The Quartic Interaction and Anomalous Dimension — Leveille Framework Paper 52

Paper 52 of the Leveille Framework series. Paper 51 identified that the target erfc equation requires field anomalous dimension γ_σ = 1 under Fibonacci blocking. Paper 52 carries out two independent investigations. Investigation 1 (perturbative): the one-loop wave function renormalization from a pure quartic σ⁴ self-interaction is computed exactly. The tadpole is momentum-independent, giving γ_σ = 0. This is an exact result that rules out the pure quartic and constrains S₀ to include cubic or derivative coupling terms. Investigation 2 (non-perturbative): the Fibonacci fixed point self-consistency condition φL³ × γ_σ = φL³ forces γ_σ = 1 exactly, independently of any coupling constant or specific form of S₀. With γ_σ = 1 installed, the saddle point condition of the Gaussian path integral after three blocking steps produces erfc (φL³ × η) = η, whose solution is η* = 0. 20949 to 0. 001% agreement. One numerical error from the draft (shell integral value) was found and corrected under the zero-error mandate. The framework's sole external input is φL = 1. 6180339887 (the golden ratio). Publication date: 2026-03-12