gamma_MF
plain-language theorem explainer
gamma_MF supplies the mean-field susceptibility exponent as the constant 1. Researchers comparing standard mean-field theory to Recognition Science φ-scaling predictions for critical phenomena would cite this value when establishing baselines. The declaration is a direct numerical assignment with no computation or lemmas required.
Claim. In mean-field theory the susceptibility diverges as $χ ∼ |t|^{-γ_{MF}}$ where the reduced temperature is $t = (T - T_c)/T_c$ and $γ_{MF} = 1$.
background
The module derives universal critical exponents from φ-scaling near phase transitions. Physical quantities diverge as power laws: specific heat $C ∼ |t|^{-α}$, order parameter $M ∼ (-t)^β$, susceptibility $χ ∼ |t|^{-γ}$, and correlation length $ξ ∼ |t|^{-ν}$. In Recognition Science, J-cost fluctuations acquire φ-structured form, which constrains the exponents independently of microscopic details.
proof idea
The declaration is a direct definition that assigns the real number 1 to the mean-field gamma exponent.
why it matters
This definition supplies the mean-field reference point inside the THERMO-005 derivation of universal critical exponents from φ-scaling. It enables direct comparison between classical mean-field results and the φ-constrained values that follow from the Recognition Composition Law and the eight-tick octave. The module targets the paper proposition on universal exponents obtained via golden-ratio scaling.
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