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Datasets:
FlippyDora
/
OpenFrontiers

Tasks:
Text Retrieval
Modalities:
Tabular
Text
Formats:
parquet
Languages:
English
Size:
10K - 100K
Tags:
mathematics
open-problems
scientific-research
lean4
msc2020
Libraries:
Datasets
pandas
Polars
License:
Dataset card Data Studio Files
xet
 Community
OpenFrontiers / README.md
FlippyDora's picture
FlippyDora
OpenFrontiers corpus (2026-10-10 snapshot, 12,151 problems)
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metadata 
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.

The Lean-stated evaluation benchmark built from this corpus is released separately as OpenFrontiers-Bench (200 items) and its evaluated subset 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:

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:

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 and dataset configuration documentation.

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 defines every key and type; 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, 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:

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.

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.