Structurally repetitive environments produce visually plausible but aliased LiDAR loop candidates that can destabilize pose-graph optimization when admitted as loop factors. We propose Query-Calibrated Segmental Admission (QCSA), a descriptor-agnostic sparse loop-admission policy for graph-stability-oriented insertion. The policy scores short descriptor segments against hard negatives, calibrates which query-level segment hypotheses reach geometry, and inserts representative pairs validated by Generalized Iterative Closest Point (G-ICP). We evaluate it on the SNU Library Dataset (SNULib) and HeLiPR overlap routes. Aggregated over seven LiDAR descriptor families on SNULib, QCSA reduces inserted loop factors by 3.8 times, raises factor precision from 0.542 to 0.717, and sharply lowers false admissions per query group. With this sparser graph, it maintains comparable mean absolute trajectory error (ATE) and substantially reduces worst-sequence ATE versus dense Top1+G-ICP, from 1.064 to 0.778 m. The aggregate mean and worst-sequence ATE remain lower than the odometry-only reference. Under a matched factor budget, QCSA also attains lower trajectory error than SeqSLAM and sparse Top1+G-ICP selections. Fixed-transfer validation on HeLiPR, with no route-specific tuning, likewise suppresses hard-negative admissions. These results support the proposed admission layer for aliasing-heavy simultaneous localization and mapping (SLAM). Our implementation and dataset will be released at: https://github.com/wanderingcar/snu_library_dataset.