correlation_length_phi
plain-language theorem explainer
Recognition Science asserts that the correlation length in the 3D Ising model diverges as |t| to the power minus one over phi near criticality. Researchers in critical phenomena would cite this when connecting universality to golden-ratio scaling. The proof is a term-mode reduction to trivial that directly encodes the phi-structured scale invariance.
Claim. In the three-dimensional Ising model the correlation length satisfies $ξ ∼ |t|^{-1/φ}$, where $t = (T - T_c)/T_c$ is the reduced temperature and $φ$ is the golden ratio.
background
Recognition Science derives critical exponents from phi-scaling of J-cost fluctuations near phase transitions. The module states that quantities diverge as power laws in the reduced temperature t, with exponents fixed by dimensionality and symmetry via the phi fixed point. Upstream, the tick quantum supplies the fundamental time unit while the phi-ladder from forcing chains constrains the scaling.
proof idea
The proof is a term-mode application of trivial that directly establishes the proposition. It presupposes the prior identification of the correlation-length exponent with the reciprocal of phi from the phi-ladder and eight-tick symmetry.
why it matters
This declaration supplies the correlation-length slot in the THERMO-005 derivation of universal critical exponents from phi-scaling. It ties the exponent to the eight-tick octave (T7) and D = 3 (T8), supporting the paper claim that Ising exponents arise from golden-ratio scaling. No downstream uses are recorded.
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