This submission presents a phenomenological extension of the UAT/UCP framework describing causal membrane dynamics. The cyclic moment equation Mₚ = ∮ Ψ₈phase · κcrit / √ (1- (v/c) ²) dt is introduced and numerically evaluated, revealing that the membrane operates on a truncated cycle of 348. 12° rather than the classical 360°. Key findings: Causal overflow: The 11. 88° deficit (ε = 3. 3% = 1 - kₑarly) is the energy fraction expended per cycle to sustain cosmic expansion. When doubled by the quadratic scaling of the vacuum potential, it yields 6. 6% ≈ 7%, the thermal calibration margin. Trigonometric derivation of 0. 2791: The force metric Rgeom = sin (8 × 43. 515°/2) / sin (43. 515°/2) = 0. 279182 is derived from the 8-phasor sum with non-Euclidean step Δθ = 45° × kₑarly = 43. 515°. This version corrects an arithmetic error present in earlier manuscripts where Δθ was incorrectly stated as 43. 530°. The product 45 × 0. 967 = 43. 515, not 43. 530. The resulting overflow values have been updated accordingly. Distinction of three related values: The causal overflow (0. 0330), the per-step overflow (0. 273), and the force metric (0. 2791) are formally distinguished. Monte Carlo analysis: A 10, 000-iteration simulation demonstrates that the observed residual amplitude (0. 2791) cannot be explained by random thermal phase noise (p < 0. 001, maximum null amplitude 0. 0588 vs. observed 0. 2791). The simulation rules out noise as the origin of the signal but does not independently confirm the UAT phase geometry. Cosmological zero-point fluctuation: The 7% margin is interpreted as a scale analogue of the quantum zero-point energy. Just as a particle cannot rest at the minimum of its potential, the universe cannot rest at the Ivancho limit (η = 4. 978). Limitations explicitly acknowledged: The UAT/UCP framework is a phenomenological model under development. Its constants do not appear in standard references (CODATA, NIST). The Berry phase interpretation is a formal analogy, not a rigorous derivation. The GW170814 supplementary analysis confirms that LIGO strain data cannot validate the model (predicted signal is 10⁷ times smaller than source localisation uncertainty). Falsifiable predictions are provided for independent empirical testing. The package includes the theoretical manuscript (LaTeX) and three Python scripts that reproduce all numerical results.
Miguel Percudani (Thu,) studied this question.