Triple

T2364757
Position Surface form Disambiguated ID Type / Status
Subject Über die Darstellbarkeit einer Funktion durch eine trigonometrische Reihe E47354 entity
Predicate relatedConcept P37 FINISHED
Object Dirichlet conditions
Dirichlet conditions are a set of sufficient criteria on a function—such as piecewise continuity and having a finite number of extrema and discontinuities on an interval—that guarantee the convergence of its Fourier series representation.
E259780 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: Dirichlet conditions | Statement: [Über die Darstellbarkeit einer Funktion durch eine trigonometrische Reihe, relatedConcept, Dirichlet conditions]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Dirichlet conditions
Context triple: [Über die Darstellbarkeit einer Funktion durch eine trigonometrische Reihe, relatedConcept, Dirichlet conditions]
  • A. Riemann–Lebesgue lemma
    The Riemann–Lebesgue lemma is a fundamental result in Fourier analysis stating that the Fourier coefficients (or transform) of an integrable function vanish at infinity.
  • B. Dirac delta function
    The Dirac delta function is a mathematical construct used in physics and engineering to model an idealized point mass or point charge, being zero everywhere except at a single point where it is infinitely large yet integrates to one.
  • C. Nyquist theorem
    The Nyquist theorem is a fundamental principle in signal processing that states a continuous signal can be perfectly reconstructed from its samples if it is sampled at more than twice its highest frequency component.
  • D. 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.
  • E. Weierstrass function
    The Weierstrass function is a classic example in mathematical analysis of a continuous function that is nowhere differentiable, illustrating the counterintuitive behavior possible in real-valued functions.
  • 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: Dirichlet conditions
Triple: [Über die Darstellbarkeit einer Funktion durch eine trigonometrische Reihe, relatedConcept, Dirichlet conditions]
Generated description
Dirichlet conditions are a set of sufficient criteria on a function—such as piecewise continuity and having a finite number of extrema and discontinuities on an interval—that guarantee the convergence of its Fourier series representation.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Dirichlet conditions
Target entity description: Dirichlet conditions are a set of sufficient criteria on a function—such as piecewise continuity and having a finite number of extrema and discontinuities on an interval—that guarantee the convergence of its Fourier series representation.
  • A. Riemann–Lebesgue lemma
    The Riemann–Lebesgue lemma is a fundamental result in Fourier analysis stating that the Fourier coefficients (or transform) of an integrable function vanish at infinity.
  • B. Dirac delta function
    The Dirac delta function is a mathematical construct used in physics and engineering to model an idealized point mass or point charge, being zero everywhere except at a single point where it is infinitely large yet integrates to one.
  • C. Nyquist theorem
    The Nyquist theorem is a fundamental principle in signal processing that states a continuous signal can be perfectly reconstructed from its samples if it is sampled at more than twice its highest frequency component.
  • D. 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.
  • E. Weierstrass function
    The Weierstrass function is a classic example in mathematical analysis of a continuous function that is nowhere differentiable, illustrating the counterintuitive behavior possible in real-valued functions.
  • 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_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.