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Interaction-centred and longitudinal research increasingly treats human-AI systems as evolving processes rather than sequences of isolated outputs. It does not yet establish when a particular interaction history warrants a distinct relational level of explanation. This paper proposes a middle-range model of recurrent relational organization and uses hybrid subject as a conditional operational designation for a coupling whose distributed history makes a prospectively specified, counterfactually demonstrable contribution to later transitions. The designation does not posit a third entity, artificial consciousness, equal autonomy between human and artificial poles, or a new thermodynamic law.

The model represents a bounded trajectory through situated human and artificial states, distributed operative memory, constraints, environment, provenance, and recurrent returns. Classification requires nine jointly necessary conditions: non-trivially transformable poles, recurrent flow, causal re-entry, operative memory, differential selection, constraining architecture, functionally relevant historical non-restorability, prospectively recognizable persistence, and incremental coupled-history contribution. The framework further distinguishes physical dissipation, informational uncertainty, and relational history.

Two epistemic constructs extend the model. The Hybrid Hall of Mirrors describes how one genealogy can return as several apparent witnesses; the Relational Black Box locates opacity in the distributed history of a composite system rather than only inside one component. The paper specifies interventions on identifiable carriers of history, provenance-sensitive experiments, interruption and reconstitution tests, and explicit rejection conditions. The central claim is therefore empirically vulnerable: the hybrid-subject interpretation should be retained only where intact coupled history explains or alters later transitions beyond isolated-pole, generic-context, ablated, scrambled, and swapped-history alternatives.