A scientific foundation is required to establish nations’ responsibilities in a hotter ‘overshoot’ world. Around ten years after the Paris climate agreement was adopted, the world is again at a crucial moment. In 2015, 195 countries committed to hold global warming “well below 2 °C” and to “pursue efforts to limit warming to 1.5 °C” to prevent dangerous human interference with the climate system. How to interpret these two temperature levels was ambiguous, but it was clear that both had not yet been reached and were being pursued from below. At the time, pathways to stay below both levels could be modelled3, but much has changed since then.