Emergence of Hadronic Physics from a Closed Quartic Variational Structure

This work presents a derivation of hadronic physics from a closed quartic variational functional SΨ, without introducing quarks, gluons, or gauge fields. Starting from the exact variational condition and its second-order expansion, the internal structure of admissible configurations is determined uniquely by cyclic closure, leading to a minimal Z₃ structure. The explicit construction of the Hessian yields a discrete spectral decomposition with eigenvalues 1, L, L, where the structural constant L is derived analytically as L = 0. 25 from the internal balance of the functional. This single parameter governs all physical predictions. The framework generates, without fitting or external inputs: the hadronic mass hierarchy, elastic scattering amplitudes, diffractive structures including multiple dips, a non-vanishing C-odd contribution (Odderon), collective light modes identified with the pion, and confinement as a variational selection property. All observables emerge from the sequence SΨ → δ → H → Spec (H) → Ω, establishing a unified multi-domain description of hadronic physics. The results indicate that the hadronic sector can be fully described as a spectral structure of the variational functional, without requiring constituent degrees of freedom. The framework is structurally closed, self-contained, and rigid, and produces testable predictions including new resonance states, scaling relations, and additional diffractive minima.