A Classical Unified Field Model Based on BT-PEC Boundary Topological Pre-emergence Theory

Albert Einstein spent decades searching for a classical unified field theory to unify gravitation and electromagnetism within a single geometric framework. This work proposes a classical unified field model built upon the BT-PEC boundary topological pre-emergence theory. The construction adopts the SL(3,Z) modular group symmetry, using automorphic forms as the fundamental field variables. Starting from the variational principle of the action functional, the unified field master equation is derived. In the low-energy limit, the master equation reduces consistently to Einstein's field equations of general relativity together with Maxwell's electromagnetic field equations. The model further gives testable cosmological predictions, including corrections to cosmic microwave background observables and gravitational wave signatures. This paper focuses on the classical sector of the framework; quantum extension of BT-PEC will be discussed in subsequent works.