Triple
T10660072
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Ulisse Dini |
E251198
|
entity |
| Predicate | notableConcept |
P201
|
FINISHED |
| Object |
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.
|
E877690
|
NE FINISHED |
How this triple was built (4 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: Dini test for convergence of Fourier series | Statement: [Ulisse Dini, notableConcept, Dini test for convergence of Fourier series]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Dini test for convergence of Fourier series Context triple: [Ulisse Dini, notableConcept, Dini test for convergence of Fourier series]
-
A.
Über die Darstellbarkeit einer Funktion durch eine trigonometrische Reihe
Über die Darstellbarkeit einer Funktion durch eine trigonometrische Reihe is Bernhard Riemann’s seminal 1854 paper that laid foundational ideas for Fourier series and modern real analysis, including the concept now known as the Riemann integral.
-
B.
Euler’s method of rearranging absolutely convergent series
Euler’s method of rearranging absolutely convergent series is a technique introduced by Leonhard Euler to systematically reorder and manipulate convergent infinite series in order to derive new identities and product expansions, such as those appearing in analytic number theory.
-
C.
Dirichlet test
The Dirichlet test is a criterion in mathematical analysis that provides sufficient conditions for the convergence of certain infinite series, particularly those involving oscillatory terms.
-
D.
Fourier series
A Fourier series is a way of representing a periodic function as an infinite sum of sines and cosines with appropriately chosen coefficients.
-
E.
The Fourier Integral and Certain of Its Applications
The Fourier Integral and Certain of Its Applications is a foundational mathematical work by Norbert Wiener that develops and applies Fourier analysis to problems in harmonic analysis and related areas.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NEDg
Description generation
gpt-5.1
Instruction
Generate a one-sentence description of the target entity. You are given a context triple in the form (subject, predicate, object), where the object is the target entity. # Instructions Use the triple to infer relevant information about the entity. Describe the entity based on what is most defining, well-known. Avoid repeating the information from the triple, unless really essential. # Response Format Return only the sentence: "Description: [one-sentence description of the target entity]"
Input
Entity: Dini test for convergence of Fourier series Triple: [Ulisse Dini, notableConcept, Dini test for convergence of Fourier series]
Generated description
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.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Dini test for convergence of Fourier series Target entity description: 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.
-
A.
Über die Darstellbarkeit einer Funktion durch eine trigonometrische Reihe
Über die Darstellbarkeit einer Funktion durch eine trigonometrische Reihe is Bernhard Riemann’s seminal 1854 paper that laid foundational ideas for Fourier series and modern real analysis, including the concept now known as the Riemann integral.
-
B.
Euler’s method of rearranging absolutely convergent series
Euler’s method of rearranging absolutely convergent series is a technique introduced by Leonhard Euler to systematically reorder and manipulate convergent infinite series in order to derive new identities and product expansions, such as those appearing in analytic number theory.
-
C.
Dirichlet test
The Dirichlet test is a criterion in mathematical analysis that provides sufficient conditions for the convergence of certain infinite series, particularly those involving oscillatory terms.
-
D.
Fourier series
A Fourier series is a way of representing a periodic function as an infinite sum of sines and cosines with appropriately chosen coefficients.
-
E.
The Fourier Integral and Certain of Its Applications
The Fourier Integral and Certain of Its Applications is a foundational mathematical work by Norbert Wiener that develops and applies Fourier analysis to problems in harmonic analysis and related areas.
- F. None of above. chosen
Provenance (5 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_69d6aa5b0d2881909584b20efc5877f0 |
completed | April 8, 2026, 7:19 p.m. |
| NER | Named-entity recognition | batch_69d6e0174dc4819093e577993c65ed32 |
completed | April 8, 2026, 11:09 p.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69d97a8375bc8190a79c09ba2626ce50 |
completed | April 10, 2026, 10:32 p.m. |
| NEDg | Description generation | batch_69d97e7330cc81908d7e35cbba5b5b0e |
completed | April 10, 2026, 10:49 p.m. |
| NED2 | Entity disambiguation (via description) | batch_69d97ef8d90c81909a2bc3adbb1f05bf |
completed | April 10, 2026, 10:51 p.m. |
Created at: April 8, 2026, 9:07 p.m.