Taxonomy induction aims to organize concept sets into coherent hierarchical structures. Recent LLM-based methods can induce taxonomies directly from flat term lists, avoiding the need for corpora, but degrade sharply as concept sets scale up. We argue that this degradation stems not only from context length limitations, but also from structural failures in hierarchical reasoning. To address this, we adopt a divide-and-merge paradigm that partitions concepts into smaller subsets, induces local taxonomies, and merges them into a global hierarchy. However, we identify two structural failure modes inherent to this paradigm: Structural Fragmentation, where partitioning weakens local hierarchical signals, and Parent Displacement, where locally plausible relations are misplaced in the global hierarchy. To address both, we propose SPARROW, a scalable taxonomy induction framework that combines structure-preserving spectral partitioning to retain hierarchical connectivity within each block, and constraint-guided incremental fusion that treats block-level relations as structural constraints rather than ground truth for global placement. Experiments on large-scale benchmarks show that SPARROW consistently achieves the strongest global structural quality, as measured by Ancestor F1, across backbones. The code is available at https://github.com/rebeccazyr/SPARROW.

Half-truths, claims that are factually correct yet misleading due to omitted context, remain a blind spot for fact verification systems focused on explicit falsehoods. Addressing such omission-based manipulation requires reasoning not only about what is said, but also about what is left unsaid. We propose RADAR, a role-anchored multi-agent debate framework for omission-aware fact verification under realistic, noisy retrieval. RADAR assigns complementary roles to a Politician and a Scientist, who reason adversarially over shared retrieved evidence, moderated by a neutral Judge. A dual-threshold early termination controller adaptively decides when sufficient reasoning has been reached to issue a verdict. Experiments show that RADAR consistently outperforms strong single- and multi-agent baselines across datasets and backbones, improving omission detection accuracy while reducing reasoning cost. These results demonstrate that role-anchored, retrieval-grounded debate with adaptive control is an effective and scalable framework for uncovering missing context in fact verification. The code is available at https://github.com/tangyixuan/RADAR.