Emergent Internal Structure of the Neutron from the Psi-Gamma Variational Functional CERN

This work derives the internal structure of the neutron from the stationary solutions of a closed variational functional involving the field $\Psi$ and a cyclic operator $\Gamma$. Starting from a single variational equation, the spectral stability analysis of the functional selects a minimal cyclic configuration of length three. The resulting triadic structure generates a three-dimensional internal vector space whose bilinear operators span the matrix algebra $M_3(\mathbb{C})$. The traceless sector of this algebra forms the Lie algebra $\mathfrak{su}(3)$, which emerges directly from the internal structure of the stationary configuration. The spectral decomposition of the internal space produces a reduction $3 = 2 \oplus 1$, allowing the construction of a diagonal operator whose eigenvalues are $2/3$, $2/3$, and $-1/3$. The admissible stationary configurations therefore take the form $(A,A,B)$ together with their cyclic permutations. The application of a global decision functional selects a coherent triadic configuration corresponding to $(d,d,u)$, which yields a neutral composite state. The spatial solution of the variational equation produces a localized triadic density whose correlation scale determines the nucleon radius and the nucleon mass scale. The resulting structure provides a mathematically coherent framework in which the triadic internal configuration of the neutron emerges directly from the spectral properties of the variational functional.