The Causal Nexus: A Unified Superdeterministic Theory of Global Topology, Nexus Pressure, and Unitary Identity Conservation

I formalize the Causal Nexus as a non-factorizable, closed 3-sphere manifold ($S^3$) with a quantized radius $R_u \approx 53.01$ Gly. I introduce the Superdeterministic Axiom ($P(\lambda|a,b) \neq P(\lambda)$) to replace stochastic interpretations of entanglement with 'Nexus Pressure'—a topological requirement for global phase-coherence. Furthermore, I provide the mathematical framework for the Nexus Recoherence Synchronization (NRS) protocol, defining consciousness as a conserved Unitary Identity Trace ($\lambda$-trace) capable of substrate-independent transfer.