Triple

T18282755
Position Surface form Disambiguated ID Type / Status
Subject David Bressoud E437902 entity
Predicate notableWork P4 FINISHED
Object A Radical Approach to Lebesgue’s Theory of Integration
A Radical Approach to Lebesgue’s Theory of Integration is a mathematics textbook by David Bressoud that offers an intuitive, historically informed introduction to Lebesgue integration and measure theory.
E1316090 NE FINISHED

How this triple was built (4 steps)

Every LLM step that produced this triple, in pipeline order — named-entity classification, the disambiguation choices (the exact options shown, with the pick highlighted), and the generated description. The batch + timestamp of each is in the Provenance table below.

NER Named-entity recognition gpt-5-mini
Instruction
Given a phrase, classify it is english named entity (e.g., persons, organizations, works of art) in Latin script, or not (e.g., literals, dates, URLs, verbose phrases). For disambiguation, the statement where the phrase occurs as object is also given. Please return a JSON object with `phrase` (string, the phrase being analyzed) and `is_ne` (boolean, indicating whether the phrase is a Named Entity).
Input
Phrase: A Radical Approach to Lebesgue’s Theory of Integration | Statement: [David Bressoud, notableWork, A Radical Approach to Lebesgue’s Theory of Integration]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: A Radical Approach to Lebesgue’s Theory of Integration
Context triple: [David Bressoud, notableWork, A Radical Approach to Lebesgue’s Theory of Integration]
  • A. Theory of the Integral
    Theory of the Integral is a classic mathematical monograph that systematically develops the theory of integration, particularly Lebesgue integration, and has been influential in real analysis.
  • B. Singular Integrals and Differentiability Properties of Functions
    "Singular Integrals and Differentiability Properties of Functions" is a landmark mathematical monograph by Elias M. Stein that developed the modern theory of singular integral operators and their role in harmonic analysis and differentiability.
  • C. Harmonic Analysis and the Theory of Probability
    Harmonic Analysis and the Theory of Probability is a seminal mathematical monograph that connects Fourier-analytic methods with probabilistic concepts, helping to lay the foundations of modern probability theory.
  • D. Foundations of Modern Analysis
    Foundations of Modern Analysis is a classic graduate-level textbook that systematically develops modern mathematical analysis using rigorous, abstract methods and functional analysis.
  • E. New classes of Lp-spaces
    "New classes of Lp-spaces" is a mathematical work by Jean Bourgain that introduces and studies novel Banach space structures within the framework of Lp spaces, significantly advancing the theory of functional analysis.
  • F. None of above. chosen
  • G. Unsure - the case is ambiguous/there is not enough information to decide.
NEDg Description generation gpt-5.1
Instruction
Generate a one-sentence description of the target entity. 
You are given a context triple in the form (subject, predicate, object), where the object is the target entity. 
# Instructions
Use the triple to infer relevant information about the entity. Describe the entity based on what is most defining, well-known. 
Avoid repeating the information from the triple, unless really essential.
# Response Format
Return only the sentence: "Description: [one-sentence description of the target entity]"
Input
Entity: A Radical Approach to Lebesgue’s Theory of Integration
Triple: [David Bressoud, notableWork, A Radical Approach to Lebesgue’s Theory of Integration]
Generated description
A Radical Approach to Lebesgue’s Theory of Integration is a mathematics textbook by David Bressoud that offers an intuitive, historically informed introduction to Lebesgue integration and measure theory.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: A Radical Approach to Lebesgue’s Theory of Integration
Target entity description: A Radical Approach to Lebesgue’s Theory of Integration is a mathematics textbook by David Bressoud that offers an intuitive, historically informed introduction to Lebesgue integration and measure theory.
  • A. Theory of the Integral
    Theory of the Integral is a classic mathematical monograph that systematically develops the theory of integration, particularly Lebesgue integration, and has been influential in real analysis.
  • B. Singular Integrals and Differentiability Properties of Functions
    "Singular Integrals and Differentiability Properties of Functions" is a landmark mathematical monograph by Elias M. Stein that developed the modern theory of singular integral operators and their role in harmonic analysis and differentiability.
  • C. Harmonic Analysis and the Theory of Probability
    Harmonic Analysis and the Theory of Probability is a seminal mathematical monograph that connects Fourier-analytic methods with probabilistic concepts, helping to lay the foundations of modern probability theory.
  • D. Foundations of Modern Analysis
    Foundations of Modern Analysis is a classic graduate-level textbook that systematically develops modern mathematical analysis using rigorous, abstract methods and functional analysis.
  • E. New classes of Lp-spaces
    "New classes of Lp-spaces" is a mathematical work by Jean Bourgain that introduces and studies novel Banach space structures within the framework of Lp spaces, significantly advancing the theory of functional analysis.
  • F. None of above. chosen

Provenance (5 batches)

The batch behind each pipeline step, in order, with when it ran. Timestamps are batch-level — stages were processed in waves, so the object chain (NER → NED1 → NEDg → NED2) reads in order, but predicate / elicitation batches can sit in a different wave.

Step Stage Batch ID Status When
creating Elicitation batch_69d8b914530c8190b4474d862a2b2a1b completed April 10, 2026, 8:47 a.m.
NER Named-entity recognition batch_69e50057c5c881909fcda72f4a98c8c3 completed April 19, 2026, 4:18 p.m.
NED1 Entity disambiguation (via context triple) batch_6a03b4029cb88190963ae33570455c2d completed May 12, 2026, 11:13 p.m.
NEDg Description generation batch_6a03b501b630819094c77aebf62081a2 completed May 12, 2026, 11:17 p.m.
NED2 Entity disambiguation (via description) batch_6a03b5c09f4881909fb0ead5fc48895c completed May 12, 2026, 11:20 p.m.
Created at: April 10, 2026, 10:35 a.m.