Quantum Gravity via S3 ↔ (S2 ⊗ T 2) Transitions at Planck Scales

This paper establishes the S3 ↔ (S2 ⊗ T 2) topological phase transition as the fundamentalmechanism for quantum gravity. We derive the generalized Ricci flow equation with tensor surgery,predict high-frequency gravitational wave spectra ΩGW(f ) ∝ f ^(−3/2), and demonstrate experimentalverification through quantum simulation of spacetime foam. The model resolves the black holeinformation paradox via topological entanglement entropy Stopo = A/(4G) ln dim Hfoam and providestestable signatures for LISA and next-generation colliders. The critical role of C2 spinor space inunifying topology with quantum statistics is rigorously demonstrated.