ClaimScope: Label-Blind Witness Verification for Mathematical Claim Auditing

We present ThinknCheck, a 1B-parameter verifier for grounded claim verification that first produces a short, structured rationale and then a binary verdict. We construct LLMAggreFact-Think, a 24.1k reasoning-augmented training set derived from LLMAggreFact, and fine-tune a 4-bit Gemma3 model to follow this format. On LLMAggreFact, ThinknCheck attains 78.1 balanced accuracy (BAcc), surpassing MiniCheck-7B (77.4) with 7x fewer parameters; removing the reasoning step reduces BAcc to 57.5. On SciFact, ThinknCheck reaches 64.7 BAcc, a +14.7 absolute gain over MiniCheck-7B. By contrast, zero-shot chain-of-thought on the base Gemma3-1B harms accuracy relative to direct answers, and preference optimization with a simple format+accuracy reward underperforms supervised reasoning. To probe the latter, we introduce GSMClaims and a domain-specialized variant, ThinknCheck-Science, which improves across benchmarks, including 61.0% accuracy on GSMClaims. Overall, explicit, supervised reasoning enables compact verifiers that are competitive while remaining resource-efficient and interpretable.

Despite rapid progress in claim verification, we lack a systematic understanding of what reasoning these benchmarks actually exercise. We generate structured reasoning traces for 24K claim-verification examples across 9 datasets using GPT-4o-mini and find that direct evidence extraction dominates, while multi-sentence synthesis and numerical reasoning are severely under-represented. A dataset-level breakdown reveals stark biases: some datasets almost exclusively test lexical matching, while others require information synthesis in roughly half of cases. Using a compact 1B-parameter reasoning verifier, we further characterize five error types and show that error profiles vary dramatically by domain -- general-domain verification is dominated by lexical overlap bias, scientific verification by overcautiousness, and mathematical verification by arithmetic reasoning failures. Our findings suggest that high benchmark scores primarily reflect retrieval-plus-entailment ability. We outline recommendations for building more challenging evaluation suites that better test the reasoning capabilities verification systems need.

Reasoning language models are trained to produce solutions, not to refuse them, and this bias persists when the problem they are handed is false. Asked to prove a corrupted theorem, a strong model will typically comply and produce a confident derivation of something untrue. We present Euston, an 8B mathematical claim-verification model trained to resist exactly this. Training data were generated with GraphSynth, a probabilistic factor-graph generator that couples attribute-level diversity to decode-time structural masking and span-synchronized verification, yielding 3{,}026 matched true/corrupted statement pairs (6,052 statements) drawn from arXiv papers spanning 2010--2025. We fine-tuned DeepSeek-R1-8B with GRPO under a rule-based, zero-API reward for 189 steps on four H100 GPUs. On a balanced 200-true/200-false held-out split, balanced accuracy rises from 29.50% to 63.75% and the discrimination gap---the difference between the rate of calling false statements false and the rate of calling true statements false moves from -0.5% (z=-0.1) to +27.5% (z=+6.0). Critically, the gain is not purchased with general mathematical ability: AIME 2026 accuracy under official semantics is 65.00% against a 69.17% base, a difference of -4.17% that is not statistically significant, whereas an earlier run of the same recipe on a smaller GraphSynth corpus collapsed to 40.00%. Median response length also falls from 19,217 to 18,296 tokens and the truncation rate from 25.8% to 8.3%, so the improvement does not come from thinking longer. We report the result together with the confounds that bound its interpretation, principally the all-false composition of the official evaluation sets and the low precision implied at realistic error prevalence.