Interactive agents can turn experience into reusable skills, yet existing self-evolving skill libraries primarily improve by accumulating new knowledge. Failures may lead to new skills, while previously stored skills are less often revisited as new evidence arrives. However, growth alone does not ensure reliability, as a retrieved skill may be inapplicable under the current task conditions, and an existing skill may encode a mis-specified operational boundary. Reliable skill evolution therefore requires not only adding knowledge, but also testing and revising what is already stored. We introduce Skill-V, a verifiable self-evolving skill library. To make stored knowledge testable, we propose representing skills as versioned, falsifiable contracts that link semantic intent to observable behavioral criteria. We use environment outcomes to drive library evolution. Specifically, task failures motivate skill addition, while disagreements between contract evaluations and task outcomes guide revisions to existing skill boundaries. To validate these revisions, we require them to preserve protected semantic constraints and satisfy non-regression criteria for rubric-outcome metrics on historical replay evidence. Finally, we employ an applicability-aware filter to exclude candidates judged confidently inapplicable to the current task. Across ALFWorld and WebShop, Skill-V achieves success rates of 95.3% and 85.9%, respectively, while maintaining a more compact skill library than growth-oriented baselines. Applicability-aware filtering reduces incorrect skill invocations, and outcome-grounded revisions correct mis-specified skill boundaries without degrading performance on previously observed evidence. These results show that reliable skill evolution requires more than accumulating experience: the library must learn which knowledge to retain, when to revise it, and when it should be applied.

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