Explosive Synchronization and Topological Resilience in Modulo-9 Bipartite Networks

Update (August 2026): This version includes new sections detailing the Empirical Quantum Verifications simulated via VQE, QPE, and Hamiltonian Dynamics on Qiskit/IBM Quantum architectures. Source codes are open-source.This paper demonstrates that a restricted modulo-9 topological network (Ouroboros Topology) acts as a natural generator for explosive synchronization within the Kuramoto model. By separating oscillators into mutually exclusive chaotic currents, the system suppresses early synchronization. At a critical coupling, the network collapses into a fully synchronized swarm state instantaneously. Formal Verification & Source Code: The rigorous Lean 4 proofs and framework codebase are open-source and available at the Ouroboros GitHub Repository.