Datasets:

zussini
/

FACBench

---
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.

	---
	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.