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

This paper introduces the Livolsi Constant L, a universal dimensionless invariant that emerges uniquely from a closed quartic variational functional without any free parameters. Unlike conventional physical constants, which enter theories as external empirical inputs, L is fixed entirely by the internal algebraic structure of the functional, by its Z3 cyclic closure, and by the normalization of the symmetric mode in the fluctuation spectrum. The second variation of the action reduces to a scale-free operator whose nontrivial eigenvalue is uniquely determined: L = 0.25. This value is invariant under all field rescalings, unit changes, and emergent dimensional scales (including those associated with h, c, and G). L governs universal ratios of frequencies, amplitudes, and noise levels in the cyclic sector, providing parameter-free predictions independent of units or phenomenology. The result shows that closed variational structures can generate fundamental constants through internal necessity rather than empirical calibration, suggesting a deeper layer of physical law governed by structural invariants rather than externally postulated constants.