citation Angeltveit & McKay (2024, arXiv:2409.15709) reduced the upper bound from 48 (their 2016 result, itself down from 49 in 1997) to 46, via linear programming plus a large computer case-check; both authors independently implemented the computational parts with consistent results. As of 2026 this is a preprint (revised v2, Sep 2025), not yet journal-published -- treat the bound as strong but not fully peer-reviewed. Predecessor bound R(5,5)<=48 appears as [AnM1] in survey DS1.