Triple
T9747019
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Alberto Calderón |
E236336
|
entity |
| Predicate | notableFor |
P22
|
FINISHED |
| Object | Calderón–Zygmund decomposition |
E544152
|
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: Calderón–Zygmund decomposition | Statement: [Alberto Calderón, notableFor, Calderón–Zygmund decomposition]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Calderón–Zygmund decomposition Context triple: [Alberto Calderón, notableFor, Calderón–Zygmund decomposition]
-
A.
Calderón–Zygmund theory
chosen
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.
-
B.
Littlewood–Paley theory
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.
-
C.
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.
-
D.
Riesz transforms
Riesz transforms are fundamental singular integral operators in harmonic analysis that generalize the Hilbert transform to higher dimensions and play a key role in studying function spaces and partial differential equations.
-
E.
Bochner–Riesz means
Bochner–Riesz means are a family of summability methods in harmonic analysis used to improve the convergence of Fourier series and Fourier integrals by smoothing their partial sums.
- 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_69ca84d3e24481908a476e2231123cf9 |
completed | March 30, 2026, 2:12 p.m. |
| NER | Named-entity recognition | batch_69cd9f677830819096d388b9c798ecd5 |
completed | April 1, 2026, 10:42 p.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69d1b00d76488190af68cba694dc329c |
completed | April 5, 2026, 12:42 a.m. |
Created at: March 30, 2026, 8:23 p.m.