Conjecture Context Ablation: dataset for "Which Mathematical Context Supports Target-Aligned Conjecture Generation? A Paired Ablation Study"

Supplementary data for a paired ablation of mathematical context in conjecture generation: 61 main theorems from 12 arXiv mathematics papers (math.AC, math.AG, math.CO, math.ST), each under 13 context conditions (full context, six leave-one-out and six single-component), for 793 generated conjectures with theorem maps, redacted seeds, DeepEval alignment and quality scores, an expert-validation set, cross-model judge agreement data, the aggregate analysis workbook, prompts and evaluation code.

Dataset accompanying the paper Which Mathematical Context Supports Target-Aligned Conjecture Generation? A Paired Ablation Study, 4th Workshop on Mathematical Natural Language Processing (MathNLP 2026), EMNLP 2026 (https://www.carlostoxtli.com/papers/mathnlp2026-which-mathematical-context.pdf).

Paper abstract. Generating mathematical conjectures from natural-language context is challenging because theorem-relevant information is distributed across multiple forms of mathematical context, including definitions, objects, assumptions, and constructions. We study which of these contextual signals help a model recover the specific claim supported by the surrounding setup, using 61 main theorems from 12 papers across four mathematical domains. For each theorem, we redact the result and represent the remaining setup using six context components. A paired ablation design compares full context, six leave-one-out conditions, and six single-component conditions, yielding 793 generated conjectures. Context components were largely complementary: removing one component usually had little effect, whereas retaining only one substantially reduced expected-theorem alignment. Local Mathematical Objects provided the strongest standalone signal, while Structural Constraints and Conditions produced the largest alignment decrease when removed. These findings suggest that target-aligned conjecture generation depends on combining information that identifies relevant objects with information that constrains admissible claims.

Known limitations.

• Theorem maps and redacted seeds quote short excerpts of the 12 source arXiv papers; the source PDFs/LaTeX are not redistributed (see sources/README.md for citations).

License: Creative Commons Attribution 4.0 International (https://creativecommons.org/licenses/by/4.0/). Source code files are released under the MIT License.