Exploratory Continuous-Relaxation Heuristics for Euclidean TSP: Physics-Inspired and Algebraic Frameworks

This repository explores continuous-relaxation heuristics for NP-hard combinatorial optimization, with a focus on the Euclidean Traveling Salesperson Problem (TSP). It contains two complementary exploratory manuscripts: a physics-inspired dynamical formulation and an algebraic convex-relaxation formulation. The work presents a unified ODE-based formulation, prototype Python code, and preliminary discussion of Lyapunov/Hessian conditions and spectral barriers. It is intended as a starting point for empirical validation and peer review. It does not claim a proof of P=NP; polynomial-time and global-convergence statements are conditional/conjectural and require rigorous proof and empirical validation.