goldenDivision
plain-language theorem explainer
The golden section of unit length is defined as the reciprocal of the golden ratio phi. Art historians and Recognition Science researchers cite this value when deriving sub-rectangle area ratios that lie on the phi-ladder for classical compositions. The definition is introduced by a direct one-line assignment to phi inverse with no lemmas or tactics applied at that step.
Claim. The golden section of a unit-length interval is the real number $1/phi$, where $phi$ is the golden ratio satisfying the fixed-point equation $phi = 1 + 1/phi$.
background
The module ArtHistory.FibonacciInComposition treats the historical recurrence of the golden section in artistic composition from antiquity onward. Recognition Science predicts that the optimal division point for a length-L composition lies at L/phi, yielding sub-segments whose ratio is phi:1 and whose areas become integer powers of phi. The supplied definition supplies the concrete real number 1/phi that serves as the base unit for these ratios.
proof idea
The declaration is a direct definition that equates the symbol to the multiplicative inverse of phi. No lemmas are invoked; the three immediate dependent results unfold the definition and apply standard facts on positive reals such as inv_pos and mul_inv_cancel.
why it matters
This definition anchors the structure FibonacciCompositionCert that packages the positivity, upper bound, and ratio properties required for certifying golden-section divisions. It realizes the RS prediction for artistic composition stated in the module documentation and connects to the phi-ladder landmark by providing the base whose powers generate the allowed area ratios. The module falsifier is any large-N eye-tracking study showing equal fixation density on golden-section versus non-golden-section layouts.
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