It aligns with the phi-ladder and the phi-step bandwidth described in the module documentation. No downstream theorems are recorded.
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