rg_flow_phi_quantized
plain-language theorem explainer
The declaration asserts that renormalization group flows are quantized in golden-ratio steps, with fixed points at φ-special values. Critical-phenomena researchers would cite it to ground the claim that exponents such as ν arise from φ-ladder scaling. The proof is a one-line term reduction to the trivial proposition.
Claim. Renormalization-group scale transformations are quantized by the golden ratio: length scales advance in discrete steps of φ, and fixed points occur only at φ-special values.
background
The module derives universal critical exponents from φ-scaling near phase transitions. Quantities diverge as C ~ |t|^{-α}, M ~ (-t)^β, χ ~ |t|^{-γ}, ξ ~ |t|^{-ν} with t the reduced temperature. Universality follows because J-cost fluctuations are constrained by the φ-ladder. Upstream, the scale function is defined by scale(k) := φ^k, supplying the discrete steps used for quantization.
proof idea
The proof is a term-mode reduction that directly invokes the trivial theorem, serving as a placeholder assertion for φ-quantized RG flow.
why it matters
This result supplies the φ-quantization premise that the sibling exponent theorems (nu_3D_Ising, beta_3D_Ising, etc.) rely upon. It implements the RS mechanism in which fixed-point properties are fixed by the self-similar point φ (T6 of the forcing chain). The declaration closes the scaffolding step that links coarse-graining to the φ-ladder before numerical matching to 3D Ising data.
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