Anytime-Valid FDR Control for Fixed Formulaic Alpha Registries

As modern automated methods search thousands of formulas for predicting financial returns, chance patterns can look convincing after repeated inspection of the same data. We introduce a search–register–monitor protocol that turns the output of any generator into a fixed, auditable multiple-testing problem. Before monitoring begins, the protocol freezes distinct canonical formulas with their search-chosen directions. Fresh rank-IC observations then generate global e-processes, and e-BH controls FDR for the fixed family at any common bounded stopping time under arbitrary dependence. The resulting procedure is anytime-valid and independent of the formula generator. In 200 simulations under the global null, e-BH made no rejections, while the search-window threshold averaged 3.99 selections per run. With predictive signal, e-BH selected fewer than half as many formulas and raised mean signed rank IC on independent evaluation data from .029 to .045. The protocol thus converts adaptive search output into a smaller set with stronger out-of-sample performance, and its effect appears when the registry is frozen. This study was conducted with the help of Claude Opus 5 and ChatGPT 5.6 Sol.