The Cubic Interaction and Perturbative Closure — Leveille Framework Paper 53

Description: Paper 53 of the Leveille Framework series. Paper 52 established that the Fibonacci fixed-point self-consistency condition forces anomalous dimension γ_σ = 1 non-perturbatively, and ruled out the pure quartic interaction as the perturbative source. Paper 53 closes the perturbative route: the one-loop bubble self-energy from a cubic coupling λ₃σ³/3! is computed explicitly in d = 3 dimensions via Feynman parameterization. The bubble diagram carries external momentum through the loop, producing momentum-dependent self-energy with wavefunction renormalization Z_σ = 1 + λ₃²ℓ₀³/(24π²) and anomalous dimension γ_σ = λ₃²ℓ₀³/(16π²). Setting γ_σ = 1 determines the cubic coupling exactly: λ₃² = 16π²/ℓ₀³, with no free parameters. The mass fixed-point condition is verified for consistency, yielding two real solutions; the physical root m* ≈ 0.682/ℓ₀ lies below the UV cutoff and is dynamically stable. The perturbative and non-perturbative routes converge on the same fixed-point structure independently. The action derivation of η* = 0.20949 is complete at both levels simultaneously. The framework's sole external input is φ_L = 1.6180339887 (the golden ratio).