Triple
T21972953
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Harmonic Analysis: Real-Variable Methods, Orthogonality, and Oscillatory Integrals |
E542636
|
entity |
| Predicate | subject |
P450
|
FINISHED |
| Object | Hardy spaces |
—
|
NE NERFINISHED |
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: Hardy spaces | Statement: [Harmonic Analysis: Real-Variable Methods, Orthogonality, and Oscillatory Integrals, subject, Hardy spaces]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Hardy spaces Context triple: [Harmonic Analysis: Real-Variable Methods, Orthogonality, and Oscillatory Integrals, subject, Hardy spaces]
-
A.
Hardy space
chosen
A Hardy space is a function space in complex analysis consisting of holomorphic functions on a domain whose mean values on boundary circles (or lines) are uniformly bounded, playing a central role in harmonic and operator theory.
-
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.
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.
-
D.
Dirichlet space
Dirichlet space is a functional Hilbert space of analytic functions on the unit disk characterized by square-integrable derivatives, playing a central role in complex analysis and potential theory.
-
E.
Jessen’s theorem in harmonic analysis
Jessen’s theorem in harmonic analysis is a result that provides conditions under which certain trigonometric or Fourier series converge almost everywhere, reflecting Børge Jessen’s contributions to the study of convergence phenomena in harmonic analysis.
- F. None of above.
- G. Unsure - the case is ambiguous/there is not enough information to decide.
Provenance (2 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_69e0c48070988190909db97667b9a0ac |
completed | April 16, 2026, 11:14 a.m. |
| NER | Named-entity recognition | batch_69f124857dcc8190ab474cd8ab9c130a |
completed | April 28, 2026, 9:20 p.m. |
Created at: April 16, 2026, 8:02 p.m.