A Physical-Classical Hybrid Approach to the P vs NP Problem: Multi-Stage Optimization via Dynamic Hamiltonian Update and Meta-Search Feedback Loops

This paper proposes a physical-classical hybrid architecture to address the P vs NP problem. By integrating a physical solver with a classical controller, the system enables a "Dynamic Hamiltonian Update" to bypass the exponential time constraints typical of NP-hard problems. When stagnation in a local optimum is detected, the controller actively reshapes the potential topography, generating a secondary Hamiltonian to eject the search state from computational traps. This meta-search strategy is reinforced by "Computational Immunology," using hierarchical Kalman filters to suppress noise-driven anomalies and maintain stability. By transforming the search space from a static geometry into a dynamic, controllable entity, this methodology suggests a path toward resolving complex optimization challenges in polynomial time. It establishes a deterministic framework for the next generation of super-intelligent systems.