phi
The declaration supplies the golden ratio as the explicit real (1 + sqrt(5))/2. Recognition Science researchers cite this value for the self-similar fixed point and phi-ladder mass formulas. The definition is a single-line noncomputable assignment with no derivation steps.
claimThe golden ratio is defined by $phi = (1 + sqrt(5))/2$.
background
The Constants module expresses quantities in RS-native units where the time quantum tau_0 equals one tick. The golden ratio enters as the self-similar fixed point forced by the J-uniqueness relation and the composition law. This supplies the concrete real used in the phi-ladder for mass assignments and Berry thresholds.
proof idea
The definition is a direct noncomputable assignment of the closed-form expression for the golden ratio.
why it matters in Recognition Science
This definition realizes the T6 fixed point in the forcing chain and anchors the phi-ladder for mass formulas. It supports the eight-tick octave and the forcing to three spatial dimensions. No downstream uses appear in the current module.
scope and limits
- Does not derive phi from the forcing chain or J-cost equation.
- Does not prove algebraic properties such as irrationality.
- Does not connect phi to numerical constants like alpha or G.
formal statement (Lean)
17noncomputable def phi : ℝ := (1 + Real.sqrt 5) / 2
proof body
Definition body.
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