Present an algorithm to prove P = NP

Aiming to prove the P vs. NP problem, a long-standing challenge in computer science, we present a novel deterministic algorithm that solves the Hamiltonian path problem, a representative NP-complete problem, in polynomial time. The proposed "Rotation-Based Search Algorithm (RBSA)" uses a novel approach that transforms the topological structure of a graph into a 3D geometric problem. Each vertex is positioned as a point in 3D space via a quaternion, and this set of points is spatially transformed by systematic rotations and oscillations. By sorting the points in each transformed state in a specific coordinate order, we obtain Hamiltonian path candidates, which are then verified to satisfy the constraints of the actual graph.