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

This paper derives the internal structure of the neutron from the stationary solutions of a closed variational functional involving a field $\Psi$ and a cyclic operator $\Gamma$. A spectral stability analysis of the functional selects a minimal cyclic configuration of length three, generating a triadic internal structure. The bilinear operators associated with the stationary configuration span the matrix algebra $M_3(\mathbb{C})$, whose traceless sector forms the Lie algebra $\mathfrak{su}(3)$. The spectral decomposition of the internal space yields the reduction $3 = 2 \oplus 1$ and allows the construction of a diagonal operator with eigenvalues $2/3$, $2/3$, 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 configuration corresponding to $(d,d,u)$, producing a neutral composite state. The spatial solution of the variational equation generates a localized triadic density whose correlation scale determines the nucleon radius and the associated mass scale. The resulting structure provides a mathematically coherent derivation of a triadic internal configuration of the neutron from the spectral properties of the variational functional.