The Möbius Nature of the Universe: The Algebraic Origin of Time Arrow and Baryon Asymmetry

This paper elucidates the Möbius nature of the universe from the perspective of algebraic ontology and geometric visualization, based on Tomita-Takesaki modular theory. It reveals that the physical essence of the universe is fully encoded in the algebraic structure of modular flows, where the modular operator carries inherent inversion involution, giving rise to modular ultraviolet-infrared duality as the algebraic root of scale self-duality. The direction of modular flow is uniquely locked by the chiral-modular sign identity, which naturally generates the irreversible arrow of time. Through scale-cycle involution flip, chirality, charge conjugation and entropy direction are inverted, yet observers inside each cycle perceive consistent forward time, cosmic expansion, baryon asymmetry and left-handed priority due to synchronous flipping of physical standards. To visualize this abstract algebra, a non-orientable, one-sided three-dimensional manifold M=RP³/Z₂ is constructed as the geometric carrier, whose topological twist corresponds to the involution of modular flows. The universe is a static four-dimensional block, with modular flow acting as the directional reading pointer; cosmic evolution is replaced by involution recurrence, and geometry serves only as the projection of fundamental algebra. This theory provides unified explanations for the origin of the time arrow, baryon asymmetry, chiral priority and cosmic expansion, and yields falsifiable predictions including normal neutrino mass ordering, precise Higgs mass, first-principles estimation of the fine-structure constant, and paired circle signals in the cosmic microwave background. The core conclusion is that the universe is fundamentally algebraic, not geometric, and all cosmic phenomena are necessary consequences of modular flow structure. Update: This version further refines the calculation by adding top-quark loop quantum corrections and self-consistent renormalization group running corrections, yielding the full physical Higgs mass mH = 125. 12\ GeV. Fundamental Physical Theory;https: //doi. org/10. 5281/zenodo. 19571808 wxsq1638@outlook. com 0009-0000-3175-1681 Xinyu Zheng