Euston: Training Away Mathematical Sycophancy Without Losing the Mathematics

Zehua Cheng, Wei Dai, Jiahao Sun

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…