Triple

T18479413
Position Surface form Disambiguated ID Type / Status
Subject Tauberian theorems E451517 entity
Predicate hasSubtype P1244 FINISHED
Object Wiener Tauberian theorems
Wiener Tauberian theorems are fundamental results in harmonic analysis that relate the behavior of a function to the properties of its Fourier transform, providing powerful tools for deducing asymptotic information from transform data.
E451517 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: Wiener Tauberian theorems | Statement: [Tauberian theorems, hasSubtype, Wiener Tauberian theorems]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Wiener Tauberian theorems
Context triple: [Tauberian theorems, hasSubtype, Wiener Tauberian theorems]
  • A. Tauberian theorems
    Tauberian theorems are results in mathematical analysis that connect the behavior of transformed series or integrals (such as those summed by Abel or Cesàro methods) back to the asymptotic behavior or convergence of the original sequences or series.
  • B. Paley–Wiener theorem
    The Paley–Wiener theorem is a fundamental result in harmonic analysis that characterizes which functions arise as Fourier transforms of compactly supported functions (or distributions), linking analytic properties of entire functions with support properties in the original domain.
  • C. Harmonic Analysis and the Theory of Probability
    Harmonic Analysis and the Theory of Probability is a seminal mathematical monograph that connects Fourier-analytic methods with probabilistic concepts, helping to lay the foundations of modern probability theory.
  • D. Herglotz's theorem
    Herglotz's theorem is a fundamental result in harmonic analysis and probability theory that characterizes positive-definite functions on the unit circle via representing measures.
  • E. Bochner–Riesz means
    Bochner–Riesz means are a family of summability methods in harmonic analysis used to improve the convergence of Fourier series and Fourier integrals by smoothing their partial sums.
  • 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: Wiener Tauberian theorems
Triple: [Tauberian theorems, hasSubtype, Wiener Tauberian theorems]
Generated description
Wiener Tauberian theorems are fundamental results in harmonic analysis that relate the behavior of a function to the properties of its Fourier transform, providing powerful tools for deducing asymptotic information from transform data.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Wiener Tauberian theorems
Target entity description: Wiener Tauberian theorems are fundamental results in harmonic analysis that relate the behavior of a function to the properties of its Fourier transform, providing powerful tools for deducing asymptotic information from transform data.
  • A. Tauberian theorems chosen
    Tauberian theorems are results in mathematical analysis that connect the behavior of transformed series or integrals (such as those summed by Abel or Cesàro methods) back to the asymptotic behavior or convergence of the original sequences or series.
  • B. Paley–Wiener theorem
    The Paley–Wiener theorem is a fundamental result in harmonic analysis that characterizes which functions arise as Fourier transforms of compactly supported functions (or distributions), linking analytic properties of entire functions with support properties in the original domain.
  • C. Harmonic Analysis and the Theory of Probability
    Harmonic Analysis and the Theory of Probability is a seminal mathematical monograph that connects Fourier-analytic methods with probabilistic concepts, helping to lay the foundations of modern probability theory.
  • D. Herglotz's theorem
    Herglotz's theorem is a fundamental result in harmonic analysis and probability theory that characterizes positive-definite functions on the unit circle via representing measures.
  • E. Bochner–Riesz means
    Bochner–Riesz means are a family of summability methods in harmonic analysis used to improve the convergence of Fourier series and Fourier integrals by smoothing their partial sums.
  • 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_69d8d38465a0819099b9b42d2a662ac1 completed April 10, 2026, 10:40 a.m.
NER Named-entity recognition batch_69e53065e8388190bb216dae89f8cf75 completed April 19, 2026, 7:43 p.m.
NED1 Entity disambiguation (via context triple) batch_6a043f2f64848190808075254008e6e1 completed May 13, 2026, 9:06 a.m.
NEDg Description generation batch_6a043fb7db388190bb50cfade4f025f9 completed May 13, 2026, 9:09 a.m.
NED2 Entity disambiguation (via description) batch_6a044063c6048190b65620af8ceed897 completed May 13, 2026, 9:12 a.m.
Created at: April 10, 2026, 11:35 a.m.