How fast to turn around: preventing tipping after a system has crossed a climate tipping threshold

A classical scenario for tipping is that a dynamical system experiences a slow parameter drift across a fold tipping point, caused by a run-away positive
feedback loop. We study what happens if one turns around after one has crossed the threshold. We derive a simple criterion that relates how far the parameter exceeds the tipping threshold maximally and how long the parameter stays above the threshold to avoid tipping in an inverse-square law to observable properties of the dynamical system near the fold. We demonstrate the inverse-square law relationship using simple models of recognised potential future tipping points in the climate system.