Triple

T6858929
Position Surface form Disambiguated ID Type / Status
Subject Wiener–Khinchin theorem E158222 entity
Predicate relatedTo P37 FINISHED
Object Parseval's theorem
Parseval's theorem is a fundamental result in Fourier analysis that equates the total energy of a function in the time (or spatial) domain with the total energy of its representation in the frequency domain.
E624505 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: Parseval's theorem | Statement: [Wiener–Khinchin theorem, relatedTo, Parseval's theorem]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Parseval's theorem
Context triple: [Wiener–Khinchin theorem, relatedTo, Parseval's theorem]
  • A. 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.
  • B. 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.
  • C. 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.
  • D. Poisson summation formula
    The Poisson summation formula is a fundamental result in harmonic analysis that links sums of a function over the integers to sums of its Fourier transform, with deep applications in number theory, signal processing, and physics.
  • E. convolution theorem
    The convolution theorem is a fundamental result in Fourier analysis stating that convolution in one domain corresponds to pointwise multiplication in the Fourier-transformed domain (and vice versa), greatly simplifying the analysis of linear systems.
  • 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: Parseval's theorem
Triple: [Wiener–Khinchin theorem, relatedTo, Parseval's theorem]
Generated description
Parseval's theorem is a fundamental result in Fourier analysis that equates the total energy of a function in the time (or spatial) domain with the total energy of its representation in the frequency domain.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Parseval's theorem
Target entity description: Parseval's theorem is a fundamental result in Fourier analysis that equates the total energy of a function in the time (or spatial) domain with the total energy of its representation in the frequency domain.
  • A. 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.
  • B. 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.
  • C. 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.
  • D. Poisson summation formula
    The Poisson summation formula is a fundamental result in harmonic analysis that links sums of a function over the integers to sums of its Fourier transform, with deep applications in number theory, signal processing, and physics.
  • E. convolution theorem
    The convolution theorem is a fundamental result in Fourier analysis stating that convolution in one domain corresponds to pointwise multiplication in the Fourier-transformed domain (and vice versa), greatly simplifying the analysis of linear systems.
  • 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_69c68830cdbc8190a8301c7a9d9f651a completed March 27, 2026, 1:37 p.m.
NER Named-entity recognition batch_69c6d8720bd48190adb446130a03d2bf completed March 27, 2026, 7:20 p.m.
NED1 Entity disambiguation (via context triple) batch_69c72fe79af081909baacbfd4d5e8f24 completed March 28, 2026, 1:33 a.m.
NEDg Description generation batch_69c7399b95e081908bbee3a598d6513c completed March 28, 2026, 2:14 a.m.
NED2 Entity disambiguation (via description) batch_69c739f1b20c8190a8ef57357d4956b4 completed March 28, 2026, 2:16 a.m.
Created at: March 27, 2026, 2:21 p.m.