Triple
T17020240
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Orlicz spaces |
E412928
|
entity |
| Predicate | basedOn |
P98
|
FINISHED |
| Object |
Orlicz function
An Orlicz function is a convex, increasing function used in functional analysis to generalize the notion of growth conditions in defining Orlicz spaces, extending classical \(L^p\) space theory.
|
E1247126
|
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 function | Statement: [Orlicz spaces, basedOn, Orlicz function]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Orlicz function Context triple: [Orlicz spaces, basedOn, Orlicz function]
-
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.
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.
-
C.
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.
-
D.
Minkowski functional
The Minkowski functional is a mathematical tool in functional analysis that assigns a nonnegative real number to each vector in a vector space based on its position relative to a given convex, balanced, absorbing set, generalizing the notion of a norm.
-
E.
Banach spaces
Banach spaces are complete normed vector spaces that provide a fundamental framework for functional analysis and the study of infinite-dimensional linear phenomena.
- 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 function Triple: [Orlicz spaces, basedOn, Orlicz function]
Generated description
An Orlicz function is a convex, increasing function used in functional analysis to generalize the notion of growth conditions in defining Orlicz spaces, extending classical \(L^p\) space theory.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Orlicz function Target entity description: An Orlicz function is a convex, increasing function used in functional analysis to generalize the notion of growth conditions in defining Orlicz spaces, extending classical \(L^p\) space theory.
-
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.
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.
-
C.
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.
-
D.
Minkowski functional
The Minkowski functional is a mathematical tool in functional analysis that assigns a nonnegative real number to each vector in a vector space based on its position relative to a given convex, balanced, absorbing set, generalizing the notion of a norm.
-
E.
Banach spaces
Banach spaces are complete normed vector spaces that provide a fundamental framework for functional analysis and the study of infinite-dimensional linear phenomena.
- 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.