Skills provide LLM agents with reusable procedural knowledge, making appropriate skill selection essential for reliable agent behavior. As skill libraries expand, distinguishing semantically similar candidates becomes increasingly difficult. Existing methods encode or rewrite skill descriptions for relevance-based ranking, yet heterogeneous descriptions can obscure capability differences. To address this challenge, we propose SKALOS, a graph-native reranker that compares skills via explicit capability evidence. Its multi-hierarchy graph aligns equivalent expressions across skills while preserving skill-specific capability evidence. Since individually relevant capability elements may not jointly support a query, semiring-based capability witness learning scores each branch by its weakest evidence, checks joint support for the extracted requirements within one implementation, and selects the strongest alternative. To reduce the influence of extraction errors, we develop ranking-feedback graph calibration that adjusts unreliable evidence for candidate comparison. Experiments on SkillRet show that SKALOS improves NDCG@10 by 2.68 percentage points over a matched text-only reranker. Witness-guided skill selection also increases ALFWorld task success rate from 22% to 29%.

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