Triple
T17020455
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Littlewood–Paley theory |
E412933
|
entity |
| Predicate | instanceOf |
P0
|
FINISHED |
| Object | theory in harmonic analysis |
C412
|
CONCEPT FINISHED |
How this triple was built (1 step)
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.
CD
Concept disambiguation
gpt-5-mini-2025-08-07
Target class: theory in harmonic analysis Context triple: [Littlewood–Paley theory, instanceOf, theory in harmonic analysis]
-
A.
area of harmonic analysis
chosen
An area of harmonic analysis is a branch of mathematics focused on representing functions or signals as superpositions of basic waves and studying the properties of these representations.
-
B.
functional analysis result
A functional analysis result is a formal conclusion or theorem that characterizes the behavior, structure, or properties of functions and operators on infinite-dimensional spaces, typically within the framework of normed, Banach, or Hilbert spaces.
-
C.
foundational work in functional analysis
Foundational work in functional analysis establishes the core concepts, theorems, and structures—such as normed spaces, Banach and Hilbert spaces, operators, and spectral theory—that underpin the rigorous study of infinite-dimensional linear systems and their applications.
-
D.
analytic functional
An analytic functional is a continuous linear functional defined on a space of analytic functions, often represented via integration against a complex measure or distribution.
-
E.
equation in functional analysis
An equation in functional analysis is a relation, typically involving functions and operators on infinite-dimensional spaces, that specifies conditions these objects must satisfy, often to study existence, uniqueness, and properties of solutions.
- F. None of above.
Provenance (1 batch)
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. |
Created at: April 10, 2026, 5:33 a.m.