Certified Alpha Capacity: Statistical Arbitrage When Learning Takes Time

Statistical validation takes time, and alpha can decay before the evidence justifies deployment. We quantify the surviving opportunity through Certified Alpha Capacity: the maximum expected value remaining under prescribed false-deployment and power constraints. In a canonical Gaussian experiment, we derive an exact certification frontier and the sharp law $\mathcal K_{\alpha,\beta}/\log(1/\varepsilon)$ for residual information capacity just above it. Near the frontier, a single interim decision can preserve orders of magnitude more capacity than fixed-time testing. Mapping information into cash reveals why equally certifiable signals can retain different economic values. In the specified competitive equilibrium, lifetime information approaches the certification frontier exponentially as research costs vanish.