Triple

T17020265
Position Surface form Disambiguated ID Type / Status
Subject Orlicz spaces E412928 entity
Predicate hasConcept P531 FINISHED
Object Orlicz–Sobolev space
Orlicz–Sobolev space is a functional space generalizing classical Sobolev spaces by replacing power-type integrability conditions with more flexible Orlicz growth functions, allowing finer control of function regularity and integrability.
E412928 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: Orlicz–Sobolev space | Statement: [Orlicz spaces, hasConcept, Orlicz–Sobolev space]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Orlicz–Sobolev space
Context triple: [Orlicz spaces, hasConcept, Orlicz–Sobolev space]
  • 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. 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.
  • 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. Sobolev inequality
    The Sobolev inequality is a fundamental result in functional analysis and partial differential equations that bounds the size of a function in certain Lebesgue spaces by the size of its derivatives, enabling key embedding and regularity properties.
  • E. 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.
  • 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: Orlicz–Sobolev space
Triple: [Orlicz spaces, hasConcept, Orlicz–Sobolev space]
Generated description
Orlicz–Sobolev space is a functional space generalizing classical Sobolev spaces by replacing power-type integrability conditions with more flexible Orlicz growth functions, allowing finer control of function regularity and integrability.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Orlicz–Sobolev space
Target entity description: Orlicz–Sobolev space is a functional space generalizing classical Sobolev spaces by replacing power-type integrability conditions with more flexible Orlicz growth functions, allowing finer control of function regularity and integrability.
  • A. Orlicz spaces chosen
    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. 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.
  • 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. Sobolev inequality
    The Sobolev inequality is a fundamental result in functional analysis and partial differential equations that bounds the size of a function in certain Lebesgue spaces by the size of its derivatives, enabling key embedding and regularity properties.
  • E. 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.
  • F. None of above.

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.