Triple

T6716290
Position Surface form Disambiguated ID Type / Status
Subject Salomon Bochner E153275 entity
Predicate notableWork P4 FINISHED
Object 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.
E613411 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: Harmonic Analysis and the Theory of Probability | Statement: [Salomon Bochner, notableWork, Harmonic Analysis and the Theory of Probability]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Harmonic Analysis and the Theory of Probability
Context triple: [Salomon Bochner, notableWork, Harmonic Analysis and the Theory of Probability]
  • A. 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.
  • B. Three regularity results in harmonic analysis
    "Three regularity results in harmonic analysis" is the doctoral thesis of mathematician Terence Tao, focusing on advanced problems in harmonic analysis and the study of regularity properties of functions and operators.
  • C. Littlewood–Paley theory
    Littlewood–Paley theory is a collection of techniques in harmonic analysis that decompose functions into frequency-localized pieces to study their behavior in L^p spaces and related function spaces.
  • D. 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.
  • E. Modern Probability Theory and Its Applications
    "Modern Probability Theory and Its Applications" is a foundational textbook by Emanuel Parzen that systematically develops modern probability theory and demonstrates its use in a wide range of statistical and applied contexts.
  • 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: Harmonic Analysis and the Theory of Probability
Triple: [Salomon Bochner, notableWork, Harmonic Analysis and the Theory of Probability]
Generated description
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.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Harmonic Analysis and the Theory of Probability
Target entity description: 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.
  • A. 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.
  • B. Three regularity results in harmonic analysis
    "Three regularity results in harmonic analysis" is the doctoral thesis of mathematician Terence Tao, focusing on advanced problems in harmonic analysis and the study of regularity properties of functions and operators.
  • C. Littlewood–Paley theory
    Littlewood–Paley theory is a collection of techniques in harmonic analysis that decompose functions into frequency-localized pieces to study their behavior in L^p spaces and related function spaces.
  • D. 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.
  • E. Modern Probability Theory and Its Applications
    "Modern Probability Theory and Its Applications" is a foundational textbook by Emanuel Parzen that systematically develops modern probability theory and demonstrates its use in a wide range of statistical and applied contexts.
  • 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_69c68809b4608190a2509ddb5ab87f05 completed March 27, 2026, 1:37 p.m.
NER Named-entity recognition batch_69c6d125db3c8190aad28919226a16da completed March 27, 2026, 6:49 p.m.
NED1 Entity disambiguation (via context triple) batch_69c700993128819081614ccfa68d7320 completed March 27, 2026, 10:11 p.m.
NEDg Description generation batch_69c70262f3e48190b544be536ee0b674 completed March 27, 2026, 10:19 p.m.
NED2 Entity disambiguation (via description) batch_69c70311418c8190a902cf21187fdc51 completed March 27, 2026, 10:22 p.m.
Created at: March 27, 2026, 2:07 p.m.