Refusal as an Optimum: Robust Regulation of a Recovered Dependence Operator under a Per-Coordinate Entropy Budget

How much should a regulator trust a statistical map of a market before acting on it, when most of it is barely pinned down? A companion study recovers the map as an operator whose leading strength marks where a rational bubble can form and certifies which parts the data support. This paper places that operator inside a robust control problem, sizing caution direction by direction with the same test that decides what the data can claim. The best cautious action shrinks as a direction is less identified and hits zero where it is unidentified, so declining to act there is an optimum, not a veto. A mirror case shows caution can instead sharpen action, so the refusal is specific. On eighteen global equity indices it acts on the one identified direction and refuses the rest, without testing the control rule.