Ill-Defined Complexity at the SAT Phase Transition Runtime Distributions and the Limits of Polynomial Bounds

This manuscript reexamines the P versus NP problem from a structural and conceptual perspective. Instead of addressing the problem as a purely technical question of algorithmic efficiency, the paper frames P=NP as an instance of criticality arising from fixed representational assumptions in computational complexity theory. By drawing analogies with phase transitions and convergence phenomena, the work argues that the persistence of the P=NP problem reflects limitations in how computational questions are formulated, rather than a lack of computational ingenuity. This manuscript is currently under review at Foundations of Physics.