This work derives the internal structure of the neutron from the stationary solutions of a closed variational functional involving the field and a cyclic operator. 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 M₃ (C). The traceless sector of this algebra forms the Lie algebra 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 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.
Livolsi Edoardo (Mon,) studied this question.