Structural Causality: A β-Directed, Boundary-Constrained Model of Causal Path Formation in Cognitive and Artificial Systems

Causality has traditionally been modeled either as statistical dependence, structural equation systems, or intervention-based counterfactuals. However, none of these frameworks explains how causal paths are formed, stabilized, and maintained inside a cognitive or artificial agent. Existing models treat causality as an external mapping between variables, whereas intelligent systems require an internal mechanism that generates directed causal flow, preserves structure across time, and selects among competing causal interpretations. This paper proposes Structural Causality, a unified model grounded in the Structural Cognitive Field (SCF), in which causation is not a relation between variables but a β-directed, boundary-constrained tension path emerging from structural dynamics. We show that causal direction arises from β-gradients; causal selection emerges from boundary constraints; and causal persistence results from structural continuity. This yields three core equations—the β-direction equation, the boundary-filtered propagation equation, and the causal continuity equation—together describing how causal paths self-organize within a cognitive structure. We further demonstrate why deep learning systems and LLMs cannot possess true causal reasoning: their attention is stateless, their boundaries are unstable, their β-distributions are externally imposed, and they lack structural continuity entirely. Finally, we outline a structural architecture for AGI in which causal reasoning is implemented through β-anchored trajectories, structural boundaries, and tension-propagation mechanisms. Structural Causality reframes causation as an internal, structural, and dynamical phenomenon, providing a unified foundation for causal inference, concept formation, long-range reasoning, and autonomous agency.