README.md

metadata

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:

Free Decimal Correspondence

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

Bloom's Taxonomy Integration

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

Document Characteristics

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

Content Quality Dimensions

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

Schema Structure

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

Quality Signals

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

Data Provenance

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

Usage Examples

Filter by quality score:

df.filter(df["quality_signals.red_pajama_v2.rps_doc_stop_word_fraction"] > 0.3)

Filter by domain:

df.filter(df["metadata.source_domain"].contains("wikipedia"))

Filter by education level:

df.filter(df["eai_taxonomy.education_level.primary.code"] == "2")  # High School Level

Filter by content type:

df.filter(df["quality_signals.fasttext.eai_web_code"] > 0.8)

Filter by document quality:

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:

df.filter(df["eai_taxonomy.reasoning_depth.primary.code"].isin(["4", "5"]))  # Advanced or Exceptional

Filter by document type:

df.filter(df["eai_taxonomy.document_type_v2.primary.code"] == "3")  # Academic Writing

Filter high-quality educational content:

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)
)

🎓 Citation

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

@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.