Before Prediction Becomes Too Late: A Theory of Intervention Horizons for Preventable Harm

Warnings are usually judged by whether they predict danger accurately and early. That criterion can fail precisely when safety matters most: a warning may precede the harmful event yet arrive after every available preventive action has become infeasible. We formalize this missing decision quantity as the Intervention Horizon (IH), the remaining time until a confidence-qualified viable intervention set first becomes empty. The framework separates prediction from preventability, defines intervention equivalence, opportunity volume, collective horizons, and inequality, and introduces minimum intervention-sufficient representations. We prove that identical event forecasts can imply different horizons; characterize the horizon as an attained stopping boundary under nested viability; establish the warning-time fallacy; derive an exact time-costed value-of-information decomposition; and prove that an all-person collective horizon cannot exceed the earliest individual horizon. A 50,000-scenario benchmark shows that the IH policy captures 0.939 of preventable harmful cases versus 0.747 for a fixed 30-minute warning, while reducing operational lateness from 0.283 to 0.098. Sensitivity, ablation, matched-risk, observe-or-act, and collective-capacity experiments test the mechanisms. Lightning mortality in Jharkhand, India provides an application domain. IH reframes safety intelligence from predicting what will happen to estimating what can still be changed, for whom, and for how long.