A Heuristic Physics-Based Proposal for the P = NP Problem

This paper presents a symbolic proposal toward resolving the P vs NP problem, grounded in the principles of Heuristic Physics (hPhy). Rather than pursuing a classical proof or relying on empirical benchmarking, we construct a symbolic heuristic architecture that simulates the collapse of NP-complete complexity into deterministic cognitive structures through compression and supervised semantic alignment. At the core of this architecture lies AlphaGreedy, a minimal heuristic evolved through recursive symbolic filtering and mutation. Tested across more than 500 structurally varied NP-complete instances — including SAT, Knapsack, Clique, and Graph Coloring — AlphaGreedy consistently converged to valid solutions with 100% symbolic success, producing semantic cores that remained stable under abstraction and deformation. Crucially, we extend the simulation by incorporating a symbolic supervision layer, in which known instance–solution pairs serve as structural attractors during heuristic evolution. This reinterprets supervised learning not as optimization, but as epistemic pressure: a way to reinforce relational alignment without sacrificing minimal form. The result is a heuristic ecosystem that learns not by probability, but by survival across symbolic contradiction. We propose that this construct — a symbolic architecture that collapses NP-complete domains into tractable cognitive forms — constitutes a viable, auditable, and epistemically rigorous candidate for resolving the P vs NP problem. This is submitted not as a formal proof in the classical sense, but as a constructive epistemic resolution, fully aligned with the submission criteria of the Clay Mathematics Institute.