Fluent but subtly wrong mathematical solutions can contaminate training, evaluation, and reward-labeling data. We present AEGIS-D (Assessment- and Evidence-Gated Inspection System via Debate), a precision-first multi-agent pipeline for blind verification of competition-level mathematics. Five same-model, role-prompted agents exchange structured arguments, while an assessment gate accepts a candidate only when at least three report positive confirming evidence rather than mere non-refutation. On 195 hard-to-verify variants from 58 IMO/USAMO/Putnam-level problems, a single judge achieves 55.1% precision; AEGIS-D achieves 92.5% precision and 63.8% recall, reducing false positives from 24.7 to 3.0 per run (8.2-fold). A repeated two-by-two factorial associates role prompting with the largest observed false-positive reduction and finds a smaller conditional benefit from gating. Paired round and threshold analyses expose the cost-precision trade-off, and single-run transfers to Omni-MATH and OlymMATH provide preliminary evidence beyond the constructed stress test.

Benchmark performance is the dominant standard for comparing large language models (LLMs), typically summarized by a single aggregate score, such as accuracy, pass rate, or rubric score. This aggregate score provides limited information about a model’s underlying capabilities, yet understanding these capabilities is crucial for model development and evaluation. To this end, we propose Tree-Induced Diagnostic Evaluation (TIDE), which recasts diagnostic evaluation as behavior-driven decision-tree induction to perform fine-grained capability diagnosis. TIDE recursively builds a hierarchical capability tree from benchmark samples and model scores: at each node, an LLM judge proposes candidate splits and performs sample-to-group classification, and behavior-based information gain selects among them. We apply TIDE to five models across four benchmarks to demonstrate its effectiveness, and find fine-grained capability contrasts invisible at the aggregate level: Claude Opus 4.6 achieves 100% on microeconomic market reasoning where GPT-5.4 scores 83.3%, but trails GPT-5.4 on contract law reasoning with 77.8% versus 88.9%. We hope TIDE can be extended to past and future benchmarks so that the rich behavioral signal in evaluation results is fully leveraged for understanding model capabilities.