nu_MF
plain-language theorem explainer
nu_MF supplies the mean-field critical exponent ν equal to 1/2 as a baseline reference inside the Recognition Science treatment of phase transitions. Workers comparing mean-field results to φ-scaled universality classes cite it when contrasting with the 3D Ising values listed in the same module. The definition is a direct constant assignment drawn from classical mean-field theory.
Claim. In the mean-field approximation the critical exponent for the correlation length satisfies $ν = 1/2$.
background
The module THERMO-005 derives universal critical exponents from RS φ-scaling near phase transitions. Standard notation defines reduced temperature t = (T − T_c)/T_c and the correlation length divergence ξ ∼ |t|^{-ν}. The RS mechanism asserts that J-cost fluctuations near criticality are φ-structured, so exponents are constrained by the golden-ratio fixed point rather than by microscopic details. Upstream, the scale function from LargeScaleStructureFromRS supplies length scales as φ^k, while Length from RSNativeUnits supplies the underlying real-valued dimension.
proof idea
The declaration is a direct constant definition that assigns the classical mean-field value 1/2 with no further reduction or lemma application.
why it matters
It supplies the mean-field reference point required by the paper proposition 'Universal Critical Exponents from Golden Ratio Scaling'. The value anchors comparisons against the φ-derived exponents (alpha_3D_Ising through delta_2D_Ising) that appear as siblings in the same file. It touches the T6 phi-forced fixed-point step of the unified forcing chain and the eight-tick octave periodicity that governs length scaling.
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