Quantum Flag Manifolds and the Algebraic Unification of Physics

This paper proposes a unified field theory framework grounded in noncommutative von Neumann algebras and Tomita-Takesaki modular theory. Built on a single minimal mathematical axiom without presupposed spacetime background, free parameters, initial conditions, or external observers, the entire physical universe is encoded in the modular quantum flag manifold algebra, which decomposes canonically as A = A₄ₗₓ A₈₍ₓ. The theory intrinsically derives the unique arrow of time via the chiral-modular sign identity, the standard model gauge group SU (3) c SU (2) L U (1) Y, three generations of fermions and their mass hierarchy, and the macroscopic spacetime topology RP³. It naturally suppresses the cosmological constant by a factor of roughly 10^120 through modular UV-IR duality, and yields a semi-quantitative estimate of the fine-structure constant ^-1 137. 03. Einstein’s field equations emerge from the spectral action heat-kernel expansion, while quantum noncommutativity originates in the conjugate action of the modular operator. This framework unifies the standard model, general relativity, and quantum mechanics as distinct projections of the same algebraic structure, with clear falsifiable predictions including normal neutrino mass ordering and RP³ cosmic topology signatures. https: //doi. org/10. 5281/zenodo. 19504572 wxsq1638@outlook. com 0009-0000-3175-1681