Triple

T11728191
Position Surface form Disambiguated ID Type / Status
Subject Lennart Carleson E278829 entity
Predicate knownFor P22 FINISHED
Object Carleson measure
A Carleson measure is a type of measure in harmonic analysis that characterizes boundary behavior and embedding properties of function spaces such as Hardy and BMO spaces.
E943110 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: Carleson measure | Statement: [Lennart Carleson, knownFor, Carleson measure]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Carleson measure
Context triple: [Lennart Carleson, knownFor, Carleson measure]
  • A. Calderón–Zygmund theory
    Calderón–Zygmund theory is a branch of harmonic analysis that studies singular integral operators and their boundedness properties on function spaces such as L^p.
  • B. Hardy space
    A Hardy space is a function space in complex analysis consisting of holomorphic functions on a domain whose mean values on boundary circles (or lines) are uniformly bounded, playing a central role in harmonic and operator theory.
  • C. Bochner–Riesz means
    Bochner–Riesz means are a family of summability methods in harmonic analysis used to improve the convergence of Fourier series and Fourier integrals by smoothing their partial sums.
  • D. 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.
  • E. 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.
  • 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: Carleson measure
Triple: [Lennart Carleson, knownFor, Carleson measure]
Generated description
A Carleson measure is a type of measure in harmonic analysis that characterizes boundary behavior and embedding properties of function spaces such as Hardy and BMO spaces.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Carleson measure
Target entity description: A Carleson measure is a type of measure in harmonic analysis that characterizes boundary behavior and embedding properties of function spaces such as Hardy and BMO spaces.
  • A. Calderón–Zygmund theory
    Calderón–Zygmund theory is a branch of harmonic analysis that studies singular integral operators and their boundedness properties on function spaces such as L^p.
  • B. Hardy space
    A Hardy space is a function space in complex analysis consisting of holomorphic functions on a domain whose mean values on boundary circles (or lines) are uniformly bounded, playing a central role in harmonic and operator theory.
  • C. Bochner–Riesz means
    Bochner–Riesz means are a family of summability methods in harmonic analysis used to improve the convergence of Fourier series and Fourier integrals by smoothing their partial sums.
  • D. 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.
  • E. 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.
  • 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_69d6aaffec6881908bead509e8621742 completed April 8, 2026, 7:22 p.m.
NER Named-entity recognition batch_69d8a4d80ef881908cab956787ab07fd completed April 10, 2026, 7:20 a.m.
NED1 Entity disambiguation (via context triple) batch_69ef83e9efdc8190830f9b9cb5362b1c completed April 27, 2026, 3:42 p.m.
NEDg Description generation batch_69ef96b286e48190adf7224749f9a01c completed April 27, 2026, 5:02 p.m.
NED2 Entity disambiguation (via description) batch_69efb51a94508190ae3159ad4a9725c8 completed April 27, 2026, 7:12 p.m.
Created at: April 8, 2026, 9:41 p.m.