Triple
T5709628
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Elias Stein |
E125871
|
entity |
| Predicate | fieldOfWork |
P3
|
FINISHED |
| Object | Littlewood–Paley theory |
E412933
|
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: Littlewood–Paley theory | Statement: [Elias Stein, fieldOfWork, Littlewood–Paley theory]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Littlewood–Paley theory Context triple: [Elias Stein, fieldOfWork, Littlewood–Paley theory]
-
A.
Littlewood–Paley theory
chosen
Littlewood–Paley theory is a collection of techniques in harmonic analysis that decompose functions into frequency-localized pieces to study their behavior in L^p spaces and related function spaces.
-
B.
Three regularity results in harmonic analysis
"Three regularity results in harmonic analysis" is the doctoral thesis of mathematician Terence Tao, focusing on advanced problems in harmonic analysis and the study of regularity properties of functions and operators.
-
C.
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.
-
D.
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.
-
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.
- 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_69c0082d6fe48190b777fb383769e5c8 |
completed | March 22, 2026, 3:18 p.m. |
| NER | Named-entity recognition | batch_69c0248c3dac8190824fca9ddde89665 |
completed | March 22, 2026, 5:19 p.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69c05a6f5ac08190b5acbccea756d2de |
completed | March 22, 2026, 9:09 p.m. |
Created at: March 22, 2026, 3:46 p.m.