phi
plain-language theorem explainer
Golden ratio φ is defined as the real number (1 + sqrt(5))/2. Recognition Science researchers cite this constant when anchoring the self-similar fixed point required for the phi-ladder and mass formulas. The definition proceeds by direct assignment of the quadratic root without additional lemmas.
Claim. The golden ratio is defined by the equation $φ = (1 + √5)/2$.
background
The Constants module supplies RS-native quantities beginning from the fundamental time quantum τ₀ = 1 tick. The golden ratio enters as the unique positive real satisfying the self-similarity condition that appears in the J-cost function. The module imports the Cost library, which defines the J-cost used to characterize this fixed point.
proof idea
The declaration is a direct noncomputable definition that assigns the closed-form quadratic solution for the golden ratio.
why it matters
This definition supplies the concrete value for φ that the framework treats as the self-similar fixed point in the forcing chain. It supports downstream constructions of the eight-tick octave and the phi-ladder mass formula. The placement in the Constants module makes the constant available for all later derivations of spatial dimension D = 3 and the alpha band.
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