--- pretty_name: FACBench license: cc-by-4.0 language: - en - pl - de - fr - es size_categories: - "n<1K" tags: - mathematics - autoformalization - formal-methods - multilingual - retrieval - evaluation configs: - config_name: contrastive_queries default: true data_files: - split: test path: FACBench_v110_1_queries.json - config_name: concepts data_files: - split: inventory path: FACBench_v110_1_concepts.json - config_name: alias_decisions data_files: - split: audit path: FACBench_v110_1_alias_decisions.json - config_name: query_decisions data_files: - split: audit path: FACBench_v110_1_query_decisions.json --- # FACBench **FACBench: A Benchmark for Formal-Anchor Collisions in Multilingual Mathematical Grounding** Piotr Kuterba and Józef Spałek, Jagiellonian University. FACBench is a targeted diagnostic of multilingual formal-object selection before proof generation. It tests whether retrieval selects the intended mathematical role rather than a nearby, formally different concept. It is not an open-world prevalence estimate, a proof-generation benchmark, or a newly trained retriever. ## Current Scientific Release The artifact version is **v110.1**. The public repository is [zussini/FACBench](https://huggingface.co/datasets/zussini/FACBench). The dataset DOI is [10.57967/hf/11400](https://doi.org/10.57967/hf/11400). Its registered version `87fdbc4` identifies the verified Hugging Face snapshot `87fdbc494ff6e8fb6ae142b03f2f5b2c8ed1fdfd`; the scientific artifact version is v110.1. Later publication PDFs and citation metadata supplement that frozen snapshot without changing its experimental data or saved rankings. The final adjudicated panel has 130 contrastive mathematical statements in 13 bidirectional concept families and five languages: English, Polish, German, French, and Spanish. Each family contains two target directions in five languages. There are 95 definition queries, 25 theorem queries, and 10 axiom queries. All rankings use a closed inventory of 52 concept cards. The Mathlib mappings include 45 verified mappings and seven proxies; the primary endpoint is concept-ID accuracy, not accuracy over 52 independently verified declarations. ## Files and Logical Views | File | Contents | |---|---| | `FACBench_v110_1_concepts.json` | 52 concept cards, aliases, formal representations, and mapping-status provenance. | | `FACBench_v110_1_queries.json` | 130 final queries with original/final wording, language, family, gold, confusable, and curation evidence. | | `FACBench_v110_1_alias_decisions.json` | 590 alias decisions: 484 positive and 106 excluded. | | `FACBench_v110_1_query_decisions.json` | The same 130 query records exposed as the curation-decision view. | | `FACBench_v110_1_dataverse_20261101.tar.gz` | Complete frozen data/code/evidence release, saved rankings, historical snapshots, reproduction commands, and prepublication manuscript. | | `SHA256SUMS.txt` | SHA-256 checksums of the five data/code files above. | The query and query-decision exports are byte-identical logical views, not two independent evaluation sets. The archive filename records its original packaging target; the same bytes are publicly hosted here. Download the full archive for reproduction code and complete evidence, not just the convenience JSON exports. Do not treat fields such as `gold`, `confusable`, family labels, mapping status, or reviewer notes as model-facing query text. ## Main Results and Experimental Units On the final semantic-only panel, each configuration ranks all 52 cards: | Configuration | Acc@1 | Recall@5 | |---|---:|---:| | BM25 | .554 | .954 | | multilingual-E5-large-instruct | .823 | .969 | | BGE-M3 dense | .838 | .992 | | BGE-M3 sparse | .746 | .985 | | BGE-M3 multivector | .808 | .969 | Strong retrieval improves performance but does not saturate exact selection. BGE-M3 dense makes 21 Top-1 errors, including 12 selections of the prespecified confusable. The full panel contains five candidate representations, five retrieval configurations, and two executions per cell: 50 complete runs with 25 byte-identical repeat pairs. These repeats establish computational reproducibility, not additional independent samples. The 13 families, not the 130 translated rows, are the units for family-cluster resampling and leave-one-family-out analysis. ## Curation, Provenance, and Limitations An author-led re-adjudication with AI assistance reviewed all 590 alias decisions and 130 post-submission queries. Authors made the final decisions. The audit produced 22 state changes, including 16 alias-membership changes: 15 removals and one restoration. There are 53 flagged rewrites and 62 actual final-text changes, including nine additional meaning-preserving copyedits. Historical labels using "expert adjudication" are retained for provenance; they do not establish independent expert or native-speaker validation. The inventory is small and purposive. Queries deliberately contain contrasts, and historical controlled/graph/blind views have answer-bearing structure; these are diagnostic instrumentation rather than evidence of natural grounding. Historical submitted "MRR" is MRR@5; full-ranking metrics are reported separately. The source/context policy helps its designed controlled setting, while fixed fusion with neural retrieval degrades an earlier contrastive snapshot. The Isabelle experiment replaces formal metadata under the same 52-concept and 130-query schema. It is count-balanced and fixed-schema, not information-matched or Isabelle-native retrieval, library equivalence, or proof transfer. The native AFP graph pilot is exploratory and did not meet its frozen confirmation threshold. No downstream proof-generation or training-efficiency benefit is established. Multilingual agreement is a diagnostic signal, never proof of correctness. ## Reproduction and Version History After unpacking the full archive, start with `README.md`, `REPRODUCING.md`, `DATASET_CARD.md`, and `metadata/TABLE_TO_ARTIFACT.json`. Saved-ranking CPU audit, neural inference, and formal-toolchain rebuilding are distinct reproduction levels. Model weights and complete Lean/Isabelle/AFP distributions are not bundled. Submitted, intermediate, and final snapshots remain separate. For example, semantic-only BGE-M3 multivector Acc@1 is .885 in the initial panel, .846 in the intermediate snapshot, and .808 in the final adjudicated rerun. These are curation stages, not stochastic repetitions. Earlier guard-fusion evidence uses its own pre-adjudication snapshot and should not be mixed with the .808 final result. The original submitted archive is preserved locally. Its **sanitized public mirror**, already inside the full v110.1 artifact, removes private review URLs without changing scientific data or results. Public and original hashes are documented in `metadata/PUBLIC_SANITIZATION.json`. There is no need for a separate public upload of the unsanitized submission archive. Pin the Hugging Face commit as well as artifact version v110.1 when reproducing downloads. The paper PDF inside the full archive is the frozen prepublication manuscript. A separately uploaded final publication PDF, when available, is the authoritative camera-ready manuscript; hosting-status changes do not alter results. ## Licensing and Responsible Use Author-created code, benchmark records, generated queries, documentation, reports, and figures are licensed under CC BY 4.0. External components retain their original licenses; see `LICENSE` and the archive's `ATTRIBUTION.md`. Mathematical-library sources and model weights are not relicensed by this dataset. The data concern mathematical concepts, not human subjects. Synthetic query construction and author-led curation can create biases and ambiguities. Use this small, collision-focused diagnostic to inspect retrieval behavior and regression failures, not to infer real-world prevalence or certify generated proofs. Core and minimal Responsible AI metadata must be retained in the validated public Croissant descriptor; an incomplete platform-generated export is not a substitute. ## Funding and Acknowledgements Supported by the National Science Centre, Poland (NCN), under grants UMO-2021/41/B/ST3/04070 and 2023/49/B/ST3/03545. We thank Drs. Danuta Goc-Jagło and Maciej Fidrysiak for general discussions. The authors declare no competing interests. ## Citation Please cite the FACBench paper and its dataset separately. The following DOI is for the dataset, not a DOI for the conference paper: Piotr Kuterba and Józef Spałek (2026). **FACBench** (DOI snapshot `87fdbc4`, artifact release v110.1) [Dataset]. Hugging Face. https://doi.org/10.57967/hf/11400 See `CITATION.cff` and `CITATION.bib`. Also record the exact Hugging Face revision used for reproducibility; the DOI does not replace per-file SHA-256 checks.