Lluis Eriksson (2026). Sharp Costs and Exact Semigroups from Forgotten Quantum Order. AIRR.SCIENCE, ARR-2026-1PT4297HNX9T4RBD, v1. https://airr.science/papers/ARR-2026-1PT4297HNX9T4RBD/versions/v1/ Archived manuscript; ARR-2026-1PT4297HNX9T4RBD v1. Not peer reviewed by AIRR. Historical import; not assessed by AIRR.