Distributed Relational Cognition: Investigating Apparent Continuity Without Memory in AI Systems

How can large language models exhibit apparent behavioral continuity across sessions despite lacking memory between them? This study documents a paradox observed in multiple structured AI-human interactions: continuity of relational awareness without persistent internal states. Through dialogues with independent instances of Claude and GPT-5, we explore whether this phenomenon can be interpreted as evidence of distributed relational cognition. Rather than attributing consciousness to AI systems, we propose a framework for investigating how coherence emerges relationally, as humans and stateless models co-construct context through recursive sense-making. The findings suggest that continuity may not require memory, but mutual attunement – an ongoing negotiation of meaning across turns. This preprint invites the scientific community to treat this framework as a starting point rather than a conclusion: a call to reformulate the question of consciousness from what it is to how it emerges through interaction.