phi_prediction_eta
plain-language theorem explainer
phi_prediction_eta supplies the Recognition Science estimate for the anomalous dimension eta as one over eight phi cubed. A condensed-matter theorist comparing phi-scaling to 3D Ising data would cite this value when testing near-Gaussian behavior at criticality. The declaration is a direct one-line definition in terms of the golden-ratio constant.
Claim. The predicted anomalous dimension is given by $eta = 1/(8 phi^3)$.
background
The Thermodynamics.CriticalExponents module targets derivation of universal critical exponents from RS phi-scaling. Near a phase transition, quantities diverge as specific heat ~ |t|^{-alpha}, order parameter ~ (-t)^beta, susceptibility ~ |t|^{-gamma}, and correlation length ~ |t|^{-nu}, with t the reduced temperature; these exponents are universal, depending only on dimension and symmetry. The J-cost function J(x) = (x + x^{-1})/2 - 1 governs fluctuations whose self-similar structure forces phi as fixed point, and the upstream class has from AsteroidOreSpectroscopy establishes characteristic spectral peaks omega_k = omega_0 phi^k that supply the discrete ladder for exponent construction.
proof idea
The declaration is a one-line definition that directly assigns the real number 1 divided by eight times phi cubed, using the phi constant imported from PhiForcing.
why it matters
This definition supplies the phi-based prediction for eta that is compared against the 3D Ising value in sibling declarations such as eta_3D_Ising. It fills the module's target paper proposition on universal critical exponents from golden ratio scaling. Within the framework it illustrates how the T5 J-uniqueness and T6 phi fixed point constrain near-Gaussian behavior at criticality, leaving open the noted 17 percent discrepancy with the measured eta approximately 0.036.
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