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It packages a 92-problem human-labeled benchmark together with the prompt, schema, and taxonomy used for the paper's 6-category semantic-audit experiments.
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This directory is meant to be self-contained for release.
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It includes:
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- `semantic_lean_errors.jsonl`
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- Canonical machine-facing dataset.
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- One record per line.
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- Recommended file for Hugging Face and downstream use.
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- `semantic_lean_errors.json`
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- Readable companion file.
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- Stores the same records as `semantic_lean_errors.jsonl`, but as a pretty-printed JSON array.
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- `ground_truth_schema.md`
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- Schema for the exported records in this release bundle.
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- `error_tags.md`
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- Taxonomy definitions, boundary rules, and detail-tag guidance.
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- `eval_prompts_v4_fewshot.md`
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- Few-shot prompt set used for the category-specific semantic-audit evaluation.
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- `README.md`
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- Dataset card and release notes.
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## Dataset Composition
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The benchmark combines four source datasets:
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- FormalMath: `22`
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- ProofNet: `13`
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- ProverBench: `23`
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- CombiBench: `34`
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Total:
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- `92` labeled problems
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- `87` error examples
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- `5` clean examples
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Primary-category counts:
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- `problem_statement_error`: `5`
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- `specification_error`: `24`
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- `formalization_error`: `8`
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- `domain_mismatch`: `14`
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- `definition_mismatch`: `26`
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- `quantifier_indexing_mismatch`: `10`
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- clean examples (`error_primary = null`): `5`
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Additional label structure:
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- rows with non-empty `error_secondary`: `33`
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- rows with non-empty `error_tags`: `87`
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## Record Schema
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Each row is a single NL/Lean pair with human labels.
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The exported per-record fields are:
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- `id`
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- `source`
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- `problem_nl`
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- `lean_code`
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- `expected_verdict`
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- `error_primary`
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- `error_secondary`
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- `error_tags`
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- `meta_tags`
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- `gold_explanation`
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Field meanings are documented in `ground_truth_schema.md`.
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Two label views are represented:
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1. Binary semantic-error detection
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- Use `expected_verdict`.
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- `YES` means the row contains some semantic error.
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- `NO` means the row is a clean example.
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2. Six-category semantic audit
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- Use `error_primary`.
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- In the current evaluation setup, a queried category expects `YES` iff `error_primary` equals that category, and `NO` otherwise.
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## Prompt Overview
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The included prompt file `eval_prompts_v4_fewshot.md` defines a 6-category evaluation setup.
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For each NL/Lean pair, the model is queried once per category:
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- `problem_statement_error`
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- `specification_error`
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- `formalization_error`
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- `domain_mismatch`
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- `definition_mismatch`
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- `quantifier_indexing_mismatch`
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Each prompt asks the model to judge one specific category and return structured JSON with:
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- `Verdict`
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- `Explanation`
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- `DetailTags`
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- `NeedsReview`
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Because the prompt is category-specific, the 92 labeled problems expand to `552 = 92 × 6` category-level classifications in the paper's evaluation setup.
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## Experimental Reproducibility
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This release includes the exact benchmark and prompt family used for the paper's semantic-audit experiments.
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Evaluation setup:
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- benchmark: `92` labeled problems
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- categories: `6`
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- total category-level judgments: `552`
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- prompt file: `eval_prompts_v4_fewshot.md`
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The paper reports results for at least these model configurations on this benchmark:
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- Sonnet 4.5 + Thinking
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- GPT-5.2 + Thinking
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### Paper-Reported Aggregate Results
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These are the paper-reported numbers for the 92-problem semantic audit and should be treated as the canonical release numbers for this version of the benchmark.
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| Model | Prec. | Rec. | F1 | Acc. | Cost |
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|-------|------:|-----:|---:|-----:|-----:|
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| Sonnet 4.5 + Thinking | 0.30 | 0.82 | 0.42 | 68.1% | $13.71 |
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| GPT-5.2 + Thinking | 0.24 | 0.91 | 0.37 | 54.6% | $6.86 |
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### Paper-Reported Per-Type F1
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| Error Type | Sonnet 4.5 | GPT-5.2 |
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|-----------|-----------:|--------:|
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| Problem Statement Error | 0.29 | 0.10 |
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| Specification Error | 0.51 | 0.48 |
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| Formalization Error | 0.18 | 0.15 |
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| Domain Mismatch | 0.33 | 0.27 |
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| Definition Mismatch | 0.57 | 0.54 |
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| Quantifier/Indexing | 0.39 | 0.33 |
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Interpretation:
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- both models have relatively high recall and lower precision
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- both models perform best on `specification_error` and `definition_mismatch`
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- both models struggle most on `formalization_error`
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Note on reproducibility:
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- this directory contains the benchmark, prompt, schema, and taxonomy
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- if the exact evaluation pipeline is rerun later, small differences can arise from model/provider/version changes
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- the table above reflects the paper-reported results for this release
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## Normalization Policy
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This release intentionally uses a single canonical code field:
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- `lean_code` is the only exported statement field
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- ProofNet rows are normalized from `original_lean_code` to `lean_code`
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- `fixed_lean_code` and `lean_code_fixed` are omitted from this canonical release
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- list-valued annotation fields are normalized to lists
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This avoids ambiguous rows that contain two different Lean statements under one set of labels.
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If repaired variants are needed for comparison studies, they should live in a separate paired comparison artifact.
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## Taxonomy
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The category taxonomy and detail-tag definitions are included in `error_tags.md`.
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That file defines:
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- the six primary semantic-error categories
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- boundary rules between overlapping categories
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- the allowed detail-tag families
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- optional meta-tag conventions
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## Release Cleanup Applied
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Before export, four internally inconsistent rows were corrected from `expected_verdict = YES` to `expected_verdict = NO` because they were clean examples with `error_primary = null` and explanations indicating no semantic error:
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- `formalmath_olymid-ref-base_5274`
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- `proofnet_rudin_exercise_2_28`
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- `proofnet_rudin_exercise_3_21`
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- `proofnet_axler_exercise_6_16`
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After this cleanup, the release contains `87` error rows and `5` clean rows.
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## Recommended Use
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For release and archival use:
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- treat `semantic_lean_errors.jsonl` as the canonical dataset file
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- keep `README.md`, `ground_truth_schema.md`, `error_tags.md`, and `eval_prompts_v4_fewshot.md` alongside it
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- treat `semantic_lean_errors.json` as a readable companion artifact rather than the canonical training/eval file
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---
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configs:
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- config_name: default
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data_files:
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- split: train
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path: semantic_lean_errors.jsonl
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---
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# Semantic Lean Errors
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92 expert-annotated examples of semantic errors in autoformalized Lean 4 mathematics.
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