Red-team evaluations of AI models support some claims and not others, and the boundary between the two is calculable rather than merely a matter of judgment. We define the evidential ceiling of an evaluation as the largest factor by which one result can move belief under a fixed testing budget, derive it in closed form for the benchmark null result, and use it to locate that boundary exactly. We find that above a calculable harm rate, a benchmark of modest size certifies a category to a stated evidentiary standard, and a clean sheet is then the stronger of the two possible observations, outweighing a single reproduced failure. Below that rate, no passive benchmark of feasible size provides the specified evidence of safety under the fixed scoring rule and approximately independent trial structure. The crossing between the two regimes has a closed form. The bound is not specific to benchmarks: written in terms of a procedure's hypothesis conditioned elicitation rates, it covers adaptive and automated red teaming as well, and shows that discrimination between the hypotheses rather than attack success is what determines evidential worth. Auditing eight evaluation suites against the boundary, we find that current benchmarks are adequate for high-frequency harm categories and several orders of magnitude short for rare, catastrophic ones. Safety benchmarks are not uninformative. They are informative about a specific and computable set of propositions, and the discipline they need is to state which.
Nuclear Magnetic Resonance (NMR) spectroscopy is the gold standard for molecular structure elucidation, yet interpreting complex spectra for unknown molecules remains a bottleneck reliant on human expertise. While artificial intelligence has advanced this field, current methods face a critical trade-off: database retrieval cannot identify novel scaffolds, while de novo molecular structure elucidation models operate as black boxes, lacking the atom-level interpretability required for rigorous scientific validation. Here, we present NMRAgent, an evidential reasoning agent powered by large language models (LLMs) that bridges this gap by integrating specialized spectral analysis tools with chemical knowledge graphs. Unlike previous approaches, NMRAgent mimics the deductive reasoning of human experts: it takes experimental NMR spectra and molecular formula as input, plans the elucidation process, proposes candidate structures, verifies peak-atom consistency, and refines misaligned substructure through formula-aware fragment optimization. Enabled by its evidential reasoning, NMRAgent outperforms state-of-the-art methods, improving top-1 accuracy by 46.5% and Tanimoto similarity by 0.502 on a scaffold-split benchmark with novel scaffolds in the test set. Besides, we demonstrate the agent's practical utility by elucidating the structures of two previously unknown natural products isolated from Hydrangea davidii and Vitex trifolia, and by correcting structural misassignments in established literature. By combining high-accuracy prediction with transparent and evidence-based reasoning, NMRAgent establishes a new paradigm for interpretable AI in analytical chemistry.