lambda
plain-language theorem explainer
lambda defines the RG normalization constant as the natural logarithm of the golden ratio. Researchers deriving mass residues or balancing curvature costs in the Recognition Science framework cite this constant when integrating anomalous dimensions. The definition is a direct assignment requiring no lemmas or tactics.
Claim. $λ := ln(φ)$ where $φ$ is the golden ratio fixed point.
background
The RGTransport module formalizes renormalization group transport for mass residues. In the Standard Model, fermion masses run with scale μ according to d(ln m)/d(ln μ) = -γ_m(μ). The integrated residue is f(μ₀, μ₁) = (1/λ) ∫_{ln μ₀}^{ln μ₁} γ_m(μ') d(ln μ'), where λ = ln φ serves as the normalization constant in the mass formula m(μ⋆) = m_phys · φ^{f(μ⋆, m_phys)}.
proof idea
This is a direct definition assigning lambda to the real logarithm of phi. No lemmas from upstream results are applied and no tactics are used.
why it matters
This supplies the normalization factor required by the balance theorems in LambdaRecDerivation, including balance_determines_lambda which states that the balance condition J_bit = J_curv uniquely determines lambda. It implements the logarithmic measure for the phi-ladder mass formula and connects to T5 J-uniqueness and T6 phi fixed point in the forcing chain. The constant appears in derivations of J_curv = 2λ² and the unique positive root for the balance residual.
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