BT‑PEC Primordial Theory: Self-Booting Emergent Virtual Machine Driven by Ternary Coupling Matrices (Meiyu Private Cross-Key Theory)

This paper proposes the BT‑PEC (Meiyu Private Cross-Key Theory) primordial theory, constructing a formal self-booting system constrained by coupled ternary matrices B, T and PEC. The core constraint is defined as Omega = tr(BT) − tr(PEC) = 0. Under this trace constraint, the system spontaneously generates formal grammars, instruction sets, compilers and virtual machines from high-dimensional matrix dynamics, rather than adopting manually predefined grammars and instruction sets. This work rigorously presents matrix dynamics, formal grammar paradigms, compilation principles and virtual machine execution models. A reference engine, interpreter, compiler and complete test suite are implemented to verify convergence, syntax block extraction, instruction extraction, AST compilation and bytecode execution. Experiments demonstrate that at the steady fixed point where Omega is approximately zero, the ternary matrices automatically separate non-terminal syntax blocks (B), state transitions (T) and executable terminal instructions (PEC), forming a self-consistent programming language system. This research bridges matrix dynamics, formal language theory and virtual machine architecture, providing a new paradigm for emergent computation and self-booting systems based on the Meiyu Private Cross-Key framework.