On the Boundary of Admission Gates: An Injected-Truth Study of Falsification-First Selection in Quantitative Strategy Research

Adaptive model search is path dependent: once a challenger is adopted, it becomes the reference from which later candidates are generated. A statistically unsupported replacement can therefore alter hypotheses that have not yet been proposed. We introduce Evidence-Gated Research (EGR), a statistical adoption layer for moving-incumbent search. EGR freezes each challenger before decision evidence is revealed, builds anytime-valid evidence across a predeclared set of environments, routes evidence predictably toward unresolved components, composes a persistent candidate e-value, and passes that e-value to an online controller. Under explicit conditional-validity and predictability conditions, the resulting procedure controls false discovery rate for the declared all-environment adoption target even though earlier adoptions change later challengers. In a 5,000-trajectory closed-loop benchmark, development-only e-LOND attains persistent FDR 0.621, whereas no persistent false-adoption path is observed for the audited EGR variants in that finite run. In matched replay over 600 challenger--incumbent pairs, Stagewise EGR preserves fixed-anytime alternative crossing decisions while using 56.1% less decision evidence at the representative threshold. A three-environment public-data study and a 40,000-sample controlled neural benchmark reproduce the evidence-efficiency pattern. These results identify model replacement as a distinct statistical control point in adaptive model development.

Scientific discovery relies on large-scale hypothesis testing. However, the capacity to identify true discoveries while controlling false discovery faces major challenges: obtaining relevant reference data (the null distribution) is resource-intensive, leaving finite-data uncertainty, and the procedure should account for the inherent structure in the hypothesis space, when such structure exists. Here, we present a framework for controlling the false discovery rate both when each hypothesis is evidenced only by a finite count of null draws, leaving its p-value uncertain, and when the hypothesis space carries arbitrary structure, requiring only that the structure be represented through a suitable reproducing kernel. We present two decision rules that are both robust to structural mis-specification, yet offer a distinct trade-off between exact FDR control and statistical power. The first rule guarantees exact FDR control; the second maximizes power by adapting mirror-statistic control into count space, utilizing an analytical framework to assess FDR control when exact mirror symmetry is relaxed. Furthermore, the tractability gained by the RKHS framework allows us to directly investigate finite-data uncertainties, which we leverage to suggest a policy for the efficient allocation of null distribution samples.

Modern applications of conformal inference to multiple testing problems, such as outlier detection and candidate selection, often involve selecting test samples whose conformal p-values fall below a threshold. The quality of such methods is often measured by the false discovery proportion (FDP), defined as the fraction of incorrect selections. Existing approaches typically control the expected value of the FDP, using methods such as the Benjamini-Hochberg procedure. This approach fails to provide high-probability bounds on the realized false discovery proportion and invalidates statistical guarantees if the rejection threshold is selected after inspecting the data. This paper establishes finite-sample, distribution-free upper bounds on the FDP that hold simultaneously over all possible rejection thresholds, enabling arbitrary post hoc selection of the threshold. Simultaneous validity is achieved by constructing a high-probability envelope for the empirical distribution function of null conformal p-values by sampling from their joint distribution. Furthermore, our framework allows practitioners to modulate the envelope's shape, thereby producing tight bounds in rejection regions of primary interest. We use this flexible approach to derive simultaneous FDP upper bounds for both outlier detection and conformal selection. We demonstrate through synthetic and real-data experiments that the resulting bounds are both valid and substantially less conservative than those derived from existing approaches.