Graviton as Ricci Flow Surgeon: Rigorous Topological Theory of Particle Transitions. Universal Graviton: Topological Surgeon and Gravitational Wave Quantum.

This paper establishes a rigorous correspondence between Perelman’s Ricci flow with surgery and graviton-mediated topological phase transitions in particle physics. We derive: (1) Ricci flow equations for particle configuration metrics, (2) Entropy monotonicity for topological transitions, (3) Rigorous surgery theorems for particle transformations. The model provides testable predictions while maintain-ing mathematical rigour in the spirit of geometric analysis.We establish the graviton as the universal topological surgeon mediating all fundamental interactions. We prove: (1) Graviton necessity in gauge interactionsvia surgery theory, (2) Derivation of gravitational wave properties from topological oscillation modes, (3) Universal coupling constant prediction. The model provides a unified topological origin for all forces while maintaining mathematical rigour through geometric analysis.