Decision Transparency: When Can a Black-Box Decision Reveal Its Hidden Information?

A good decision can be correct for the wrong reason. Decision quality asks whether an action performs well. Decision transparency asks what the released action reveals about the information that shaped it. This is a missing evaluation dimension for black-box decision systems. We call this method FanOpt, a public regret-to-evidence compiler. It makes decision transparency testable from one action under a structured alternative. If the null and alternative induce the same action law, no action-only test can have power above its Type-I error. FanOpt breaks this barrier when low regret meets a public geometric contract. Before private observations arrive, the public evaluator fixes a source-independent baseline and a public distance. Under the null, low regret keeps the returned action near the baseline. Under a structured alternative, low regret forces the action away because remaining near the baseline gives up the information-dependent utility gain. A fixed distance threshold can then turn one released action into statistical evidence. We prove finite-sample Type I and Type II error bounds and an explicit certified regret radius. A marginal-load bound carries estimation and rounding error into the regret condition required by the test. We give certificates for 2-factors and the stated spanning-tree policy. Matching also fits the framework when its family certificate holds. In controlled experiments, power rises from 16.0% at q = 1 to 100.0% at q = 2, while none of 2,196 low-regret outputs falls on the wrong side of the public threshold. These results show when one black-box combinatorial decision provides valid decision-transparency evidence under a structured alternative. The test does not need the private model, objective, or solver trace.