Against Cyclic Speculation The Livolsi Constant L and the Algebraic Failure of CCC

This work presents a structural critique of the Conformal Cyclic Cosmology (CCC) and contrasts it with a closed quartic variational framework capable of extracting invariant signatures directly from raw gravitational interferometry data. CCC lacks a self-contained variational principle, and therefore cannot define admissible physical states, stability thresholds, or invariant quantities. Its reliance on ad hoc entities such as Erebons reflects the absence of an algebraic architecture capable of constraining the behaviour of spacetime fluctuations. In contrast, the quartic functional provides a fully closed structure whose stationary solutions and Hessian spectrum impose non-phenomenological constraints on the geometry of spacetime. Analysis of the LIGO O3 dataset reveals a universal spectral threshold consistent with the invariant predicted by the theory, known as the Livolsi Constant L. This threshold marks the minimal admissible curvature and the transition between symmetric and cyclic sectors of the functional. The findings show that the supposed “signals” invoked by CCC are instead geometric vibrations at the stability boundary of a closed variational system. The emergence of L from experimental data demonstrates that spacetime is governed by algebraic closure rather than phenomenological narratives, and establishes L as a fundamental structural invariant in the foundations of physics.