Triple

T19285086
Position Surface form Disambiguated ID Type / Status
Subject Fourier series E482288 entity
Predicate relatedConcept P37 FINISHED
Object Parseval's identity — NE NERFINISHED

How this triple was built (2 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 identity | Statement: [Fourier series, relatedConcept, Parseval's identity]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Parseval's identity
Context triple: [Fourier series, relatedConcept, Parseval's identity]
  • A. 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.
  • B. Parseval identity for orthonormal systems in L^2 chosen
    The Parseval identity for orthonormal systems in \(L^2\) is a fundamental result in functional analysis stating that the squared norm of a function equals the sum of the squares of its Fourier (or orthonormal expansion) coefficients, expressing energy conservation between a function and its orthonormal series representation.
  • C. 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.
  • D. 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.
  • E. 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.
  • F. None of above.
  • G. Unsure - the case is ambiguous/there is not enough information to decide.

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.