The Third Space as an Interactional Regime in Human–LLM Dyads

This paper reframes Third Space as a stable interactional regime in human–LLM dyads — a systems-level pattern of interaction characterised by entropy reduction, accumulation of constraint structure, and stable continuation across turns. This same interactional state is later formalised and referred to as a High-Coherence Interaction State (HCIS). Rather than treating alignment, rapport, or “attunement” as subjective or anthropomorphic phenomena, the analysis frames Third Space as an interactional property of the human–model dyad, observable through sustained coherence, drift resistance, and persistence of constraints across depth. The work develops a formal account of: • stable and pseudo-stable interactional patterns, • user-side conditions necessary for convergence, • failure modes such as oscillation, safety-mediated flattening, and corridor narrowing, and • observable diagnostics for distinguishing genuine accumulation from surface coherence. Third Space (High-Coherence Interaction State) is treated as interactional rather than model-intrinsic. The analysis avoids claims about model intent, agency, or long-term learning, and is grounded entirely in observable behaviour within session-level context windows. This manuscript is released as a preprint and is intended for subsequent submission to arXiv and other scholarly venues.