Triple
T12797520
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Functional analysis |
E305927
|
entity |
| Predicate | fieldOfStudy |
P3
|
FINISHED |
| Object | Sobolev spaces |
E412927
|
NE FINISHED |
How this triple was built (2 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: Sobolev spaces | Statement: [Functional analysis, fieldOfStudy, Sobolev spaces]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Sobolev spaces Context triple: [Functional analysis, fieldOfStudy, Sobolev spaces]
-
A.
Sobolev spaces
chosen
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.
-
B.
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.
-
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.
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.
-
E.
Calderón–Zygmund theory
Calderón–Zygmund theory is a branch of harmonic analysis that studies singular integral operators and their boundedness properties on function spaces such as L^p.
- F. None of above.
- G. Unsure - the case is ambiguous/there is not enough information to decide.
Provenance (3 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_69d7bdf366888190a8cccb982606889c |
completed | April 9, 2026, 2:55 p.m. |
| NER | Named-entity recognition | batch_69d96e6db68481909a2ca8da1287f3e0 |
completed | April 10, 2026, 9:41 p.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69f68ec0d5dc819099a8036c6cbac634 |
completed | May 2, 2026, 11:54 p.m. |
Created at: April 9, 2026, 5:30 p.m.