Abstract: The theory of extended cognition posits that human cognitive processes can extend to external entities. In an era marked by the widespread application of generative artificial intelligence (AI), AI has increasingly become an effective vehicle for human cognition, fostering a symbiotic cognitive model between humans and machines. As human cognition extends to AI systems, the authority over cognitive attribution remains solely with humans—neither shared nor usurped by AI. While AI functionally constitutes part of the cognitive system, its role is contingent upon human agency, specifically the delegation of active epistemic authority and the assignment of cognitive project qualifications. AI lacks independent agential authority or inherent eligibility for cognitive projects. However, given that human intentionality often relies on technological mediation, the concept of “mediatory-constitutive intentionality” offers a framework to interpret the interactive structure between humans and AI.