| --- |
| pretty_name: OpenFrontiers |
| language: |
| - en |
| license: other |
| license_name: mixed-source-terms |
| license_link: https://huggingface.co/datasets/FlippyDora/OpenFrontiers/blob/main/NOTICE.md |
| task_categories: |
| - text-retrieval |
| tags: |
| - mathematics |
| - open-problems |
| - scientific-research |
| - lean4 |
| - msc2020 |
| size_categories: |
| - 10K<n<100K |
| configs: |
| - config_name: problems |
| default: true |
| data_files: |
| - split: train |
| path: data/problems.parquet |
| - config_name: catalogues |
| data_files: |
| - split: train |
| path: data/catalogues.parquet |
| - config_name: archive |
| data_files: |
| - split: train |
| path: data/archive.parquet |
| - config_name: all_records |
| data_files: |
| - split: train |
| path: |
| - data/problems.parquet |
| - data/catalogues.parquet |
| - data/archive.parquet |
| --- |
| |
| # OpenFrontiers: research-problem corpus |
|
|
| A structured snapshot of the OpenFrontiers research-problem index, including mathematical |
| and scientific problem statements, source attribution, MSC 2020 mappings, collected |
| Lean 4 material and research-status evidence. The exact snapshot date, counts and |
| coverage are in [statistics.json](statistics.json). |
|
|
| The Lean-stated evaluation benchmark built from this corpus is released separately as |
| [OpenFrontiers-Bench](https://huggingface.co/datasets/FlippyDora/OpenFrontiers-Bench) |
| (200 items) and its evaluated subset |
| [OpenFrontiers-HQ50](https://huggingface.co/datasets/FlippyDora/OpenFrontiers-HQ50). |
|
|
| The default `problems` configuration contains every published problem in the database, |
| including solved, disputed and status-unassessed records. It is **not a claim that |
| every row is currently an unsolved problem**, nor a complete census of any discipline. |
| One row corresponds to one indexed problem record; a paper can contain multiple |
| subquestions in the same record. Overlapping formulations from different sources |
| are retained with their own provenance. Unique IDs do not imply mathematical deduplication. |
|
|
| `catalogues` retains source problem-number indices, workshop lists, document listings, |
| journals and archived redirects. These rows have `problem_statement: null`; they are |
| not additional extracted problems. `linked_problem_ids` connects a catalogue entry |
| to an indexed problem. Different catalogues may point to the same item. |
| `archive` retains nonpublished historical research records separately. `all_records` |
| combines these three disjoint row sets with exactly the same schema. |
|
|
| `train` is a Hugging Face storage split name only. No train/test separation or |
| evaluation-contamination control has been performed. |
|
|
| ## Load |
|
|
| Install the versions in `requirements.txt`. From the dataset directory: |
|
|
| ```python |
| from datasets import load_dataset |
| |
| # Reads the configurations in this dataset card. |
| ds = load_dataset(".", name="problems", split="train") |
| row = ds[0] # a Python dictionary, including nested dictionaries and lists |
| |
| # Explicit file loading is also supported. |
| ds = load_dataset("parquet", data_files="data/problems.parquet", split="train") |
| math = ds.filter(lambda r: r["field"]["main"] == "math") |
| open_math = math.filter(lambda r: r["status"] == "open") |
| |
| # From the Hugging Face Hub: |
| ds = load_dataset("FlippyDora/OpenFrontiers", name="problems", split="train") |
| ``` |
|
|
| The equivalent JSONL files have one JSON dictionary per UTF-8 line. Use the supplied |
| loader for exact string preservation and explicit nullable types: |
|
|
| ```python |
| from load_jsonl import load_jsonl |
| ds = load_jsonl("data/problems.jsonl") |
| ``` |
|
|
| The helper uses `json.loads` and `Dataset.from_generator` with `features.json`. |
| This avoids the generic JSON loader's automatic date inference before string |
| casting (observed with the pinned version), which can change `2026-09-08` into |
| `2026-09-08 00:00:00`. Standard Python `json.loads` also reads the JSONL verbatim. |
| The default Parquet configurations preserve these strings without a custom loader. |
|
|
| These formats and configurations follow the official |
| [Hugging Face loading documentation](https://huggingface.co/docs/datasets/loading) |
| and [dataset configuration documentation](https://huggingface.co/docs/hub/datasets-data-files-configuration). |
|
|
| ## Dictionary fields |
|
|
| All rows have all keys. Unknown scalar values are JSON `null` / Python `None`; |
| empty lists mean no collected items. Missing data is not converted into invented |
| statements or proofs. [schema.json](schema.json) defines every key and type; |
| [features.json](features.json) defines the matching Hugging Face schema. |
|
|
| | Field | Meaning | |
| | --- | --- | |
| | `id`, `record_kind`, `slug`, `title` | Stable namespaced identifier, row type and problem identity. | |
| | `field.main`, `field.sub` | Broad discipline and subject, e.g. `math`, `number theory`. Original field name, slug and discipline are also retained. | |
| | `additional_fields` | Additional subject mappings without duplicating the primary field. | |
| | `msc2020` | MSC codes plus mapping basis and evidence. Editorial/inferred mappings are distinguished from source mappings. A missing narrow code is not invented. | |
| | `problem_statement` | Existing Markdown/LaTeX statement, preserved verbatim. May be a summary or excerpt; see provenance. | |
| | `status` | Existing editorial status: `open`, `unassessed`, `partially-solved`, `solved`, `disputed`, `withdrawn`. Catalogue status can also include source review labels. | |
| | `source` | Collection key, source title/type/URL/citation/DOI/arXiv ID, recorded license wording and notes. | |
| | `lean4_statement` | Existing Lean 4 material, or the first deterministic linked upstream source file when the database has no Lean attachment. Can be a fragment, a whole file, or a proposition definition. | |
| | `proof`, `proof_status` | Accepted full-solution submission text if collected; otherwise null / `not-recorded`. Acceptance is editorial, not mathematical certification. | |
| | `lean4_proof`, `lean4_proof_status` | An accepted solution's existing verified proof, bound to the current stored target and known verification profile; otherwise null / `not-recorded`. | |
| | `lean4_target` | Separately stored target proposition, if available. | |
| | `formalizations` | Every collected attachment/linked Lean file, with code, language, hash, source URL, license, toolchain/commit where known, lexical placeholder flags and verification/correspondence status. | |
| | `contributions` | Collected submissions, public comments and public AI attempts. Rejected/partial/unverified attempts remain contributions rather than canonical proofs. | |
| | `teaser`, `background`, `partial_results`, `why_it_matters` | Existing contextual research text, preserved verbatim. | |
| | `references` | All collected citations, links, notes and original ordering. | |
| | `provenance`, `source_status_json` | Import/status dates, original record IDs and evidence; dated upstream status claims remain separate from local verification. | |
| | `review_state`, `horizon`, `difficulty`, `tags` | Original editorial/research labels; not a benchmark difficulty scale. | |
| | `posed_by`, `posed_year`, `prize_amount_usd`, `prize_sponsor` | Existing historical information; no fresh financial or historical verification. | |
| | `quality_flags`, `linked_problem_ids` | Missing full text, known formula issues, unverified source claims, source-file enrichment and catalogue links. | |
| | `dates`, `snapshot_at` | Stored record dates and dataset snapshot timestamp in ISO format. | |
| | `metadata_json` | JSON-encoded ancillary metadata. Catalogue rows retain their original index metadata; problem rows retain their original database ID/number and format-audit details. | |
|
|
| ## Formal statements and proofs |
|
|
| FormalConjectures source files are retained at the pinned commit recorded in |
| `statistics.json`; their own Lean toolchain and dependency manifest are in `metadata/`. |
| The full upstream repository is required to compile source files with their imports. |
| Those files can contain multiple conjectures, solved helper lemmas, `answer(sorry)`, |
| or admitted declarations. A file's presence does not establish a proof of the |
| associated natural-language problem. All variants are preserved in `formalizations`. |
|
|
| This export does **not** execute Lean. Lexical `sorry`/`admit`/`axiom` flags mask nested |
| comments and strings, but are not a Lean parser or proof checker. Old source-side |
| "verified" labels are retained as claims in `source_status_json`, not promoted to |
| locally verified proofs. If a source reports a proof whose text was not collected, |
| the text remains null and a quality flag records that gap. |
|
|
| For any existing local verification receipt, the exporter requires the known |
| `lean4-core-4.19.0-v1` profile, matching target and proof content hashes, a current |
| matching target, and an explicit axiom list contained in `propext`, `Classical.choice`, |
| `Quot.sound`. Only accepted full-solution submissions can populate canonical proof |
| fields. Even `verified-target-only` does not certify correspondence between the |
| Lean target and the natural-language problem. Multiple attempts remain available |
| in `contributions`; when multiple qualifying solutions exist, the most recently |
| created qualifying submission is selected deterministically. |
|
|
| ## Collection, coverage and limitations |
|
|
| The export uses a repeatable-read, read-only database snapshot plus existing source |
| catalogues and pinned source artifacts. It preserves the corpus, rather than |
| silently dropping uncertain or older records. No new open-problem status review |
| is implied by export time. The metadata folder preserves source registries, |
| selection decisions, import manifests, MSC taxonomy, review evidence and known |
| format issues. Source catalogues are partial and differ in scope. |
|
|
| The sources include ICM Conjectures, COLT, TheoremDB, AIM Problem Lists, Erdős Problems, |
| Clay, Wikipedia subject lists, specialist collections and selected journal/workshop |
| articles. Source descriptions and license wording appear in `metadata/sources.json`. |
| These are not rankings or endorsements. Some inherited records are summaries rather |
| than complete standalone formulations; `provenance.has_full_text` and quality flags |
| make recorded gaps filterable. Source-reported solved or open status can be outdated. |
|
|
| Markdown/LaTeX and Unicode are preserved, including known upstream formatting |
| problems rather than silently rewriting mathematics. Site-relative figure/document |
| links remain verbatim; `metadata/asset-manifest.json` records referenced assets and |
| `metadata/aim-documents.json` maps cached AIM documents to original URLs. Binary PDFs |
| and figures are not bundled in this text dataset. Some records therefore require |
| the cited source for figures or complete context. |
|
|
| Operational accounts, sessions, credentials, private AI prompts, private attempts, |
| payments and usage logs are outside the research-data export. Public research |
| authorship/citations are retained. There are no inferred demographic annotations. |
|
|
| ## Reuse and upload |
|
|
| This is a **mixed-source dataset**, not a blanket CC0/Apache-licensed corpus. |
| See [NOTICE.md](NOTICE.md), each row's `source.license`, attachment licenses and |
| original source notices. Technical upload readiness does not establish unrestricted |
| redistribution or training rights for every source. The dataset preserves all |
| existing research records so downstream users can apply source-specific policies. |
|
|
| Authenticate using the Hugging Face CLI, then preview the upload file list: |
|
|
| ```sh |
| hf auth login |
| python upload.py --repo-id OWNER/DATASET |
| # When ready, this creates/updates a private dataset repository: |
| python upload.py --repo-id OWNER/DATASET --upload |
| # To choose public visibility when creating a NEW repository, also pass --public. |
| ``` |
|
|
| The upload helper checks `checksums.sha256` and the successful validation report |
| before sending files. No upload occurs without `--upload`. Existing repository |
| visibility is not changed by this helper. Uploading does not delete older remote |
| files, so a new versioned repository is the simplest way to publish an exact snapshot. |
|
|
| ## Reproducibility and validation |
|
|
| `input-manifest.json` records input hashes. `validation.json` records the completed |
| schema, count, reference, content-preservation and JSONL/Parquet/Hugging Face loading |
| checks. `checksums.sha256` covers all packaged files except itself. Export scripts |
| and pinned dependencies are in `reproduce/`. Archived TypeScript scripts use |
| `.ts.txt` names so this package does not alter the application's build; restore |
| their `.ts` extension under `scripts/dataset/` in the application repository to run them. |
|
|
| To rebuild from the application repository, first stop its preview if it shares |
| the embedded database, then take a read-only research snapshot (or use a fully |
| offline database copy through `PGLITE_DATA_DIR`). Restart the preview afterward. |
| Never open the embedded database from two processes at once. |
|
|
| ```sh |
| node --import tsx scripts/dataset/snapshot.ts .tmp/hf-dataset-snapshot.json |
| python scripts/dataset/export.py --snapshot .tmp/hf-dataset-snapshot.json \ |
| --formal-root PATH/TO/PINNED/formal-conjectures-COMMIT \ |
| --theorem-snapshot PATH/TO/theorem-all.json --output datasets/NEW-VERSION |
| python scripts/dataset/verify.py --snapshot .tmp/hf-dataset-snapshot.json \ |
| --dataset datasets/NEW-VERSION |
| ``` |
|
|
| Inputs must be the matching saved versions, not a fresh download at a moving branch. |
| The raw application database and source-account API responses are not included in |
| the upload package. JSONL and Parquet data rows can be checked independently without |
| those private operational inputs. |
|
|
