Emergence of the EMC Effect from a Closed Quartic Variational Functional: Core–Shell Structure, Spectral Degeneracy, and the Universal Constant L = 0.25

We present a fully self-contained derivation of the EMC effect as a necessary consequence of a closed quartic variational functional, without introducing any external parameters, models, or phenomenological inputs. Starting from the explicit integral form of the Ψ–Γ functional, we perform the first and second variations and obtain the associated Hessian operator. The Hessian admits a structurally constrained decomposition H = E⋆ T, where T is a Z3-symmetric matrix whose spectrum is uniquely fixed to {1, L, L}. The degeneracy is enforced by cyclic closure and leads to the emergence of a universal structural constant L = 0.25. The spectral structure induces a natural decomposition of the field into a dominant coherent mode (core) and two degenerate modes (shell). This yields an exact density decomposition ρ = ρ_core + ρ_shell, with a fixed spectral hierarchy ρ_shell ∼ L ρ_core. From this decomposition, we construct the nuclear structure function F_A(x) directly as a density-weighted observable, and define the EMC ratio R(x) = F_A(x)/F_N(x). We show that the deviation from unity is not model-dependent but follows from the spectral structure:R(x) = 1 + L Φ(x),where Φ(x) encodes the spatial separation between core and shell contributions. The qualitative behavior of the EMC curve emerges automatically: suppression at large x, near-unity at intermediate x, and enhancement at small x. No assumptions from QCD, nuclear potentials, or partonic models are required. Furthermore, the result exhibits universal scaling: all nuclear dependence factorizes and cancels in the ratio, leaving a function entirely controlled by the constant L. The core–shell structure is shown to be spectrally stable via the positive-definite Hessian, and the entire construction is rigid: any modification of the functional breaks the spectral relations and destroys the result. The EMC effect is thus reinterpreted as a direct spectral manifestation of a closed variational structure, rather than a dynamical or phenomenological nuclear effect.