The Adelic Langlands Program: Adelic P vs NP

A theoretical framework for resolving the P versus NP problem by translating computational complexity into the Adelic Langlands Program. This unified approach suggests that the gap between polynomial-time (P) and non-deterministic (NP) classes is not merely an algorithmic limitation, but an intrinsic geometric property of the universe. By embedding Turing machine operations into adelic data streams, the sources argue that P $\neq$ NP remains true for any observer within a continuous real spacetime. However, the text proposes that this complexity gap collapses into an identity (P = NP) if the observer’s perspective shifts from the Archimedean real field into the non-Archimedean p-adic places. Ultimately, the sources use advanced concepts like analytic torsion, Donaldson-Thomas invariants, and modular bootstrap equations to demonstrate that computational complexity is a structural artifact of living in a real-valued manifold.