Möbius Algebra and Loop Quantum Gravity: A Unified Theory of the Eternal Recurrent Universe

We present a complete, parameter-free, and self-consistent unification of Möbius algebraic ontology and loop quantum gravity (LQG), yielding the first rigorous framework for the ultimate cosmic picture. The non-orientable spacetime topology RP^3/Z_2 provides the rigid algebraic foundation for the standard model gauge group, three generations of fermions, the arrow of time, and baryon asymmetry. Loop quantum gravity resolves singularities and realizes cosmic collapse and quantum bounce, whose dynamical critical transition is identified as the Z_2 involution of the underlying topological structure. Our unified model demonstrates that the entire universe collapses into a cosmic ultimate black hole, undergoes a deterministic black-hole-to-white-hole bounce via topological involution, and restarts with perfect exact recurrence. This theory naturally solves the cosmological constant problem, accurately predicts the Higgs boson mass and fine-structure constant, and yields falsifiable experimental signatures. The universe exists as an eternally recurrent, deterministic, and topologically closed Möbius system with infinite exact cycles.