A Physical Constraint Framework for P vs NP (Polynomial Time vs Nondeterministic Polynomial Time) Based on Finite Observers

This work presents a physics-only constraint framework for the P vs NP problem, reframing it as a question of physical realizability rather than formal computational equivalence. Computation is treated as a physical process carried out by finite systems embedded in thermodynamic environments. Within this framework, solution verification and solution generation are shown to be fundamentally asymmetric operations: verification is a local symmetry-breaking interaction that stabilizes or rejects an existing configuration, while generation is the global ordering of a specific, low-entropy configuration from a larger accessible phase space. This asymmetry is enforced by non-negotiable physical laws—including locality, conservation, thermodynamics, stability, and irreversibility—independent of algorithms or mathematical formalism. The result is not a proof of P ≠ NP, but a closure of the physically realizable alternative space, demonstrating that P = NP cannot be physically instantiated without violating foundational laws of nature.