Retrieval systems return scored answers, but a high score does not show that an answer should be trusted. The proposed training-free abstention method applies the boundary cut to the selected evidence in an evidence graph. The signal is the weighted cut between selected and unselected candidates and requires no correctness labels or confidence-model training. On MemoryAgentBench (MAB) FactConsolidation multi-hop, with unresolved queries ranked last for every selector, it raises area under the precision-coverage curve from 0.736 for the best score baseline to 0.785 (+0.049, 95% CI [+0.008, +0.092]); under the native evaluation, where score baselines keep their unresolved values, the gap is +0.108. A zero-cut subset contains 71 of 400 queries at 100% observed precision. In this pipeline, the subset corresponds to structural closure; controlled analyses attribute much of the remaining separation to resolution status, with little benefit from continuous edge weights. Across external benchmarks, usefulness varies with graph construction, edge semantics, and relation; typed structure alone does not ensure useful confidence. A supervised gradient-boosted selector achieves 0.814 versus the boundary cut's 0.785 when the retrieval stack matches. These findings provide empirical guidance for using available evidence graphs for lightweight, auditable post-retrieval abstention without additional model inference.

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