BT‑PEC Tripartite Coupling Theory: A Self-Consistent Framework Across Physics, Information and Complex Systems

Modern natural science and complex system science have long suffered from theoretical fragmentation. Mathematical architectures of branches in fundamental physics are mutually incompatible, leading to scale conflicts in quantum gravity. Meanwhile, studies of life, economics, cognition and artificial intelligence lack universal mathematical paradigms for steady-state evolution. This paper proposes the BT‑PEC tripartite coupling self-consistent framework. Five core components, namely Base (B), Transfer (T), Symmetry Group (P), Evaluation Functional (E) and Constraints (C), construct an axiomatic model for dynamical systems. The global self-consistency functional is defined as Ω = ⟨B,T⟩ − ⟨P,E,C⟩. A closed and complete system satisfies the steady-state self-consistency condition Ω = 0. This work unifies notations for traces of finite-dimensional matrices and functional pairings in infinite-dimensional spaces. Classical mechanics, electromagnetism, thermodynamics, quantum mechanics, general relativity and gauge field theories are incorporated into one unified theoretical system, and isomorphic mapping derivation of general relativity is completed. The theory is further extended to three classes of complex systems: biological evolution, financial markets and cognitive consciousness. A prototype of BT‑PEC self-consistent learning AI algorithm independent of pure backpropagation is constructed. Ten hierarchical, computable, reproducible and falsifiable scientific predictions are put forward, with experimental pathways, quantitative criteria and falsification boundaries specified for each prediction. Systematic benchmarking against the free energy principle, synergetics and classical system theory demonstrates that BT‑PEC possesses more complete dimensions, stricter constraints and stronger engineering practicability. This research indicates that the BT‑PEC tripartite coupling theory can serve as a general underlying modeling framework connecting fundamental physical laws, information evolution rules and steady-state phase transitions of complex systems, offering new theoretical support for quantum gravity research, complex system forecasting and new-generation self-consistent artificial intelligence.