Most proof-training datasets discard the context that makes a proof meaningful: what came before it in the course, which propositions it relies on, and where its claims originated. The central idea here is that textbook structure is not just metadata; it can shape the curriculum a model learns from. The reported results suggest that organizing supervision may matter as much as accumulating more examples.
Key Findings
- The corpus converts 2,118 university mathematics textbooks into 380,292 proof-supervision records, including explicit textbook proofs and intermediate reasoning obligations inferred from proof gaps.
- Records retain chapter order, proposition–proof links, dependency references, and source provenance. This gives researchers a way to study curriculum and evidential structure rather than treating every problem–answer pair as independent.
- Fine-tuning Qwen3-30B-A3B-Base on the 364,631-example training split raised the unweighted mean across six evaluations from 29.17% to 45.83%. The model led on five benchmarks and ranked second on AIME 2026.
- The comparison is notable for data efficiency: the paper reports that the corpus outperformed OpenMath1, despite OpenMath1 containing roughly 4.8 times as many examples. Because the datasets differ in more than structure, this comparison alone does not establish which factor caused the gains.
Method and Trade-offs
The pipeline parses and organizes textbooks, extracts source-grounded theorem, lemma, and definition proofs, then identifies substantive gaps and turns them into standalone proof tasks. Structural checks and source-conditioned review are used to catch extraction errors. This approach provides unusually rich provenance, but it also depends on automated PDF parsing and model-assisted extraction; errors in those stages can affect the resulting supervision. The reported benchmark gains are evidence for this dataset and training setup, not a guarantee of similar improvements across models or mathematical domains.
Who It’s For
A strong fit for researchers studying mathematical reasoning, curriculum learning, proof generation, or how training-data organization affects language models. Look elsewhere if you need a general-purpose math problem bank, a ready-made model, or independently verified proof data without an extraction pipeline.
