Major Conjectures and Cosmological Tests N: The Cosmological Falsifiability of the P vs NP Problem

This paper places the core challenge of computational complexity theory—the Pvs NP problem—within the context of the evolution of the physical universe. By establishing three postulates—cosmic computability, complexity correspondence, andscale correspondence—we map the abstract distinction between “polynomial-timesolvable (P-class)” and “nondeterministic polynomial-time verifiable (NP-class)”onto the scaling behavior of the intrinsic complexity of macroscopic cosmic structures (such as the cosmic microwave background radiation and large-scale structure). Based on the axioms of information conservation and computability, we derive that if cosmic history belongs to the P class (i.e., can be simulated efficiently),its logical depth should follow polynomial growth; if it exhibits NP-class characteristics, it should display exponential growth. Utilizing observational data fromPlanck and DESI, we measure the multi-scale scaling exponent of logical depth andfind it consistent with the P-class prediction within errors, significantly rejectingsimple exponential growth models. This study proposes, for the first time, a pathin principle that can empirically test and potentially falsify the physical hypothesisof “whether cosmic evolution belongs to the P class” using next-generation astronomical observation facilities (such as CMB-S4 and SKA-2), thereby providing aunique evidential chain and inspiration for the P vs NP mathematical conundrumfrom cosmology