Triple

T7047107
Position Surface form Disambiguated ID Type / Status
Subject Lynn Harold Loomis E163664 entity
Predicate notableWork P4 FINISHED
Object Introduction to Abstract Harmonic Analysis
Introduction to Abstract Harmonic Analysis is a foundational graduate-level textbook that systematically develops the theory of harmonic analysis on topological groups and related abstract structures.
E639088 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: Introduction to Abstract Harmonic Analysis | Statement: [Lynn Harold Loomis, notableWork, Introduction to Abstract Harmonic Analysis]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Introduction to Abstract Harmonic Analysis
Context triple: [Lynn Harold Loomis, notableWork, Introduction to Abstract Harmonic Analysis]
  • A. 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.
  • B. Harmonic Analysis: Real-Variable Methods, Orthogonality, and Oscillatory Integrals
    "Harmonic Analysis: Real-Variable Methods, Orthogonality, and Oscillatory Integrals" is a foundational graduate-level textbook by Elias Stein that systematically develops modern harmonic analysis using real-variable techniques, emphasizing singular integrals, Littlewood–Paley theory, and oscillatory integral methods.
  • C. L’intégration dans les groupes topologiques et ses applications
    L’intégration dans les groupes topologiques et ses applications is a foundational mathematical monograph by André Weil that develops the theory of integration on topological groups and explores its far-reaching applications in analysis and number theory.
  • D. Lectures on Fourier Integrals
    Lectures on Fourier Integrals is a classic mathematical monograph by Salomon Bochner that systematically develops the theory and applications of Fourier integrals and transforms.
  • E. Functional Analysis: Introduction to Further Topics in Analysis
    "Functional Analysis: Introduction to Further Topics in Analysis" is an advanced graduate-level textbook by Elias Stein that develops modern functional analysis with applications to areas such as operator theory, harmonic analysis, and partial differential equations.
  • 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: Introduction to Abstract Harmonic Analysis
Triple: [Lynn Harold Loomis, notableWork, Introduction to Abstract Harmonic Analysis]
Generated description
Introduction to Abstract Harmonic Analysis is a foundational graduate-level textbook that systematically develops the theory of harmonic analysis on topological groups and related abstract structures.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Introduction to Abstract Harmonic Analysis
Target entity description: Introduction to Abstract Harmonic Analysis is a foundational graduate-level textbook that systematically develops the theory of harmonic analysis on topological groups and related abstract structures.
  • A. 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.
  • B. Harmonic Analysis: Real-Variable Methods, Orthogonality, and Oscillatory Integrals
    "Harmonic Analysis: Real-Variable Methods, Orthogonality, and Oscillatory Integrals" is a foundational graduate-level textbook by Elias Stein that systematically develops modern harmonic analysis using real-variable techniques, emphasizing singular integrals, Littlewood–Paley theory, and oscillatory integral methods.
  • C. L’intégration dans les groupes topologiques et ses applications
    L’intégration dans les groupes topologiques et ses applications is a foundational mathematical monograph by André Weil that develops the theory of integration on topological groups and explores its far-reaching applications in analysis and number theory.
  • D. Lectures on Fourier Integrals
    Lectures on Fourier Integrals is a classic mathematical monograph by Salomon Bochner that systematically develops the theory and applications of Fourier integrals and transforms.
  • E. Functional Analysis: Introduction to Further Topics in Analysis
    "Functional Analysis: Introduction to Further Topics in Analysis" is an advanced graduate-level textbook by Elias Stein that develops modern functional analysis with applications to areas such as operator theory, harmonic analysis, and partial differential equations.
  • 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_69c6885f598c8190b6b6495c59d8d962 completed March 27, 2026, 1:38 p.m.
NER Named-entity recognition batch_69c6e23a72f481909ce77ef73b06ea95 completed March 27, 2026, 8:02 p.m.
NED1 Entity disambiguation (via context triple) batch_69c7887e6e50819088c23c9b45861a54 completed March 28, 2026, 7:51 a.m.
NEDg Description generation batch_69c78a822ab0819097e2b40d4b9e044f completed March 28, 2026, 8 a.m.
NED2 Entity disambiguation (via description) batch_69c78b33f5308190a3f234a2c0bd8b9c completed March 28, 2026, 8:03 a.m.
Created at: March 27, 2026, 2:37 p.m.