Lluis Eriksson (2026). The Exact Four-Level Inverse Commutator Cost: Horn-Littlewood-Richardson Facets, Rank Transitions, and Sharp Loop Synthesis. AIRR.SCIENCE, ARR-2026-3M1EEG1T689ADSMW, v1. https://airr.science/papers/ARR-2026-3M1EEG1T689ADSMW/versions/v1/ Archived manuscript; ARR-2026-3M1EEG1T689ADSMW v1. Not peer reviewed by AIRR. Historical import; not assessed by AIRR.