Why P = NP? The Heuristic Physics Perspective

This paper develops a symbolic-argumentative expansion of the P = NP conjecture, grounded in the principles of Heuristic Physics (hPhy). It is offered as a formal continuation and epistemic complement to an earlier submission [1], which was presented upon the first emergent results suggesting the viability of the P = NP hypothesis. That initial paper served as a conceptual milestone, laying the foundation for a new interpretive framework. The present work builds upon that foundation, aiming to deepen the analysis, formalize the symbolic architecture, and consolidate the theoretical implications. Rather than relying on algorithmic execution or classical proof construction, the work introduces a multi-layered epistemic architecture, composed of three interdependent layers: (i) an operational layer, where heuristic agents confront problem generators in dynamic SAT-based simulations; (ii) a tactical layer, where competing P vs NP hypotheses are ranked, critiqued, and validated symbolically; and (iii) a strategic layer, which reinterprets complexity through narrative resilience, symbolic survival, and contradiction-aware compression. This framework is tested both theoretically and within its dedicated heuristic systems, simulating adversarial conditions in which symbolic solvers and entropy-maximizing generators engage in recursive, semantically volatile encounters. Results consistently show that compression-based agents outperform their complexity-inducing counterparts not by brute force, but through adaptive pattern recognition, contradiction navigation, and epistemic reformulation. This convergence supports the claim that P = NP becomes epistemically plausible when the problem space is reframed through symbolic persistence rather than classical time complexity. Accordingly, this paper is submitted as an official argumentative contribution to the Clay Mathematics Institute’s Millennium Problem on P vs NP, asserting that under symbolic collapse and cognitive structuring, the classical boundary between P and NP may no longer be ontologically stable.