Triple
T19456673
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Almost Periodic Functions |
E486749
|
entity |
| Predicate | centralConcept |
P533
|
FINISHED |
| Object | Bohr–Fourier series |
—
|
NE NERFINISHED |
How this triple was built (3 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: Bohr–Fourier series | Statement: [Almost Periodic Functions, centralConcept, Bohr–Fourier series]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Bohr–Fourier series Context triple: [Almost Periodic Functions, centralConcept, Bohr–Fourier series]
-
A.
Fejér’s theorem on Fourier series
Fejér’s theorem on Fourier series is a fundamental result in harmonic analysis stating that the Cesàro means (Fejér means) of the Fourier series of a continuous periodic function always converge uniformly to the function itself.
-
B.
Dirichlet theorem on Fourier series
The Dirichlet theorem on Fourier series gives conditions under which a periodic function can be represented by a convergent Fourier series, specifying how and where the series converges to the function.
-
C.
Dini test for convergence of Fourier series
The Dini test for convergence of Fourier series is a classical criterion in harmonic analysis that gives sufficient conditions, involving the behavior of a function near a point, to ensure the pointwise convergence of its Fourier series there.
-
D.
Trigonometric Series, Vol. I
Trigonometric Series, Vol. I is a foundational mathematical monograph by Antoni Zygmund that systematically develops the theory of trigonometric series and Fourier analysis.
-
E.
Trigonometric Series, Vol. II
"Trigonometric Series, Vol. II" is a classic advanced mathematics text by Antoni Zygmund that develops the modern theory of trigonometric series and Fourier analysis.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Bohr–Fourier series Target entity description: The Bohr–Fourier series is a generalization of the classical Fourier series that represents almost periodic functions as infinite sums of complex exponentials with possibly incommensurable frequencies.
-
A.
Fejér’s theorem on Fourier series
Fejér’s theorem on Fourier series is a fundamental result in harmonic analysis stating that the Cesàro means (Fejér means) of the Fourier series of a continuous periodic function always converge uniformly to the function itself.
-
B.
Dirichlet theorem on Fourier series
The Dirichlet theorem on Fourier series gives conditions under which a periodic function can be represented by a convergent Fourier series, specifying how and where the series converges to the function.
-
C.
Dini test for convergence of Fourier series
The Dini test for convergence of Fourier series is a classical criterion in harmonic analysis that gives sufficient conditions, involving the behavior of a function near a point, to ensure the pointwise convergence of its Fourier series there.
-
D.
Trigonometric Series, Vol. I
Trigonometric Series, Vol. I is a foundational mathematical monograph by Antoni Zygmund that systematically develops the theory of trigonometric series and Fourier analysis.
-
E.
Trigonometric Series, Vol. II
"Trigonometric Series, Vol. II" is a classic advanced mathematics text by Antoni Zygmund that develops the modern theory of trigonometric series and Fourier analysis.
- F. None of above. chosen
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_69d8e8d86d608190bd199a98d0297f27 |
completed | April 10, 2026, 12:11 p.m. |
| NER | Named-entity recognition | batch_69e633c4088881908f23f25a82a513f6 |
completed | April 20, 2026, 2:10 p.m. |
Created at: April 10, 2026, 1:38 p.m.