Triple

T2364607
Position Surface form Disambiguated ID Type / Status
Subject Riemann–Lebesgue lemma E47351 entity
Predicate appliesTo P1129 FINISHED
Object Fourier transform
The Fourier transform is a mathematical operation that decomposes a function or signal into its constituent frequencies, forming a cornerstone of harmonic analysis and signal processing.
E173 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 transform | Statement: [Riemann–Lebesgue lemma, appliesTo, Fourier transform]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Fourier transform
Context triple: [Riemann–Lebesgue lemma, appliesTo, Fourier transform]
  • A. Fourier analysis
    Fourier analysis is a mathematical method for decomposing functions or signals into sums of sinusoidal components, widely used in fields such as signal processing, physics, and engineering.
  • B. FFT
    FFT is the ICAO airline designator used in aviation to identify Frontier Airlines in flight plans and air traffic control communications.
  • C. 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.
  • D. Laplace transform
    The Laplace transform is an integral transform widely used in mathematics, physics, and engineering to convert functions of time into functions of a complex variable, simplifying the analysis and solution of differential equations and linear systems.
  • E. Wiener–Khinchin theorem
    The Wiener–Khinchin theorem is a fundamental result in signal processing and probability theory that relates a wide-sense stationary random process’s autocorrelation function to its power spectral density via the 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 transform
Triple: [Riemann–Lebesgue lemma, appliesTo, Fourier transform]
Generated description
The Fourier transform is a mathematical operation that decomposes a function or signal into its constituent frequencies, forming a cornerstone of harmonic analysis and signal processing.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Fourier transform
Target entity description: The Fourier transform is a mathematical operation that decomposes a function or signal into its constituent frequencies, forming a cornerstone of harmonic analysis and signal processing.
  • A. Fourier analysis chosen
    Fourier analysis is a mathematical method for decomposing functions or signals into sums of sinusoidal components, widely used in fields such as signal processing, physics, and engineering.
  • B. FFT
    FFT is the ICAO airline designator used in aviation to identify Frontier Airlines in flight plans and air traffic control communications.
  • C. 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.
  • D. Laplace transform
    The Laplace transform is an integral transform widely used in mathematics, physics, and engineering to convert functions of time into functions of a complex variable, simplifying the analysis and solution of differential equations and linear systems.
  • E. Wiener–Khinchin theorem
    The Wiener–Khinchin theorem is a fundamental result in signal processing and probability theory that relates a wide-sense stationary random process’s autocorrelation function to its power spectral density via the 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_69a88a1a4a6081908645b0f2914521ab completed March 4, 2026, 7:38 p.m.
NER Named-entity recognition batch_69abc7486cb48190acef1891cc87bdb1 completed March 7, 2026, 6:35 a.m.
NED1 Entity disambiguation (via context triple) batch_69aea896e0388190aabff2d70787dc43 completed March 9, 2026, 11:01 a.m.
NEDg Description generation batch_69aea91ce164819091aa24b287f9fb8e completed March 9, 2026, 11:03 a.m.
NED2 Entity disambiguation (via description) batch_69aea999b864819084134c670e7c5d9c completed March 9, 2026, 11:06 a.m.
Created at: March 4, 2026, 7:55 p.m.