Triple

T5790563
Position Surface form Disambiguated ID Type / Status
Subject Jean Bourgain E128380 entity
Predicate notableWork P4 FINISHED
Object 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.
E547407 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: New classes of Lp-spaces | Statement: [Jean Bourgain, notableWork, New classes of Lp-spaces]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: New classes of Lp-spaces
Context triple: [Jean Bourgain, notableWork, New classes of Lp-spaces]
  • A. Orlicz spaces
    Orlicz spaces are a class of function spaces that generalize Lebesgue spaces by measuring integrability via convex Orlicz functions rather than fixed power exponents.
  • B. Lebesgue spaces
    Lebesgue spaces are function spaces, denoted \(L^p\), that consist of measurable functions whose absolute values raised to the \(p\)-th power are integrable, forming a fundamental framework in modern analysis and probability theory.
  • C. 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.
  • 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. Sobolev spaces
    Sobolev spaces are function spaces that incorporate both functions and their weak derivatives, providing a fundamental framework for studying partial differential equations and variational problems.
  • 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: New classes of Lp-spaces
Triple: [Jean Bourgain, notableWork, New classes of Lp-spaces]
Generated description
"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.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: New classes of Lp-spaces
Target entity description: "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.
  • A. Orlicz spaces
    Orlicz spaces are a class of function spaces that generalize Lebesgue spaces by measuring integrability via convex Orlicz functions rather than fixed power exponents.
  • B. Lebesgue spaces
    Lebesgue spaces are function spaces, denoted \(L^p\), that consist of measurable functions whose absolute values raised to the \(p\)-th power are integrable, forming a fundamental framework in modern analysis and probability theory.
  • C. 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.
  • 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. Sobolev spaces
    Sobolev spaces are function spaces that incorporate both functions and their weak derivatives, providing a fundamental framework for studying partial differential equations and variational problems.
  • 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_69c00845ca68819081a2ce3ecca577f7 completed March 22, 2026, 3:18 p.m.
NER Named-entity recognition batch_69c02a5585788190821b8da40259e0e7 completed March 22, 2026, 5:43 p.m.
NED1 Entity disambiguation (via context triple) batch_69c09820f5c08190811e848eb44ce5b9 completed March 23, 2026, 1:32 a.m.
NEDg Description generation batch_69c0990bf38081908c09c5dfe660c35b completed March 23, 2026, 1:36 a.m.
NED2 Entity disambiguation (via description) batch_69c099b4bc4481909e7cf6886e5ccbea completed March 23, 2026, 1:39 a.m.
Created at: March 22, 2026, 3:51 p.m.