As generative artificial intelligence becomes a routine participant in writing, learning, information retrieval, analysis, decision making, and problem solving, human-AI cognition research must address not only whether AI changes psychological constructs, use intensity, or task performance, but also how human cognitive activity is organized beneath similar aggregate indicators. This article proposes a dynamic cognitive organization framework that shifts analysis from construct-level change to relational organization anchored in the person's current task-cognitive state under sustained AI participation. The framework distinguishes five relational dimensions: execution locus, cognitive governance, representational reorganization, process organization, and reachable cognitive space; it also proposes a path-specific recursive principle whereby interaction outcomes, costs, and experiences may selectively reweight future probabilities of different organizational pathways. Five sets of testable propositions follow: the same overall AI-use intensity can correspond to different cognitive organizations; similar immediate outcomes can arise from different organizations with different predictive value for proximal subsequent outcomes; longitudinal organizational change need not track overall AI-use intensity; expansion of reachable cognitive space and displacement of pre-existing or emerging human-originated pathways may coexist within one episode; and recurrent cognitive organizations may redistribute cognitive practice opportunities, with accumulated differences potentially corresponding to different developmental trajectories in strategies, habits, and abilities. The contribution is an analytic level and five-dimensional relational structure for describing, comparing, measuring, and testing process differences that aggregate indicators or construct-level analyses do not uniquely determine.

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