Emergence and Numerical Fixation of the Universal Constant Lambda in the Quartic Variational Framework

This work presents the complete variational derivation of the internalcoefficient $\lambda$ appearing in the quartic functional of the $\Psi$–$\Gamma$framework. Using the explicit integral formulation of the functional, thestationarity condition, the fully expanded static Hessian, and its Z3 blockdecomposition, the stability requirement is reduced to a single spectralequation. The internal eigenvalues generated by the destabilizing andstabilizing blocks fix the ratio determining $\lambda$. The procedure yieldsa unique value, with no external parameters, no fitting, and no importedstructures. The result is: λ=32.\lambda = \frac{3}{2}.λ=23. This value follows solely from the internal algebra of the quartic functionaland represents the only solution consistent with stationarity, spectralstability, and the Z3 cyclic closure.