Triple

T17020276
Position Surface form Disambiguated ID Type / Status
Subject Orlicz spaces E412928 entity
Predicate relatedTo P37 FINISHED
Object Grand Lebesgue spaces
Grand Lebesgue spaces are a class of function spaces that generalize classical Lebesgue and Orlicz spaces by controlling integrability through variable exponents or parameter ranges, making them useful in fine-scale analysis of functions and operators.
E1247128 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: Grand Lebesgue spaces | Statement: [Orlicz spaces, relatedTo, Grand Lebesgue spaces]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Grand Lebesgue spaces
Context triple: [Orlicz spaces, relatedTo, Grand Lebesgue 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. 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.
  • 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. Gowers dichotomy for Banach spaces
    Gowers dichotomy for Banach spaces is a fundamental result in functional analysis that classifies infinite-dimensional Banach spaces by showing that each contains either a subspace with an unconditional basis or a hereditarily indecomposable subspace.
  • 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: Grand Lebesgue spaces
Triple: [Orlicz spaces, relatedTo, Grand Lebesgue spaces]
Generated description
Grand Lebesgue spaces are a class of function spaces that generalize classical Lebesgue and Orlicz spaces by controlling integrability through variable exponents or parameter ranges, making them useful in fine-scale analysis of functions and operators.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Grand Lebesgue spaces
Target entity description: Grand Lebesgue spaces are a class of function spaces that generalize classical Lebesgue and Orlicz spaces by controlling integrability through variable exponents or parameter ranges, making them useful in fine-scale analysis of functions and operators.
  • 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. 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.
  • 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. Gowers dichotomy for Banach spaces
    Gowers dichotomy for Banach spaces is a fundamental result in functional analysis that classifies infinite-dimensional Banach spaces by showing that each contains either a subspace with an unconditional basis or a hereditarily indecomposable subspace.
  • 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_69d886cc4170819093deddc7b8b4b6a7 completed April 10, 2026, 5:12 a.m.
NER Named-entity recognition batch_69e3d482c3a0819099e6ea4acb0a08ee completed April 18, 2026, 6:59 p.m.
NED1 Entity disambiguation (via context triple) batch_6a011b4f9dfc819085639edb5cda1cca completed May 10, 2026, 11:57 p.m.
NEDg Description generation batch_6a011cc1afc48190b83e3203407c1d7f completed May 11, 2026, 12:03 a.m.
NED2 Entity disambiguation (via description) batch_6a011d67c82c8190b737406e8952eb2b completed May 11, 2026, 12:05 a.m.
Created at: April 10, 2026, 5:33 a.m.