BT-PEC Triadic-Coupling Theory: Rigorous Derivation of Einstein's Unified Field Theory

This paper establishes the BT-PEC triadic-coupling primordial topological theory. Taking two globally self-consistent primordial axioms of the universe as the only foundation, it rigorously derives the spontaneous emergence of SL(3,ℤ) modular group topological constraints and constructs the cosmic triadic-coupling dynamical system. Under the classical macroscopic limit reduction, the framework recovers the gravitational geometry of general relativity, Maxwell’s electromagnetic equations and the full structure of Einstein’s asymmetric unified field theory. It explains the natural origin of symmetric metric components and antisymmetric electromagnetic components at the primordial level, and proposes six quantitatively testable, falsifiable scientific predictions.