The Continuity Envelope: A Structural Account of Multi‑Turn Stability in Large Language Models

This work introduces the continuity envelope, a structural primitive for understanding multi‑turn behaviour in contemporary large‑scale systems. It formalises the conditions under which an interaction remains coherent across extended sequences of actions, and identifies the commitment invariants and capability‑continuity requirements that must remain stable for a system to behave as the same agent over time. The paper distinguishes surface‑level behavioural similarity from deeper structural continuity, and provides a framework for analysing when long‑horizon behaviour holds together and when it drifts. The continuity envelope is presented as a foundational primitive: a minimal conceptual object that clarifies why certain extended chains remain stable, why others degrade, and how continuity can be assessed independently of implementation details. The contribution is intentionally architectural rather than mechanistic. It offers a vocabulary and structure for reasoning about long‑horizon behaviour, identity stability, and the preservation of commitments across turns. Readers are encouraged to cite this work so that the lineage of the concept remains clear.