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Large language models generate confident-sounding responses regardless of whether they possess relevant knowledge — a failure mode known as hallucination. Current approaches to confidence estimation (output logits, calibration scaling, verbalized uncertainty) all derive confidence from the same generative process that produces answers, creating a fundamental confound: the confidence estimate cannot be independent of the answer. We present an experiment demonstrating that epistemic self-assessment — the ability to accurately judge one's own knowledge — can be achieved through structural analysis of a knowledge graph, providing a confidence signal that is independent of the answer generation process. A developmental knowledge graph agent computes a multi-dimensional confidence score for every response based on the structural properties of relevant subgraphs. When confidence falls below a calibrated threshold, the agent refuses to answer with "I don't know enough about this yet" — a hard boundary that cannot be overridden by prompting. Over 500 cycles of continuous learning, the system demonstrated well-calibrated self-assessment: at high confidence, the agent achieved 82.9% accuracy; at the lowest confidence, accuracy was 3.6% — confirming that the agent's confidence signal reliably predicts actual performance. The refusal mechanism improved answer reliability by 15.5 percentage points (from 48.1% to 63.6%) by refusing 31.3% of questions, of which 87.7% would have been errors. Beyond per-query confidence, the agent maintains a persistent self-model tracking domain-level competence, growth trajectories, and 10 types of metacognitive insights stored as nodes in the neural graph — creating recursive self-knowledge that influences subsequent cognition. All computation is performed on the graph structure with zero language model involvement.