# Data statement

## Summary

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.

## Composition

- 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.

Selection indexes and source-file hashes are recorded in `MANIFEST.json`. The private source pools are not included.

## Authorship and sources

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.

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.

## Novelty and mathematical status

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.

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.

## Personal and sensitive data

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.

## Public/hidden separation

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.

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.

## Known limitations

- 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.