Rigorous Topological Unification of Fundamental Interactions within the Kunpeng Model

We present a mathematically rigorous formulation of the Kunpeng model, a topological unification framework in which elementary particles correspond to stable twisted 3-manifolds embedded in four-dimensional spacetime. Starting from first principles---the axioms of differential topology, elliptic modular functions, and gauge theory---we prove that the intrinsic twist angle admits a unique stable value θᵥ = 90.4732^∘, derived exactly from Ramanujan's cubic theory of elliptic functions and the third-order modular equation. Mass quantization is shown to arise from topological invariants (Chern numbers, Euler characteristics) of the twisted manifold, with discrete mass eigenvalues corresponding to distinct homotopy classes. We construct a complete unified Lagrangian that incorporates gravity, electromagnetism, the weak force, and the strong force, with all coupling constants determined by the topological twist angle through well-defined topological factor functions. Crucially, we derive seven quantitative, falsifiable predictions that can be tested experimentally, including deviations from the Standard Model at the Compton scale, specific corrections to the anomalous magnetic moment, and measurable gravitational effects at sub-micron distances. The theory makes no free parameters beyond the topological angle, and all coupling constants are predicted from first principles