Research on Mathematical Modeling of Mind, Consciousness, and Free Will Based on BT‑PEC Ternary Coupling Origin Topology Theory

Aiming at the long‑standing theoretical fragmentation in consciousness and free will research, this paper, based on the BT‑PEC ternary coupling origin topology theory, constructs human brain consciousness as a high‑dimensional topological dynamical system with coordinated ontology, evolution, and constraints. By establishing the topological deviation equation, critical threshold criterion, and Lyapunov stability model, the three‑state structure of consciousness---steady state, metastable state, and collapse---is quantitatively divided. The research proves that the degree of autonomous evolutionary freedom of thought within the consciousness steady‑state interval is the core dynamic necessary condition for the establishment of free will. This paper simultaneously proposes ten falsifiable scientific predictions, providing a new theoretical paradigm and experimental direction for the mathematical and quantitative research of consciousness.