Triple

T19285057
Position Surface form Disambiguated ID Type / Status
Subject Fourier series E482288 entity
Predicate hasComponent P35 FINISHED
Object Fourier sine series
The Fourier sine series is a representation of a function as an infinite sum of sine terms, typically used for functions defined on a finite interval with certain boundary conditions.
E482288 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: Fourier sine series | Statement: [Fourier series, hasComponent, Fourier sine series]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Fourier sine series
Context triple: [Fourier series, hasComponent, Fourier sine series]
  • A. 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.
  • B. 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.
  • C. Serie di Fourier e altre rappresentazioni analitiche delle funzioni di una variabile reale
    "Serie di Fourier e altre rappresentazioni analitiche delle funzioni di una variabile reale" is a classic mathematical treatise by Ulisse Dini on Fourier series and related analytic methods for representing real-valued functions.
  • D. Fourier
    Fourier is a French surname most famously associated with Jean-Baptiste Joseph Fourier, the mathematician and physicist known for developing Fourier analysis and Fourier series.
  • E. Fourier inversion theorem
    The Fourier inversion theorem is a fundamental result in harmonic analysis that guarantees, under suitable conditions, that a function can be exactly reconstructed from its Fourier transform.
  • 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: Fourier sine series
Triple: [Fourier series, hasComponent, Fourier sine series]
Generated description
The Fourier sine series is a representation of a function as an infinite sum of sine terms, typically used for functions defined on a finite interval with certain boundary conditions.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Fourier sine series
Target entity description: The Fourier sine series is a representation of a function as an infinite sum of sine terms, typically used for functions defined on a finite interval with certain boundary conditions.
  • A. Fourier series chosen
    A Fourier series is a way of representing a periodic function as an infinite sum of sines and cosines with appropriately chosen coefficients.
  • B. 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.
  • C. Serie di Fourier e altre rappresentazioni analitiche delle funzioni di una variabile reale
    "Serie di Fourier e altre rappresentazioni analitiche delle funzioni di una variabile reale" is a classic mathematical treatise by Ulisse Dini on Fourier series and related analytic methods for representing real-valued functions.
  • D. Fourier
    Fourier is a French surname most famously associated with Jean-Baptiste Joseph Fourier, the mathematician and physicist known for developing Fourier analysis and Fourier series.
  • E. Fourier inversion theorem
    The Fourier inversion theorem is a fundamental result in harmonic analysis that guarantees, under suitable conditions, that a function can be exactly reconstructed from its Fourier transform.
  • F. None of above.

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_69d8e8cf61b0819096fe3e4107827c4e completed April 10, 2026, 12:10 p.m.
NER Named-entity recognition batch_69e5fc0152d48190b92272d4c7caa708 completed April 20, 2026, 10:12 a.m.
NED1 Entity disambiguation (via context triple) batch_6a070e80d5b08190b304a874dac3d21d completed May 15, 2026, 12:16 p.m.
NEDg Description generation batch_6a070ef513888190b8c9f8c2de36f234 completed May 15, 2026, 12:17 p.m.
NED2 Entity disambiguation (via description) batch_6a070feb5d948190b8d05d13f250d2ab completed May 15, 2026, 12:22 p.m.
Created at: April 10, 2026, 1:30 p.m.