Skill Is Not Document: Query-Conditioned Compatibility for LLM Agent Skill Routing

Large language model agents increasingly rely on reusable skills, making skill retrieval a critical front-end component of agent systems. Skill retrieval, however, is not ordinary document retrieval: a useful top-$K$ result must contain individually relevant skills that also form an executable set for the current query. Existing benchmarks and training pipelines largely supervise pairwise relevance and discard the rejection decisions produced when a language model judges a sampled skill combination to be implausible. We introduce R3-Skill, a Chinese--English benchmark that retains these rejections as query-conditioned compatibility supervision. R3-Skill contains 10,246 deduplicated skills, 41,592 accepted queries, and 32,828 rejected annotations across four language directions; all multi-skill test labels were independently reviewed by multiple experts, and 15,962 parseable rejections are organized into an eight-class taxonomy. We further propose a two-stage system composed of R3-Embedding, a multi-positive bi-encoder for large-pool recall, and R3-Reranker, a cross-encoder trained with graded ListNet supervision. Our analysis shows that this signal is stage-dependent, helping cross-encoder reranking while providing no benefit for the tested bi-encoder objective. On R3-Skill, the complete pipeline achieves $75.39\%$ Hit@1, $81.97\%$ NDCG@10, and $33.27\%$ Set-Compat, a $36.6\%$ relative gain over the strongest reranking baseline. It also obtains $83.87\%$ NDCG@10 on SkillRet, demonstrating transfer beyond R3-Skill.