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.