Open-ended scientific discovery asks agents to move beyond executing analyses for predefined questions. Across multiple rounds of exploration, a discovery agent must decide which phenomena warrant investigation while avoiding overinterpretation, where emerging claims exceed the evidential scope of the analyses. This creates an evidence-calibration problem: the exploration trajectory must be coupled with claim status so that evidence can guide both what to investigate next and what can be claimed. We introduce StatefulDiscovery, a discovery framework that externalizes investigation state and uses it to coordinate frontier selection, evidence acquisition, and claim adjudication. We evaluate StatefulDiscovery across 40 real-data discovery tasks. Compared with several baselines, StatefulDiscovery produces more claims overall judged to be both well-supported and high-value. Ablations indicate distinct roles for structured hypotheses, local adjudication, frontier control and persistent states. Together, these results suggest that explicit discovery state can couple exploration with evidence-calibrated claim formation.

Scientific discovery workflows rely heavily on lab notes, where researchers record observations, interpret uncertain results, and plan follow-up experiments. Unlike polished publications, lab notes preserve evolving scientific reasoning, tacit scientific knowledge, and author uncertainty, giving AI agents access to the process of science. However, most prior work on scientific text focuses on papers, protocols, or structured databases, leaving informal laboratory notes underexplored as inputs to AI agents for science. This gap matters because tacit knowledge in lab notes is not written as a clean set of instructions: validated observations, tentative judgments, and possible experimental next steps often appear in the same passage. If these signals are conflated, an AI agent may mistake uncertain scientific judgments for confirmed conclusions or executable actions. To this end, we present Notes2Skills, a two-stage framework for turning lab notebooks into verifiable skills for scientific AI agents while preserving the author’s certainty. Across three wet-lab sessions and seven original downstream configurations, Notes2Skills is the only tested configuration that avoids both observed regime-level failures: over-acting on uncertain notes and missing firm directives. We show that certainty preservation is a key missing piece between lab notebooks and reliable agent skills, opening a path toward safer AI co-scientist systems.

Long-context inference remains challenging for large language models due to attention dilution and out-of-distribution degradation. Context selection mitigates this limitation by attending to a subset of key-value cache entries, yet most methods allocate a fixed context budget throughout decoding despite highly non-uniform token-level contextual demands. To address this issue, we propose Uncertainty-Triggered Adaptive Context Allocation (UT-ACA), an inference-time framework that dynamically adjusts the context window based on token-wise uncertainty. UT-ACA learns an uncertainty detector that combines semantic embeddings with logit-based confidence while accounting for uncertainty accumulation across decoding steps. When insufficient evidence is indicated, UT-ACA selectively rolls back, expands the context window, and regenerates the token with additional support. Experiments show that UT-ACA substantially reduces average context usage while preserving generation quality in long-context settings. Code and dataset are available at https://github.com/Tommy307/UT-ACA.