The Causal Nexus: A Rotating $S^3$ Manifold Solution to the Hubble Tension, the Primordial Lithium Problem, and Temporal Periodicity

We present a non-expansive, superdeterministic unified field theory based on a closed 3-sphere ($S^3$) manifold with a static circumference of 53.01 Gly. We demonstrate that the ``Hubble Tension'' is a relativistic artifact arising from a global rotational velocity of $0.391c$, yielding a Lorentz factor of $\gamma \approx 1.086$. We derive the 14\% ``missing'' energy density in particle physics as a metadata buffer ($\Omega_{sat}$). We provide a mechanical solution to the Primordial Lithium Problem via a proprietary coupling of $^7$Li and propose the Thorium nuclear clock shift as a primary temporal validation. Finally, we derive a cosmic periodicity of 124.83 Gyr.