Triple

T3072659
Position Surface form Disambiguated ID Type / Status
Subject Annals of Mathematics Studies E64059 entity
Predicate hasNotableWork P4 FINISHED
Object 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.
E325281 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: Singular Integrals and Differentiability Properties of Functions | Statement: [Annals of Mathematics Studies, hasNotableWork, Singular Integrals and Differentiability Properties of Functions]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Singular Integrals and Differentiability Properties of Functions
Context triple: [Annals of Mathematics Studies, hasNotableWork, Singular Integrals and Differentiability Properties of Functions]
  • A. 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.
  • B. Hardy–Littlewood maximal function
    The Hardy–Littlewood maximal function is a fundamental operator in real analysis and harmonic analysis that controls the local averages of a function and plays a key role in differentiation theorems and singular integral theory.
  • C. Méthodes de calcul différentiel absolu et leurs applications
    Méthodes de calcul différentiel absolu et leurs applications is a foundational mathematical work that systematically develops the theory of tensor calculus and its applications, laying groundwork later used in general relativity.
  • D. Lezioni di calcolo differenziale assoluto
    "Lezioni di calcolo differenziale assoluto" is a foundational mathematical text by Tullio Levi-Civita that systematically develops the theory of absolute differential calculus, now known as tensor calculus, with applications to geometry and physics.
  • E. Israel–Carter–Robinson uniqueness theorems
    The Israel–Carter–Robinson uniqueness theorems are a set of results in general relativity showing that stationary, asymptotically flat black holes in four-dimensional spacetime are completely characterized by just their mass, charge, and angular momentum.
  • 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: Singular Integrals and Differentiability Properties of Functions
Triple: [Annals of Mathematics Studies, hasNotableWork, Singular Integrals and Differentiability Properties of Functions]
Generated description
"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.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Singular Integrals and Differentiability Properties of Functions
Target entity description: "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.
  • A. 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.
  • B. Hardy–Littlewood maximal function
    The Hardy–Littlewood maximal function is a fundamental operator in real analysis and harmonic analysis that controls the local averages of a function and plays a key role in differentiation theorems and singular integral theory.
  • C. Méthodes de calcul différentiel absolu et leurs applications
    Méthodes de calcul différentiel absolu et leurs applications is a foundational mathematical work that systematically develops the theory of tensor calculus and its applications, laying groundwork later used in general relativity.
  • D. Lezioni di calcolo differenziale assoluto
    "Lezioni di calcolo differenziale assoluto" is a foundational mathematical text by Tullio Levi-Civita that systematically develops the theory of absolute differential calculus, now known as tensor calculus, with applications to geometry and physics.
  • E. Israel–Carter–Robinson uniqueness theorems
    The Israel–Carter–Robinson uniqueness theorems are a set of results in general relativity showing that stationary, asymptotically flat black holes in four-dimensional spacetime are completely characterized by just their mass, charge, and angular momentum.
  • 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_69ad857a8aec8190bfdfd9c14554ac5a completed March 8, 2026, 2:19 p.m.
NER Named-entity recognition batch_69ada14e372c81908c25c7f3e7e0c864 completed March 8, 2026, 4:18 p.m.
NED1 Entity disambiguation (via context triple) batch_69b1f8828c488190877902a6c2dfcb5e completed March 11, 2026, 11:19 p.m.
NEDg Description generation batch_69b1f930321081908f98aa5f9b8ba611 completed March 11, 2026, 11:22 p.m.
NED2 Entity disambiguation (via description) batch_69b1f9ad0b148190b98f93699598dd1e completed March 11, 2026, 11:24 p.m.
Created at: March 8, 2026, 3:02 p.m.