The Viability of an Adaptive Economy: A viability functional, and why recoverability is its boundary

When is an economy that keeps learning and changing still a system we can hope to keep going? This paper poses that as a question of viability: the largest set of states from which the economy can be kept inside safe limits forever, using only the interventions the data actually support. The main finding is that survival hinges on recoverability, whether comovement data still reveal enough of the economy's dependence structure to steer it. When that structure erodes, the economy becomes unsteerable and fails at a sharp threshold, even before any visible limit is crossed. The results are mathematical theorems, not an empirical test; the analysis illustrates rather than measures, and treats recoverability as the binding constraint by assumption.