Topological Origin of the Imaginary Unit i and Universal Complex Field Theory

This paper reveals the topological origin of the imaginary unit i, proving that it is the topological identifier for the orthogonal coupling between spatial dimensions and topological evolution directions. A universal complex field theory is constructed on the framework of two-dimensional compact Kähler manifolds, rigorously demonstrating that π, e, and φ are the unique intrinsic topological solutions of complex topological manifolds under closure, continuous evolution, and self-similarity constraints. Based on the topological projection property of i, a unified topological interpretation of quantum entanglement nonlocality is provided, and a complete logical closed loop of (i −e−φ information substrate is established, realizing the underlying unification of the ontological meaning of imaginary numbers, complex analysis structures and physical spacetime. This theory does not overthrow or contradict the existing Standard Model, quantum mechanics and general relativity, but provides a unified topological origin for them, and puts forward falsifiable precise predictions for the Bell parameter of quantum entanglement and its correction under extreme conditions (Planck scale/strong gravitational field). The whole paper adopts pure text and mathematical expressions, maintaining the abstractness and universality of the top-level theory, and providing a new path for the unification of fundamental physics.