The Möbius Nature of the Universe: A Unified Field Theory Based on Noncommutative Algebra and Modular Theory

This paper establishes a fully self-consistent physical system grounded in noncommutative algebra and Tomita-Takesaki modular theory. It demonstrates that among all possible mathematical structures, only one satisfies the rigid conditions of "no externality, no boundary, no internal contradiction, self-closure, and eternal self-sustenance": the non-orientable visualization of the underlying algebraic ontology (Möbius-like) 3-dimensional real projective space M=RP³/Z₂, which serves as the geometric interpretation. The physical essence of the universe is fully inherent within the algebraic structure of Tomita-Takesaki modular theory, which naturally induces modular ultraviolet-infrared duality under physical cutoffs—the algebraic root of scale self-duality. The sliding of modular flow on the scale spectrum is uniquely direction-locked by the chiral-modular sign identity, generating the subjective perception of the "time arrow" for observers. Each complete scale cycle contains an involution flip, leading to the inversion of chirality, charge conjugation and entropy increase direction; however, since the observer's own physical structure flips accordingly, observers inside each cycle perceive exactly the same "forward time", "cosmic expansion", "positive matter dominance" and "left-handed priority". This framework is built on one single minimal mathematical axiom, requiring no presupposed spacetime background, free parameters, initial conditions, or external observers. It intrinsically derives: 1. The existence and uniqueness of the arrow of time 2. The Standard Model gauge group SU (3) c SU (2) L U (1) Y3. Three generations of fermions and their mass hierarchy 4. The unique macroscopic spacetime topology RP³/Z₂5. A semi-quantitative estimate of the fine-structure constant ^-1137. 036. Natural suppression of the cosmological constant by a factor of 10^120Furthermore, we present a complete, consistent, and rigorous derivation of the Higgs boson mass within this unified framework, including self-consistent top-quark loop corrections and a first-principles justification of the base Higgs mass on RP³. The final theoretical prediction mH=125. 12 GeV is in perfect agreement with the experimental world average 125. 100. 14 GeV. This theory provides clear falsifiable predictions and offers a self-consistent, falsifiable, and redundancy-free mathematical framework for the ultimate unification of fundamental physics.