Emergence of the Universal Livolsi Constant (L=0.25) from a Closed Quartic Variational Functional

This work derives a new universal dimensionless constant, denoted L, entirely fromthe internal structure of a closed quartic variational functional. No external scales, noparameters, and no inserted constants are used at any stage. The constant emergesas the rst nontrivial eigenvalue of the fully dimensionless operator T, obtained fromthe second variation of the functional after complete elimination of all physical scales.The derivation is rigorous, fully explicit, and performed in complete compliance withthe structural closure conditions, the decision operator, and the Z3 internal symmetryof the functional. The nal result is the numerical xation of the Livolsi constant L= 0.25, which is shown to be unique, unavoidable, scale-free, and independent of allknown physical constants. This establishes the existence of a new universal invariantdictated solely by the intrinsic quartic structure of the variational principle.