| # Data statement |
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| ## Summary |
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| This is a deliberately small public showcase of 20 internally authored mathematics tasks. It is not a random or representative sample of all Ulam.ai work. Selection optimized for domain breadth, statement quality, verifiability, research depth, and usefulness in demonstrating long-horizon mathematical RL. |
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| ## Composition |
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| - Five records were selected from a pool of 149 Erdős-inspired variants. |
| - All ten records in the AIM-AG client sample were retained. |
| - Five records were selected from a pool of 139 bounded object-finding variants inspired by conjectures. |
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| Selection indexes and source-file hashes are recorded in `MANIFEST.json`. The private source pools are not included. |
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| ## Authorship and sources |
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| The released prompts, discussions, RL metadata, schemas, and packaging were authored internally at Ulam.ai. Some tasks identify a classical conjecture or published theorem as mathematical inspiration. Those labels establish lineage; the variants are not presented as canonical transcriptions of the source problems. |
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| The AIM-AG records include bibliographic references used to describe their literature boundary. Citation does not imply endorsement, and cited works are not redistributed in this dataset. |
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| ## Novelty and mathematical status |
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| Each headline task is a candidate research problem. Targeted searches and internal review cannot prove global novelty. Literature boundaries, open/closed status, and attribution should be refreshed by a qualified domain expert before a claimed solution or commercial evaluation is treated as final. |
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| The counterexample-oriented stream uses bounded finite searches. Depending on the optimum, some tasks may produce an actual counterexample in the specified subclass, while others yield only a certified near-miss. The formulation does not preassert either result. |
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| ## Personal and sensitive data |
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| The dataset contains no intended personal data, user conversations, or private customer material. It contains author names and publication metadata only where needed for scholarly citation. |
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| ## Public/hidden separation |
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| The RL companion is policy-visible material only. Grader-only research guidance, hidden targets, hidden fixtures, calibration answers, and expert reviews from the internal production package are excluded. This public sample must not be treated as a secret held-out evaluation set. |
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| The included train/dev/eval labels are organizational. Every included prompt and fixture is public, and the public curriculum configuration explicitly overrides production-language that could otherwise imply holdout status. |
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| ## Known limitations |
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| - Twenty tasks are too few for claims about broad model capability. |
| - Domain coverage is intentionally weighted toward advanced pure mathematics. |
| - Most terminal tasks require expert judgment and do not have canonical known answers. |
| - Machine-checkable milestones can certify only their stated subproblems. |
| - Public prompts can enter model training corpora, so future evaluations should use fresh private variants. |
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