Four Complementary Models of the Universe: Exact Classical-Quantum Equivalence for the Ouroboros v11 Lagrangian Across Classical, Canonical, Statistical, and Boundary Geometries

For nearly a century, theoretical physics has stalled over the incompatibility between quantum field theory and general relativity. This paper presents a rigorous evaluation of the Ouroboros v11 framework, demonstrating how dynamical gravity is unified with bosonic field theory through strict superrenormalizable power counting. Rather than relying on straw-man control models, we examine the identical v11 Lagrangian under its two true theoretical realizations: the classical deterministic field interpretation and the canonical quantized operator interpretation on Fock space. Furthermore, we map this landscape across four complementary perspectives—incorporating statistical thermal quantum annealing (Model 3) and time-symmetric boundary topologies (Model 4)—to provide a complete, mathematically sound taxonomy of physical reality.