This paper constructs a BT-PEC tripartite coupling topological framework to model mind, consciousness and free will. B denotes personality substrate and subconscious ontology, T represents the flow of thoughts and iterative mental dynamics, and PEC corresponds to cognitive rules, attentional constraints and emotional thresholds. The theory regards consciousness as emergent dynamics within a multi-dimensional cognitive fibre bundle, and derives the topological necessary condition for free will rather than attempting a full proof of its existence. Ten falsifiable scientific predictions are proposed, including experiments based on hyperscanning for two-body high-intimacy interactive systems. This preprint provides a mathematical topology approach for cognitive science and philosophy of mind, and links individual mental activity to the universal BT-PEC origin theory.
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Lihua Lu (2026) studied this question.
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