README.md

---
license: apache-2.0
---

# 🧮 Taxonomy Math w/ FM

A high-quality mathematics dataset curated from web data using taxonomy-based filtering, containing **34 billion tokens** of mathematical content.

## 🎯 Dataset Overview

This dataset is part of the **EssentialWeb** project, which introduces a new paradigm for dataset curation using expressive metadata and simple semantic filters. Unlike traditional math datasets that require complex domain-specific pipelines, our approach leverages a 12-category taxonomy to efficiently identify and extract high-quality mathematical content.

**🔬 Taxonomy Math w/ FM** (34B tokens): Documents labeled as `51 - Mathematics` in our taxonomy, with all 116M recalled documents then scored by the FineMath classifier and filtered to the top 34B tokens.

## 🏆 Performance

Our taxonomy-based approach achieves competitive results with significantly less curation effort:

| Dataset | GSM8K | MATH | Curation Complexity |
|---------|-------|------|-------------------|
| FineMath 3+ | **26.4%** | **11.7%** | Complex domain pipeline |
| OpenWebMath | 14.6% | 9.3% | Complex domain pipeline |
| MegaMath Web | 9.8% | 7.9% | Complex domain pipeline |
| Taxonomy Top Math | 21.3% | 11.0% | Simple semantic filter |
| Taxonomy Math w/ FM | 22.4% | 11.5% | + FineMath classifier |

*Results show our datasets perform within 15% of SOTA while requiring minimal domain-specific tuning.*

## ✨ Key Features

- **🎯 Direct Distribution Targeting**: Leverage existing taxonomy labels to target math content from web-scale data without training custom high-recall classifiers
- **🚀 Rapid Curation**: Skip the expensive classifier training phase and go straight to content selection
- **💰 Cost Effective**: Avoid the need to train high-recall domain-specific classifiers for content discovery
- **🔍 Two-Stage Approach**: Use taxonomy for recall, then apply existing quality classifiers for selection
- **🌐 Web-Scale**: Access to math content identified across 23.6B web documents

## 🛠️ Curation Method

Our approach simplifies math dataset creation:

1. **Traditional Method**: Train high-recall classifiers → Run on billions of documents
2. **Our Method**: Query taxonomy metadata for `51 - Mathematics` → Apply FineMath classifier to all recalled documents → Select top-scoring content

# Dataset Schema Documentation

## Overview

This dataset contains web-crawled text data with comprehensive metadata, quality signals, and taxonomic classifications. Each record represents a document extracted from web archives with detailed provenance tracking and quality assessment metrics.

## EAI Taxonomy Classification

Comprehensive hierarchical classification system with primary and secondary labels - the most important feature of this dataset:

<details>
<summary><strong>Free Decimal Correspondence</strong></summary>

Dewey Decimal-inspired classification with 3-level hierarchical labels:

| Component | Description | Path |
|-----------|-------------|------|
| Primary Code | Main classification code | `eai_taxonomy.free_decimal_correspondence.primary.code` |
| Primary Level 1 | Top-level category | `eai_taxonomy.free_decimal_correspondence.primary.labels.level_1` |
| Primary Level 2 | Mid-level category | `eai_taxonomy.free_decimal_correspondence.primary.labels.level_2` |
| Primary Level 3 | Specific category | `eai_taxonomy.free_decimal_correspondence.primary.labels.level_3` |
| Secondary Code | Alternative classification code | `eai_taxonomy.free_decimal_correspondence.secondary.code` |
| Secondary Level 1 | Alternative top-level category | `eai_taxonomy.free_decimal_correspondence.secondary.labels.level_1` |
| Secondary Level 2 | Alternative mid-level category | `eai_taxonomy.free_decimal_correspondence.secondary.labels.level_2` |
| Secondary Level 3 | Alternative specific category | `eai_taxonomy.free_decimal_correspondence.secondary.labels.level_3` |

We recommend this viewer for easily navigating the FDC categories when curating filters: https://www.librarything.com/mds

</details>

<details>
<summary><strong>Bloom's Taxonomy Integration</strong></summary>

### Cognitive Process
Learning and thinking skill levels:

| Component | Description | Path |
|-----------|-------------|------|
| Primary Code | Main cognitive process code | `eai_taxonomy.bloom_cognitive_process.primary.code` |
| Primary Label | Main cognitive process label | `eai_taxonomy.bloom_cognitive_process.primary.label` |
| Secondary Code | Alternative cognitive process code | `eai_taxonomy.bloom_cognitive_process.secondary.code` |
| Secondary Label | Alternative cognitive process label | `eai_taxonomy.bloom_cognitive_process.secondary.label` |

**Possible Values:**
| Code | Label |
|------|-------|
| `-1` | Abstain |
| `1` | Remember |
| `2` | Understand |
| `3` | Apply |
| `4` | Analyze |
| `5` | Evaluate |
| `6` | Create |

### Knowledge Domain
Subject matter categorization:

| Component | Description | Path |
|-----------|-------------|------|
| Primary Code | Main knowledge domain code | `eai_taxonomy.bloom_knowledge_domain.primary.code` |
| Primary Label | Main knowledge domain label | `eai_taxonomy.bloom_knowledge_domain.primary.label` |
| Secondary Code | Alternative knowledge domain code | `eai_taxonomy.bloom_knowledge_domain.secondary.code` |
| Secondary Label | Alternative knowledge domain label | `eai_taxonomy.bloom_knowledge_domain.secondary.label` |

**Possible Values:**
| Code | Label |
|------|-------|
| `-1` | Abstain |
| `1` | Factual |
| `2` | Conceptual |
| `3` | Procedural |
| `4` | Metacognitive |

</details>

<details>
<summary><strong>Document Characteristics</strong></summary>

### Document Type v1
Format and structure classification:

| Component | Description | Path |
|-----------|-------------|------|
| Primary Code | Main document type code | `eai_taxonomy.document_type_v1.primary.code` |
| Primary Label | Main document type label | `eai_taxonomy.document_type_v1.primary.label` |
| Secondary Code | Alternative document type code | `eai_taxonomy.document_type_v1.secondary.code` |
| Secondary Label | Alternative document type label | `eai_taxonomy.document_type_v1.secondary.label` |

**Possible Values:**
| Code | Label |
|------|-------|
| `-1` | Abstain |
| `1` | News/Editorial |
| `2` | Academic/Research |
| `3` | Reference/Encyclopedic/Educational |
| `4` | Code/Software |
| `5` | Social/Forum |
| `6` | Promotional/Advertisement |
| `7` | Search/Directory/Bibliography |
| `8` | Adult/Pornographic |
| `9` | Personal/Misc |
| `10` | Machine-Generated |
| `11` | Legal/Regulatory |
| `12` | Government/Political |
| `13` | Literary/Creative |
| `14` | Reviews/Critiques |
| `15` | E-Commerce/Marketplace |
| `16` | Images/Videos/Audio |
| `17` | Other/Unclassified |

### Document Type v2
Updated format and structure classification:

| Component | Description | Path |
|-----------|-------------|------|
| Primary Code | Main document type code (v2) | `eai_taxonomy.document_type_v2.primary.code` |
| Primary Label | Main document type label (v2) | `eai_taxonomy.document_type_v2.primary.label` |
| Secondary Code | Alternative document type code (v2) | `eai_taxonomy.document_type_v2.secondary.code` |
| Secondary Label | Alternative document type label (v2) | `eai_taxonomy.document_type_v2.secondary.label` |

**Possible Values:**
| Code | Label |
|------|-------|
| `-1` | Abstain |
| `1` | About (Org.) |
| `2` | About (Personal) |
| `3` | Academic Writing |
| `4` | Audio Transcript |
| `5` | Comment Section |
| `6` | Content Listing |
| `7` | Creative Writing |
| `8` | Documentation |
| `9` | FAQ |
| `10` | Knowledge Article |
| `11` | Legal Notices |
| `12` | Listicle |
| `13` | News (Org.) |
| `14` | News Article |
| `15` | Nonfiction Writing |
| `16` | Personal Blog |
| `17` | Product Page |
| `18` | Q&A Forum |
| `19` | Spam / Ads |
| `20` | Structured Data |
| `21` | Customer Support |
| `22` | Truncated |
| `23` | Tutorial |
| `24` | User Review |
| `25` | Other/Unclassified |

### Extraction Artifacts
Technical extraction quality indicators:

| Component | Description | Path |
|-----------|-------------|------|
| Primary Code | Main extraction artifact code | `eai_taxonomy.extraction_artifacts.primary.code` |
| Primary Label | Main extraction artifact label | `eai_taxonomy.extraction_artifacts.primary.label` |
| Secondary Code | Alternative extraction artifact code | `eai_taxonomy.extraction_artifacts.secondary.code` |
| Secondary Label | Alternative extraction artifact label | `eai_taxonomy.extraction_artifacts.secondary.label` |

**Possible Values:**
| Code | Label |
|------|-------|
| `-1` | Abstain |
| `0` | No Artifacts |
| `1` | Leftover HTML |
| `2` | Text Extraction Errors |
| `3` | Irrelevant Content |
| `4` | Indeterminate |

### Missing Content
Content completeness assessment:

| Component | Description | Path |
|-----------|-------------|------|
| Primary Code | Main missing content code | `eai_taxonomy.missing_content.primary.code` |
| Primary Label | Main missing content label | `eai_taxonomy.missing_content.primary.label` |
| Secondary Code | Alternative missing content code | `eai_taxonomy.missing_content.secondary.code` |
| Secondary Label | Alternative missing content label | `eai_taxonomy.missing_content.secondary.label` |

**Possible Values:**
| Code | Label |
|------|-------|
| `-1` | Abstain |
| `0` | No missing content |
| `1` | Truncated Snippets |
| `2` | Click Here References |
| `3` | Incoherent Flow |
| `4` | Missing Images or Figures |
| `5` | Missing Referenced Data |
| `6` | Indeterminate |

</details>

<details>
<summary><strong>Content Quality Dimensions</strong></summary>

### Reasoning Depth
Complexity of logical reasoning:

| Component | Description | Path |
|-----------|-------------|------|
| Primary Code | Main reasoning depth code | `eai_taxonomy.reasoning_depth.primary.code` |
| Primary Label | Main reasoning depth label | `eai_taxonomy.reasoning_depth.primary.label` |
| Secondary Code | Alternative reasoning depth code | `eai_taxonomy.reasoning_depth.secondary.code` |
| Secondary Label | Alternative reasoning depth label | `eai_taxonomy.reasoning_depth.secondary.label` |

**Possible Values:**
| Code | Label |
|------|-------|
| `-1` | Abstain |
| `1` | No Reasoning |
| `2` | Basic Reasoning |
| `3` | Intermediate Reasoning |
| `4` | Advanced Reasoning |
| `5` | Exceptional Reasoning |
| `6` | Indeterminate |

### Technical Correctness
Accuracy of technical information:

| Component | Description | Path |
|-----------|-------------|------|
| Primary Code | Main technical correctness code | `eai_taxonomy.technical_correctness.primary.code` |
| Primary Label | Main technical correctness label | `eai_taxonomy.technical_correctness.primary.label` |
| Secondary Code | Alternative technical correctness code | `eai_taxonomy.technical_correctness.secondary.code` |
| Secondary Label | Alternative technical correctness label | `eai_taxonomy.technical_correctness.secondary.label` |

**Possible Values:**
| Code | Label |
|------|-------|
| `-1` | Abstain |
| `1` | Technically Flawed |
| `2` | Partially Correct |
| `3` | Mostly Correct |
| `4` | Highly Correct |
| `5` | Exceptionally Correct |
| `6` | Not Applicable/Indeterminate |

### Education Level
Appropriate educational grade level:

| Component | Description | Path |
|-----------|-------------|------|
| Primary Code | Main education level code | `eai_taxonomy.education_level.primary.code` |
| Primary Label | Main education level label | `eai_taxonomy.education_level.primary.label` |
| Secondary Code | Alternative education level code | `eai_taxonomy.education_level.secondary.code` |
| Secondary Label | Alternative education level label | `eai_taxonomy.education_level.secondary.label` |

**Possible Values:**
| Code | Label |
|------|-------|
| `-1` | Abstain |
| `1` | General Audience |
| `2` | High School Level |
| `3` | Undergraduate Level |
| `4` | Graduate/Expert Level |
| `5` | Indeterminate |

</details>

<details>
<summary><strong>Schema Structure</strong></summary>

## Core Fields

| Field | Type | Description | Path |
|-------|------|-------------|------|
| `id` | `Int64` | Unique identifier for each document | `id` |
| `text` | `String` | The main textual content of the document | `text` |

## Metadata Structure

The `metadata` field contains a nested structure with web archive information:

| Field | Type | Description | Path |
|-------|------|-------------|------|
| **URL Information** | | | |
| URL | `String` | Original URL of the document | `metadata.url` |
| Source Domain | `String` | Domain name of the source | `metadata.source_domain` |
| Snapshot ID | `String` | Identifier for the web archive snapshot | `metadata.snapshot_id` |
| **WARC Metadata** | | WARC (Web ARChive) format metadata | |
| Content Length | `String` | Size of the content | `metadata.warc_metadata.Content-Length` |
| Content Type | `String` | MIME type of the content | `metadata.warc_metadata.Content-Type` |
| Block Digest | `String` | Checksum of the WARC block | `metadata.warc_metadata.WARC-Block-Digest` |
| Concurrent To | `String` | Related WARC records | `metadata.warc_metadata.WARC-Concurrent-To` |
| Date | `String` | Timestamp of the crawl | `metadata.warc_metadata.WARC-Date` |
| IP Address | `String` | Source server IP address | `metadata.warc_metadata.WARC-IP-Address` |
| Payload Type | `String` | Identified content type | `metadata.warc_metadata.WARC-Identified-Payload-Type` |
| Payload Digest | `String` | Checksum of the payload | `metadata.warc_metadata.WARC-Payload-Digest` |
| Record ID | `String` | Unique WARC record identifier | `metadata.warc_metadata.WARC-Record-ID` |
| Target URI | `String` | Original target URL | `metadata.warc_metadata.WARC-Target-URI` |
| Truncated | `String` | Truncation status | `metadata.warc_metadata.WARC-Truncated` |
| Type | `String` | WARC record type | `metadata.warc_metadata.WARC-Type` |
| Warcinfo ID | `String` | Associated warcinfo record | `metadata.warc_metadata.WARC-Warcinfo-ID` |
| **Additional Info** | | | |
| WARC Info | `String` | Additional WARC information | `metadata.warc_info` |

## Text Structure Information

| Field | Type | Description | Path |
|-------|------|-------------|------|
| Line Start Indices | `List[Int32]` | Starting indices of each line | `line_start_n_end_idx.line_start_idx` |
| Line End Indices | `List[Int32]` | Ending indices of each line | `line_start_n_end_idx.line_end_idx` |

</details>

<details>
<summary><strong>Quality Signals</strong></summary>

The dataset includes two comprehensive quality assessment frameworks:

## Red Pajama v2 Quality Metrics

Text quality indicators derived from the Red Pajama v2 filtering pipeline:

### Content Structure Metrics
| Metric | Description | Path |
|--------|-------------|------|
| Original Length | Original document length | `quality_signals.red_pajama_v2.ccnet_original_length` |
| Original Lines | Number of lines in original document | `quality_signals.red_pajama_v2.ccnet_original_nlines` |
| Sentence Count | Total sentence count | `quality_signals.red_pajama_v2.rps_doc_num_sentences` |
| Word Count | Total word count | `quality_signals.red_pajama_v2.rps_doc_word_count` |
| Mean Word Length | Average word length | `quality_signals.red_pajama_v2.rps_doc_mean_word_length` |

### Language Quality Metrics
| Metric | Description | Path |
|--------|-------------|------|
| Stop Word Fraction | Proportion of stop words | `quality_signals.red_pajama_v2.rps_doc_stop_word_fraction` |
| Unique Words Fraction | Fraction of unique words | `quality_signals.red_pajama_v2.rps_doc_frac_unique_words` |
| All Caps Words | Fraction of words in all capitals | `quality_signals.red_pajama_v2.rps_doc_frac_all_caps_words` |
| Non-Alphabetic Words | Fraction of non-alphabetic words | `quality_signals.red_pajama_v2.rps_doc_frac_no_alph_words` |
| Unigram Entropy | Entropy measure of word distribution | `quality_signals.red_pajama_v2.rps_doc_unigram_entropy` |

### Content Pattern Analysis
| Metric | Description | Path |
|--------|-------------|------|
| Curly Bracket Density | Curly bracket density (code indicator) | `quality_signals.red_pajama_v2.rps_doc_curly_bracket` |
| Symbol-to-Word Ratio | Symbol-to-word ratio | `quality_signals.red_pajama_v2.rps_doc_symbol_to_word_ratio` |
| Ellipsis Line Endings | Lines ending with ellipsis | `quality_signals.red_pajama_v2.rps_doc_frac_lines_end_with_ellipsis` |
| Lorem Ipsum Detection | Lorem ipsum text detection | `quality_signals.red_pajama_v2.rps_doc_lorem_ipsum` |
| Offensive Content | Potentially offensive content detection | `quality_signals.red_pajama_v2.rps_doc_ldnoobw_words` |
| UT1 Blacklist | UT1 blacklist filtering score | `quality_signals.red_pajama_v2.rps_doc_ut1_blacklist` |

### Duplication Detection
| Metric | Description | Path |
|--------|-------------|------|
| 5-gram Duplication | Character-level duplication for 5-grams | `quality_signals.red_pajama_v2.rps_doc_frac_chars_dupe_5grams` |
| 6-gram Duplication | Character-level duplication for 6-grams | `quality_signals.red_pajama_v2.rps_doc_frac_chars_dupe_6grams` |
| 7-gram Duplication | Character-level duplication for 7-grams | `quality_signals.red_pajama_v2.rps_doc_frac_chars_dupe_7grams` |
| 8-gram Duplication | Character-level duplication for 8-grams | `quality_signals.red_pajama_v2.rps_doc_frac_chars_dupe_8grams` |
| 9-gram Duplication | Character-level duplication for 9-grams | `quality_signals.red_pajama_v2.rps_doc_frac_chars_dupe_9grams` |
| 10-gram Duplication | Character-level duplication for 10-grams | `quality_signals.red_pajama_v2.rps_doc_frac_chars_dupe_10grams` |
| Top 2-gram Coverage | Most frequent 2-gram coverage | `quality_signals.red_pajama_v2.rps_doc_frac_chars_top_2gram` |
| Top 3-gram Coverage | Most frequent 3-gram coverage | `quality_signals.red_pajama_v2.rps_doc_frac_chars_top_3gram` |
| Top 4-gram Coverage | Most frequent 4-gram coverage | `quality_signals.red_pajama_v2.rps_doc_frac_chars_top_4gram` |

### Domain Importance Scores
| Metric | Description | Path |
|--------|-------------|------|
| Books Importance | Similarity to book content | `quality_signals.red_pajama_v2.rps_doc_books_importance` |
| Books Importance (Length Corrected) | Length-corrected books similarity | `quality_signals.red_pajama_v2.rps_doc_books_importance_length_correction` |
| OpenWebText Importance | Similarity to OpenWebText | `quality_signals.red_pajama_v2.rps_doc_openwebtext_importance` |
| OpenWebText Importance (Length Corrected) | Length-corrected OpenWebText similarity | `quality_signals.red_pajama_v2.rps_doc_openwebtext_importance_length_correction` |
| Wikipedia Importance | Similarity to Wikipedia | `quality_signals.red_pajama_v2.rps_doc_wikipedia_importance` |
| Wikipedia Importance (Length Corrected) | Length-corrected Wikipedia similarity | `quality_signals.red_pajama_v2.rps_doc_wikipedia_importance_length_correction` |

## FastText Classification Scores

Domain and content type classification probabilities:

| Metric | Description | Path |
|--------|-------------|------|
| DCLM Score | DataComp-LM classifier score | `quality_signals.fasttext.dclm` |
| English Confidence | English language confidence | `quality_signals.fasttext.english` |
| Educational Content | Educational content approximation | `quality_signals.fasttext.fineweb_edu_approx` |
| General Math | General mathematics content | `quality_signals.fasttext.eai_general_math` |
| Web Math | Web-based mathematics content | `quality_signals.fasttext.eai_open_web_math` |
| Code Content | Code content detection | `quality_signals.fasttext.eai_web_code` |

</details>

<details>
<summary><strong>Data Provenance</strong></summary>

All documents originate from web crawls with full WARC metadata preservation, enabling:
- Source verification and attribution
- Temporal analysis of web content
- Content deduplication across crawls
- Quality assessment pipeline reconstruction

</details>

<details>
<summary><strong>Usage Examples</strong></summary>

**Filter by quality score:**
```python
df.filter(df["quality_signals.red_pajama_v2.rps_doc_stop_word_fraction"] > 0.3)
```

**Filter by domain:**
```python
df.filter(df["metadata.source_domain"].contains("wikipedia"))
```

**Filter by education level:**
```python
df.filter(df["eai_taxonomy.education_level.primary.code"] == "2")  # High School Level
```

**Filter by content type:**
```python
df.filter(df["quality_signals.fasttext.eai_web_code"] > 0.8)
```

**Filter by document quality:**
```python
df.filter(
    (df["quality_signals.red_pajama_v2.rps_doc_word_count"] > 100) &
    (df["quality_signals.red_pajama_v2.rps_doc_stop_word_fraction"] > 0.2) &
    (df["quality_signals.red_pajama_v2.rps_doc_frac_unique_words"] > 0.3)
)
```

**Filter by reasoning depth:**
```python
df.filter(df["eai_taxonomy.reasoning_depth.primary.code"].isin(["4", "5"]))  # Advanced or Exceptional
```

**Filter by document type:**
```python
df.filter(df["eai_taxonomy.document_type_v2.primary.code"] == "3")  # Academic Writing
```

**Filter high-quality educational content:**
```python
df.filter(
    (df["eai_taxonomy.education_level.primary.code"].isin(["2", "3"])) &  # High School or Undergraduate
    (df["eai_taxonomy.technical_correctness.primary.code"].isin(["4", "5"])) &  # Highly or Exceptionally Correct
    (df["eai_taxonomy.extraction_artifacts.primary.code"] == "0") &  # No Artifacts
    (df["quality_signals.fasttext.fineweb_edu_approx"] > 0.7)
)
```

</details>

<details>
<summary><strong>Usage Notes</strong></summary>

- **Quality Filtering**: Use Red Pajama v2 metrics for content quality thresholds
- **Domain Selection**: Leverage FastText scores for domain-specific filtering  
- **Educational Applications**: Utilize EAI taxonomy for curriculum-aligned content selection
- **Deduplication**: Apply n-gram duplication metrics for corpus cleaning
- **Attribution**: WARC metadata enables proper source citation

</details>

## 🎓 Citation

If you use this dataset, please cite our EssentialWeb paper:

```bibtex
@article{essentialweb2025,
  title={Essential-Web: 24T tokens of organized web data},
  author={[Authors]},
  year={2025}
}
```

---

*Part of the EssentialWeb ecosystem: Making dataset curation accessible, interpretable, and efficient.*