Triple

T19285058
Position Surface form Disambiguated ID Type / Status
Subject Fourier series E482288 entity
Predicate hasComponent P35 FINISHED
Object Fourier cosine 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: Fourier cosine series | Statement: [Fourier series, hasComponent, Fourier cosine series]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Fourier cosine series
Context triple: [Fourier series, hasComponent, Fourier cosine 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. 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.
  • 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. 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.
  • E. Fourier transform
    The Fourier transform is a mathematical operation that decomposes a function or signal into its constituent frequencies, widely used in engineering, physics, and signal processing.
  • 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: Fourier cosine series
Target entity description: The Fourier cosine series is a trigonometric expansion that represents a function as a sum of cosine terms, typically used for even functions or problems with certain boundary conditions in Fourier analysis.
  • 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. 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.
  • 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. 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.
  • E. Fourier transform
    The Fourier transform is a mathematical operation that decomposes a function or signal into its constituent frequencies, widely used in engineering, physics, and signal processing.
  • F. None of above.

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_69d8e8cf61b0819096fe3e4107827c4e completed April 10, 2026, 12:10 p.m.
NER Named-entity recognition batch_69e5fc0152d48190b92272d4c7caa708 completed April 20, 2026, 10:12 a.m.
Created at: April 10, 2026, 1:30 p.m.