BT‑PEC Ternary Coupling Topological Emergence Theory: Model Internal Self-Consistent Deduction of the Quantum Anomalous Hall Effect (Full Version with 10 Quantum Scientific Predictions)

Based on the BT‑PEC ternary coupling topological emergence framework, this paper completes the self-consistent deduction of the Quantum Anomalous Hall Effect (QAHE) within a rigorous axiomatic system. The theory defines the matter tensor operator B, spacetime metric tensor operator T, and observation filtering tensor operator PEC within the same Hilbert space, establishing the fundamental conservation axiom: Ω=tr(BT)−tr(PEC)=0. The topological evolution of the system is characterized by Betti numbers from persistent homology, and the topological information increment satisfies ΔI=Δb_k·log₂N. Under low-energy, weak-observation and locally two-dimensional confinement conditions, the evolution rate of the ternary coupling trace functional approaches zero, the system undergoes topological freezing, and the dynamic spacetime manifold degenerates into an approximate fixed background structure. In the frozen steady state, the model can self-consistently reproduce all core topological transport features of the quantum anomalous Hall effect, including spontaneous topological phase transition without external magnetic field, non-zero Chern number topological protection, bulk insulation and unidirectional dissipationless edge transport. This paper uses numerical simulation fully compatible with native BT‑PEC syntax to verify the self-consistency of the model, proving that QAHE can be obtained as a low-energy emergent steady-state solution of the BT‑PEC axiomatic system. Ten experimentally testable quantum scientific predictions are further proposed based on this theoretical framework. This work only conducts internal self-consistency tests of the model, does not replace traditional condensed matter microscopic mechanisms, and makes no claim regarding the physical reality of the universe.