The Algorithmic Cyclic Universe: Bridging Cosmological Expansion and P vs NP Complexity

This paper introduces the Algorithmic Cyclic Model (ACM). We map the P vs NP problem onto cosmological evolution, identifying Heat Death as an NP-hard state. We provide numerical proof of the "sawtooth" entropic evolution as a stable solution for an infinite universe. This preprint proposes a novel framework treating the Universe as a computational manifold, where expansion serves as a processing task. It includes a modified Einstein-Hilbert action with an informational term, conservation laws for cyclic resets, and numerical simulations demonstrating stable entropic cycles. Implications for resolving the Heat Death paradox and potential observational signatures (e.g., CMB anomalies) are discussed.