beta_MF
plain-language theorem explainer
Mean-field theory assigns the classical value 1/2 to the order-parameter exponent beta. Researchers comparing Recognition Science phi-scaling against standard critical phenomena cite this baseline before introducing corrections. The declaration is a direct noncomputable assignment with no lemmas or computation.
Claim. In mean-field theory the critical exponent beta takes the classical value $beta_{MF} = 1/2$.
background
Critical phenomena near a phase transition are described by power-law divergences of specific heat, order parameter, susceptibility and correlation length with exponents alpha, beta, gamma, nu, eta and delta. In Recognition Science these exponents follow from phi-structured fluctuations in the J-cost near criticality, with universality arising because the scaling depends only on dimensionality and symmetry. The module sets the mean-field values as the classical reference that must be corrected for d less than 4.
proof idea
The definition directly assigns the real number 1/2.
why it matters
This supplies the mean-field reference used when the module compares against the phi-corrected exponents such as beta_3D_Ising. It fills the classical limit inside the paper proposition on universal critical exponents from golden ratio scaling. The accompanying comment records that a naive phi correction moves beta in the wrong direction, indicating the need for more advanced scaling.
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