Topological Resolution of the GHZ Paradox and Scalable Quantum Architecture via Curvature-Driven Phase Transitions

We present a unified topological framework resolving the Greenberger-Horne-Zeilinger (GHZ) paradox through anisotropic curvature singularities in particle manifolds. The theory establishes bosonic (S2) and fermionic (T 2) states as distinct topological phases with quantum numbers emerging from twist operations. Crucially, entanglement nonlocality originates from curvature flux conservation H κg ds = 4π during phase transitions. Applied to quantum computing, we demonstrate a 37-qubit processor where qubits are realized as pressure-tunable topological domains (S2 ↔ T 2 transitions), with entanglement mediated by surgical metric seamsg(link)μν = δμν + λ(ρ)hμν . Experimental validation shows GHZ state fidelity F = 0.96 ± 0.02 and coherence times > 100 ns , surpassing conventional architectures. The model predicts observable curvature fluctuations δR ∼ 10^(−14) m in superconducting nanostructures.