BT‑PEC Foundational Coupling Theory and the Emergent Programming Language System

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A core tension persists across complex systems science, theoretical physics, and computer programming: natural complex systems achieve self‑organization and emergence through topological coupling, while mainstream general‑purpose computer programs are essentially predefined, open‑loop static systems lacking native structural emergence. Existing evolutionary computation and adaptive programming mostly optimize at the parameter level, unable to autonomously generate or iteratively upgrade the underlying syntactic structure and causal topology of programs. This paper proposes BT‑PEC (Base‑Time‑Power‑Emergent Coupling) Foundational Coupling Theory, constructing the Ω ternary coupling operator based on the SL(3,ℤ) modular group, and establishing a four‑dimensional axiomatic system composed of Base, Temporal Iteration, Effect Potential, and Topological Coupling, to describe the self‑organizing evolution and emergent transition of closed dynamical systems. Based on this theory, this paper originally designs the BT‑PEC emergent programming language, natively supporting four paradigms—imperative, functional, object‑oriented, and emergent—compatible with Java/C++/Python semantics, accompanied by a complete coupling‑aware compiler and self‑evolving virtual machine. This paper elaborates the BT‑PEC axiomatic system, core dynamical equations, language syntax design, Ω-AST coupled abstract syntax tree, coupled intermediate representation (IR), .btpec bytecode specification, and vm.btpec virtual machine runtime mechanism. Through mathematical simulation and engineering prototype testing, model self‑consistency is verified, and the compiler and virtual machine are evaluated on topological closed‑loop verification, controlled structural emergence, and cross‑platform deployment. The research demonstrates that the BT‑PEC system bridges complex systems emergence theory and programming language engineering, providing a novel theoretical framework and implementation path for next‑generation computing infrastructure with native self‑evolution capabilities.