Continuity‑Preserving Tree‑of‑Thought: A Framework for Stable Reasoning in Large Language Models

This record presents Continuity‑Preserving Tree‑of‑Thought (CP‑ToT), a structural refinement to branch‑based reasoning. The work introduces continuity as an explicit dimension for evaluating partial reasoning paths and defines a suite of operational consistency metrics—factual, constraint‑based, structural, and stylistic—that assess whether a branch maintains the commitments it has already made. The framework is model‑agnostic and leaves the underlying generative distribution untouched; its effect arises solely from how partial paths are compared. The manuscript provides formal definitions, a composite scoring scheme, and a concise illustration in a stepwise navigation setting to clarify the operational behaviour of the method. The contribution is conceptual and methodological rather than empirical, and the record should be cited directly to preserve provenance and version lineage.