Complete Emergence of Proton Observables from a Closed Variational Functional

We present a closed variational framework in which a multi-component field is governed by a quartic functional with no external parameters or phenomenological inputs. Starting from the stationary condition and the associated Hessian operator, we derive a rigid spectral structure characterized by a fixed eigenvalue pattern {1, L, L} with L = 1/4, enforced by the internal algebraic closure of the system. This structure induces a minimal cyclic configuration space compatible with a Z3 symmetry, within which admissible solutions are selected by a global decisional functional. The resulting configuration defines a unique minimal coherent domain determined entirely by spectral consistency, stability, and closure conditions. A reduced effective description of the dominant mode allows the emergence of a finite spatial scale and a localized profile, from which observable quantities can be consistently constructed. These results follow from the internal spectral–dynamical closure of the variational structure and do not rely on fitting procedures or externally imposed scales. The framework suggests a reinterpretation of particle-like entities as coherent domains selected by global consistency conditions, rather than fundamental objects introduced a priori.