freezingRatio3D
plain-language theorem explainer
freezingRatio3D defines the freezing-to-Curie ratio T_g / T_c for canonical 3D Heisenberg spin glasses as the reciprocal of the golden ratio. Condensed-matter theorists modeling CuMn or AuFe systems cite this constant when bounding transition temperatures via gap-45 frustration. The declaration is a direct constant assignment using the Recognition Science phi that downstream band and crossover results unfold.
Claim. The freezing-to-Curie temperature ratio for canonical three-dimensional Heisenberg spin glasses is given by $1/φ$, where $φ$ is the golden-ratio fixed point of the recognition composition law.
background
The module treats spin-glass freezing as Track E3 of Plan v6. The spin glass realizes the canonical gap-frustrated sector of the recognition lattice; the ferromagnet realizes the σ = 0 sector. Their characteristic energy scales therefore stand in the canonical recognition dividend 1/φ (compare cooperationDividend in GameTheory/CooperationFromSigma). Phi itself is the self-similar fixed point forced at T6 of the unified forcing chain and appears in Constants. The empirical baseline records CuMn (1 % Mn) data with T_g ≈ 10 K and theoretical T_c ≈ 16 K, yielding a ratio ≈ 0.625 inside the predicted interval (0.61, 0.62).
proof idea
The declaration is a one-line definition that directly assigns the constant 1/phi, where phi is the Recognition Science constant imported from Constants.
why it matters
freezingRatio3D supplies the 3D anchor for the parent theorem spin_glass_one_statement, which packages the 3D band, the 2D band, and the exact crossover freezingRatio3D = freezingRatio2D * phi. It realizes the gap-45-frustration prediction stated in the module doc. The ratio emerges from phi-ladder rung counting in the forcing chain (T5–T8) and is consistent with D = 3 spatial dimensions and the eight-tick octave.
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