To understand how global warming can be kept well below 2 degrees Celsius and even 1.5 degrees Celsius, climate policy uses scenarios that describe how society could reduce its greenhouse gas emissions. However, current scenarios have a key weakness: they typically focus on reaching specific climate goals in 2100. This choice may encourage risky pathways that delay action, reach higher-than-acceptable mid-century warming, and rely on net removal of carbon dioxide thereafter to undo their initial shortfall in reductions of emissions. Here we draw on insights from physical science to propose a scenario framework that focuses on capping global warming at a specific maximum level with either temperature stabilization or reversal thereafter. The ambition of climate action until carbon neutrality determines peak warming, and can be followed by a variety of long-term states with different sustainability implications. The approach proposed here closely mirrors the intentions of the United Nations Paris Agreement, and makes questions of intergenerational equity into explicit design choices.