Dimensional Field Theory

This paper presents a two-scalar field theory in which every coupling constant is derived from the algebraic identity 1 − 1/rₙ = 2 − rₙⁿ⁻¹, satisfied by all roots of xⁿ = x + 1.

L = −¼F² + |DΦ|² + |DΨ|² − V(Φ,Ψ)

V = λ₃(|Φ|² − v²)² + λ₄(|Ψ|² − u²)² + ψ²|Φ|²|Ψ|²

The field Φ governs 3D classical structure (λ₃ = 1 − 1/ρ, where ρ is the plastic constant, root of x³ = x + 1). The field Ψ governs 4D quantum dynamics (λ₄ = 1 − 1/Q, where Q is the root of x⁴ = x + 1). The portal coupling ψ² = (Q/ρ)² connects them. No free parameters remain.