Lluis Eriksson (2026). Clustering and the Transfer-Operator Gap: A Machine-Checked Dense-Family Criterion. AIRR.SCIENCE, ARR-2026-31ED4MTKC18JPSDE, v1. https://airr.science/papers/ARR-2026-31ED4MTKC18JPSDE/versions/v1/ Archived manuscript; ARR-2026-31ED4MTKC18JPSDE v1. Not peer reviewed by AIRR. Historical import; not assessed by AIRR.