phi_prediction_gamma
plain-language theorem explainer
The definition supplies the Recognition Science numerical forecast for the susceptibility critical exponent γ. Researchers comparing φ-scaling predictions to 3D Ising data would cite this value when tabulating universal exponents. It is obtained by direct algebraic substitution of the golden ratio into the supplied expression.
Claim. The RS-predicted susceptibility exponent is given by $γ = φ - (φ - 1)^2$, where $φ = (1 + √5)/2$ is the golden-ratio fixed point of the forcing chain.
background
The Thermodynamics.CriticalExponents module derives universal critical exponents from RS φ-scaling near phase transitions. Quantities diverge as χ ~ |t|^{-γ} for susceptibility, with t the reduced temperature; the module treats these exponents as independent of microscopic details and fixed by dimensionality and symmetry. The golden ratio φ is the self-similar fixed point (T6) imported from PhiForcing and satisfies the J-cost functional equation.
proof idea
This is a one-line definition that evaluates the algebraic expression φ - (φ - 1)^2 directly on the golden ratio. No lemmas or tactics are invoked; the result follows from ordinary real arithmetic.
why it matters
The definition supplies the γ entry in the THERMO-005 table of RS-predicted critical exponents and supports the paper proposition on universal exponents from golden-ratio scaling. It connects to the T6 phi fixed point and the eight-tick octave that constrains spatial scaling in the foundation. The sibling definitions for α, β, ν and the 2D/3D Ising cases rely on the same φ-construction.
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