Financial research agents can generate and monitor trading rules faster than a human can document the resulting selection process. Candidates appear at data-dependent times, weak rules are abandoned, and promising ones are watched until they cross a reporting threshold. We introduce PROMOTE, a protocol that assigns every candidate predictable testing wealth at birth and accumulates a cost-aware e-process only from subsequent returns. If lifetime allocations sum to at most one, a weighted Ville argument bounds the probability of ever promoting a rule whose declared bounded net score has always had nonpositive conditional mean. The result permits dependent candidates, adaptive births, and indefinite monitoring. We audit the implementation in two settings. A retrospective pseudo-out-of-sample replay contains 24 panel--rule hypotheses, 3,000 shared-sign null paths, injected alternatives, and public ETF and industry data. Repeated unadjusted tests produce a family crossing in 94.5% of null paths, versus 0.0% for PROMOTE; at a 15-bp aligned ETF-component perturbation, PROMOTE has 70.1% target power and median crossing session 2,327. A separate exact mean-zero experiment lets an agent select candidate identities and birth times from past scores; the funded gate has 1.77% false-family crossings across 3,000 programs. The market replay produces zero promotions after costs. The certificate controls historical false promotion under the declared null; it is not a certificate that an earlier edge remains profitable at deployment. AI-use disclosure. Generative AI tools, including OpenAI Codex, assisted manuscript preparation. For this preprint version, Codex assisted with LaTeX editing, author and venue metadata, compilation, and layout checks.
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