97,497 benchmark-formatted items: 35,274 numerical + 62,223 yes/no from ArXivOpenProblems

README.md

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+---
+license: cc-by-4.0
+task_categories:
+- question-answering
+language:
+- en
+tags:
+- mathematics
+- arxiv
+- open-problems
+- benchmark-format
+size_categories:
+- 10K<n<100K
+configs:
+- config_name: numerical
+  data_files:
+  - split: train
+    path: data/numerical-*.parquet
+- config_name: yesno
+  data_files:
+  - split: train
+    path: data/yesno-*.parquet
+---
+
+# ArXivOpenProblems — Benchmark Formats
+
+**97,497 research-level mathematics questions reformatted into benchmark-shaped items**,
+derived from [`amphora/ArXivOpenProblems`](https://huggingface.co/datasets/amphora/ArXivOpenProblems).
+
+Two configs:
+
+| config | rows | the answer is |
+|---|---:|---|
+| `numerical` | **35,274** | a single number |
+| `yesno` | **62,223** | Yes or No |
+
+## ⚠️ There are no answer keys
+
+Every item derives from a **future-work or open-problem statement** in an arXiv paper. The
+answers are, by construction, **not known** — not to the source paper and in most cases not to
+the literature. This is a corpus of *well-posed unanswered questions*, **not a scoreable
+benchmark**. Do not use it to compute accuracy without sourcing answers independently.
+
+## How a research question becomes a number
+
+Most source questions ask whether something holds, not for a value. The conversion uses seven
+routes; `route` records which was applied.
+
+| route | construction | share of `numerical` |
+|---|---|---:|
+| **B** | minimal counterexample: "smallest *p* at which the property fails; −1 if none" | **80.8%** |
+| E | size of the exceptional set (0 = the original's "yes") | 6.6% |
+| A | the question already asked for a quantity | 6.0% |
+| C | the sharp constant in an inequality | 2.5% |
+| D | the critical value of a continuous parameter | 2.4% |
+| G | count of a finite classification | 1.4% |
+| F | minimal/maximal multiplicity or order (1 = the original's "yes") | 0.3% |
+
+Route B dominates. `distinguished_value` gives the number corresponding to the original
+question's "yes" — usually `-1`.
+
+**Route B strengthens the problem.** "Is there a counterexample?" and "what is the smallest
+counterexample?" are different questions; the second is strictly harder. The reformulation is
+faithful in that the distinguished value is equivalent to the original's affirmative answer,
+but the item is not of equal difficulty to its source.
+
+## Fields
+
+| field | description |
+|---|---|
+| `uid` | `<arxiv_id>#<index>`, joins to the source dataset |
+| `arxiv_id`, `paper_url` | provenance |
+| `primary_category` | arXiv category of the source paper |
+| `signal_type` | source statement type: `conjecture`, `limitation`, `open_problem`, `natural_extension`, `announced_forthcoming` |
+| `question_category` | logical shape of the **original** question (see below) |
+| `format` | `numerical` or `yesno` |
+| `route` | `A`–`G` for numerical items, `null` for yes/no |
+| `question` | the reformatted item |
+| `answer_convention` | one sentence on what the answer means |
+| `distinguished_value` | number equal to the original's "yes", or `null` |
+| `source_question` | the unmodified original |
+| `engine` | `openai/gpt-6-sol` |
+
+`question_category` is one of `universality`, `existence`, `extension`, `characterization`,
+`construction`, `comparison`, `classification`, `quantity` — assigned during conversion, so no
+re-classification is needed.
+
+## What converts, and what doesn't
+
+Numerical yield by logical shape of the source question:
+
+| question_category | → numerical |
+|---|---:|
+| universality ("does P hold for every X") | **~65%** |
+| quantity | ~59% |
+| classification | ~42% |
+| existence | ~29% |
+| extension | ~21% |
+| construction | ~19% |
+| characterization | ~13% |
+| comparison | ~9% |
+
+By source statement type, measured on the full run:
+
+| signal_type | n | → numerical |
+|---|---:|---:|
+| conjecture | 39,444 | **50%** |
+| open_problem | 8,756 | 37% |
+| announced_forthcoming | 897 | 31% |
+| limitation | 41,265 | 25% |
+| natural_extension | 7,197 | 24% |
+
+Universality statements convert because negating "for all *n*" yields a minimal counterexample.
+Questions asking for a *construction*, a *characterization*, or a qualitative *comparison* have
+no number in them, and no reformulation produces one — those became yes/no items.
+
+## Construction and filtering
+
+Converted with `openai/gpt-6-sol` via the OpenRouter batch API, temperature 0.2. 98,000 source
+questions in, 97,497 kept. Removed: 441 unparseable responses, 55 items where a yes/no answer
+had been encoded numerically (indicator variables, `2a+b`), 4 degenerate short items, 3
+duplicate uids.
+
+The conversion prompt forbade encoding booleans as numbers; the residual rate was 0.16% before
+filtering and 0 after.
+
+## Caveats
+
+- **No answer keys.** Restating the warning above because it determines what this dataset is for.
+- **`yesno` items are unverified claims**, not labelled true/false.
+- **Route B items are harder than their sources.**
+- **A small number of `arxiv_id` values are wrong**, inherited from the source dataset: for part
+  of that corpus the id came from a model-written field rather than the filename, so a few
+  questions are attached to the wrong paper.
+- **`signal_type` is an extraction label**, not a verified claim that a problem is still open.
+
+## Licensing
+
+Questions and derived fields: CC-BY-4.0. `source_question` is inherited from
+`amphora/ArXivOpenProblems`. Unlike that dataset, no verbatim paper excerpts are included here.
+
+## Citation
+
+```
+@article{son2026researchmath,
+  title={ResearchMath-14K: Scaling Research-Level Mathematics via Agents},
+  author={Son, Guijin and Yi, Seungyeop and Gwak, Minju and Ko, Hyunwoo and Jang, Wongi and Yu, Youngjae},
+  journal={arXiv preprint arXiv:2605.28003},
+  year={2026}
+}
+```
+
+## Collaborations
+
+I'm interested in creating larger datasets to train open models for research-level math.
+If you are interested let me know. ([guijin.son@snu.ac.kr](mailto:guijin.son@snu.ac.kr))

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stats.json

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+{
+ "kept": 97497,
+ "numerical": 35274,
+ "yesno": 62223,
+ "dropped": {
+  "parse_error": 441,
+  "bit_packed": 55,
+  "too_short": 4,
+  "duplicate_uid": 3
+ }
+}