Emergence of a Universal Energetic Scale from the Quartic Variational Framework

This work derives a universal energetic scale emerging exclusively from the closed quartic variational framework defined by its four fundamental equations. No thermodynamic assumptions, dimensional insertions, phenomenological inputs, or external theoretical structures are introduced. Starting from the full unreduced quartic functional, we compute the exact second variation within the internally isotropic structural class selected by the global decision principle. The internal torsional sector of the Hessian is shown to be finite-dimensional, positive definite, and spectrally discrete. Its first non-zero eigenvalue is strictly positive, isolated, and determined solely by the representation structure of the internal algebra. This minimal torsional excitation defines a universal energetic scale fixed entirely by internal degeneracy. By reconstructing the dependence of both the fine-structure constant and the torsional gap on the same representation dimension, we obtain a second alpha-scaling relation in which the energetic scale is proportional to the square root of the fine-structure constant. The resulting scale is universal, independent of boundary conditions, and selected by the global admissibility operator. Temperature-like conversion constants are therefore not primitive inputs but derived structural consequences of quartic internal degeneracy. The framework remains algebraically closed, parameter-free, and internally self-determined.