The Livolsi Constant as a Structural Constraint Across Five Fundamental Anomalies

This work shows that the Livolsi constant L=0.25L = 0.25L=0.25 acts as a universal structural threshold emerging from the closed quartic variational framework, and that this invariant simultaneously constrains five major anomalies across modern physics. By deriving the stability conditions of the symmetric and cyclic sectors, we demonstrate that LLL defines the minimal positive curvature compatible with variational closure. This structural threshold propagates into observable regimes, producing quantitative predictions without external parameters or tuning. The analysis reveals that:(1) the neutrino mass arises as the first admissible excitation above the threshold;(2) rare kaon decay rates inherit a suppression factor directly linked to the cyclic sector;(3) correlated gravitational-wave noise reflects the universal response ratio fixed by LLL;(4) galactic rotation curves emerge without invoking dark matter when the effective acceleration is constrained by the same threshold;(5) local deviations in the Hubble parameter follow from differential activation of symmetric and cyclic curvature modes. Across all five domains, the same structural constant determines the accessible physical regime, implying that these anomalies share a single variational origin. The Livolsi constant therefore provides a unified, parameter-free explanation for observational patterns that remain unexplained in conventional theoretical frameworks.