External skills provide domain knowledge and procedures without updating model parameters, but flat collections obscure skill applicability, dependencies, and composition. Graphs organize skills into addressable nodes and explicit relations, supporting selection and composition. Yet existing skill-graph methods use this structure mainly for retrieval, rather than to localize updates, scope retesting, or precisely roll back rejected changes. We introduce GRAPHSKILLAA (GraphSkill Abductive Attribution), which uses one addressable graph for skill selection, execution, failure attribution, targeted updating, validation, and rollback. Nodes separate applicability, execution, and exclusion conditions; typed edges encode prerequisite and enhancement relations. The frozen student records used nodes and edges, while the teacher contrasts related successes and failures to route each supported repair to the smallest relevant field or relation; execution lapses or insufficient evidence leave the graph unchanged. A Local Gate retests affected examples, while a Big Gate evaluates the merged graph on the complete update pool; rejected changes are rolled back. With GPT-5.6-sol, GRAPHSKILLAA reaches 81.5%, 66.7%, and 91.2% on SearchQA, LiveMath, and DocVQA, respectively, and attains the highest observed mean in every main setting. These results show that object-level attribution and graph-scoped validation make a skill graph a locally optimizable, testable, and reversible external state.

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