Superfluid Vacuum Vorticity and the Hubble Crisis: Metric Relaxation as a Second-Order Phase Transition in the Lippa 3-Sphere (V₋₃ₒ)

PROPRIETARY NOTICE: This manuscript represents the definitive version of the Lippa 3-Sphere (V₋₃ₒ) framework. All intellectual property, including the Unified Lippa Constant (L = 1. 08285) and the verified monochromatic resonance at 368. 124 nHz, are the exclusive property of Michael J. Lippa and the Appil Research Group. LICENSING AND USE: This work is protected under the Creative Commons Attribution-NonCommercial 4. 0 International license. Use of these geometric constants or the V₋₃ₒ manifold logic for commercial engineering, proprietary simulations, or for-profit research is strictly prohibited without a formal licensing agreement.