universalityClasses
plain-language theorem explainer
The declaration enumerates the four principal universality classes in critical phenomena and pairs each with its canonical physical realizations. A condensed-matter physicist would cite the list when mapping RS φ-scaling predictions onto measured exponents in magnets or superfluids. The body is a direct list construction that supplies the classification used by the module's later exponent formulas.
Claim. The universality classes are the list of pairs $(``Ising (N=1)'', ``Uniaxial magnet, liquid-gas'')$, $(``XY (N=2)'', ``Superfluid He$^4$, planar magnet'')$, $(``Heisenberg (N=3)'', ``Isotropic magnet'')$, $(``O(4)'', ``QCD at finite T?'')$.
background
Critical phenomena are described by power-law divergences near a continuous phase transition: specific heat $C sim |t|^{-alpha}$, order parameter $M sim (-t)^{beta}$, susceptibility $chi sim |t|^{-gamma}$, and correlation length $xi sim |t|^{-nu}$, where $t = (T-T_c)/T_c$ is the reduced temperature. Universality asserts that the exponents depend only on spatial dimension and the symmetry of the order parameter, so that microscopically distinct systems fall into the same class. In Recognition Science the module derives these exponents from φ-scaling of J-cost fluctuations, with the listed classes serving as the concrete targets for the φ-modified scaling relations.
proof idea
The definition is a direct enumeration of four string pairs. No lemmas or tactics are invoked; the list is written out explicitly to serve as a reference table for the exponent predictions that follow in the same module.
why it matters
The definition supplies the classification required to attach RS predictions (ν ≈ 1/φ, γ ≈ φ - (φ-1)²) to concrete systems such as the 3D Ising model. It supports the paper proposition on universal critical exponents from golden ratio scaling and links to the φ-forcing chain by providing the symmetry classes whose exponents are constrained by self-similar J-cost scaling. No downstream theorems yet consume the list.
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