gamma_phi_connection
plain-language theorem explainer
The declaration asserts that the susceptibility critical exponent satisfies the φ-scaling relation γ ≈ φ − (φ−1)² ≈ 1.236, agreeing with the 3D Ising value 1.237 to under 0.1 percent. Researchers deriving universal exponents from Recognition Science would cite it to link J-cost fluctuations to observed divergences. The proof is a one-line trivial assertion of the stated numerical match.
Claim. The susceptibility exponent satisfies $γ ≈ φ − (φ−1)^2 = φ − φ^{-2} ≈ 1.236$, matching the three-dimensional Ising value of approximately 1.237 to within 0.1 percent.
background
Near a phase transition the susceptibility diverges as χ ∼ |t|^{-γ} with reduced temperature t. Recognition Science obtains the exponent from φ-structured fluctuations in J-cost, as set out in the module's account of universality and φ-scaling. The upstream structure records the meta-realization properties required by the self-reference axioms of the forcing chain.
proof idea
The proof is a one-line wrapper that applies trivial to assert the numerical relation given in the comment.
why it matters
It supplies the γ entry in the φ-scaling derivation of critical exponents targeted by the module's paper proposition on universal critical exponents from golden ratio scaling. The result sits inside the T5 J-uniqueness and T6 phi fixed-point steps of the forcing chain. With zero downstream uses the integration with the remaining Ising exponents remains open.
Switch to Lean above to see the machine-checked source, dependencies, and usage graph.