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.