Triple

T17872314
Position Surface form Disambiguated ID Type / Status
Subject Antoni Zygmund E446864 entity
Predicate notableWork P4 FINISHED
Object Trigonometric Series, Vol. I
Trigonometric Series, Vol. I is a foundational mathematical monograph by Antoni Zygmund that systematically develops the theory of trigonometric series and Fourier analysis.
E1295075 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: Trigonometric Series, Vol. I | Statement: [Antoni Zygmund, notableWork, Trigonometric Series, Vol. I]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Trigonometric Series, Vol. I
Context triple: [Antoni Zygmund, notableWork, Trigonometric Series, Vol. I]
  • A. Über die Darstellbarkeit einer Funktion durch eine trigonometrische Reihe
    Über die Darstellbarkeit einer Funktion durch eine trigonometrische Reihe is Bernhard Riemann’s seminal 1854 paper that laid foundational ideas for Fourier series and modern real analysis, including the concept now known as the Riemann integral.
  • B. Dirichlet theorem on Fourier series
    The Dirichlet theorem on Fourier series gives conditions under which a periodic function can be represented by a convergent Fourier series, specifying how and where the series converges to the function.
  • C. Lectures on Fourier Integrals
    Lectures on Fourier Integrals is a classic mathematical monograph by Salomon Bochner that systematically develops the theory and applications of Fourier integrals and transforms.
  • D. Serie di Fourier e altre rappresentazioni analitiche delle funzioni di una variabile reale
    "Serie di Fourier e altre rappresentazioni analitiche delle funzioni di una variabile reale" is a classic mathematical treatise by Ulisse Dini on Fourier series and related analytic methods for representing real-valued functions.
  • E. Theory of Multiply Periodic Functions
    Theory of Multiply Periodic Functions is a foundational mathematical work by Henry Frederick Baker that systematically develops the theory of functions with multiple complex periods, including abelian and related 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: Trigonometric Series, Vol. I
Triple: [Antoni Zygmund, notableWork, Trigonometric Series, Vol. I]
Generated description
Trigonometric Series, Vol. I is a foundational mathematical monograph by Antoni Zygmund that systematically develops the theory of trigonometric series and Fourier analysis.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Trigonometric Series, Vol. I
Target entity description: Trigonometric Series, Vol. I is a foundational mathematical monograph by Antoni Zygmund that systematically develops the theory of trigonometric series and Fourier analysis.
  • A. Über die Darstellbarkeit einer Funktion durch eine trigonometrische Reihe
    Über die Darstellbarkeit einer Funktion durch eine trigonometrische Reihe is Bernhard Riemann’s seminal 1854 paper that laid foundational ideas for Fourier series and modern real analysis, including the concept now known as the Riemann integral.
  • B. Dirichlet theorem on Fourier series
    The Dirichlet theorem on Fourier series gives conditions under which a periodic function can be represented by a convergent Fourier series, specifying how and where the series converges to the function.
  • C. Lectures on Fourier Integrals
    Lectures on Fourier Integrals is a classic mathematical monograph by Salomon Bochner that systematically develops the theory and applications of Fourier integrals and transforms.
  • D. Serie di Fourier e altre rappresentazioni analitiche delle funzioni di una variabile reale
    "Serie di Fourier e altre rappresentazioni analitiche delle funzioni di una variabile reale" is a classic mathematical treatise by Ulisse Dini on Fourier series and related analytic methods for representing real-valued functions.
  • E. Theory of Multiply Periodic Functions
    Theory of Multiply Periodic Functions is a foundational mathematical work by Henry Frederick Baker that systematically develops the theory of functions with multiple complex periods, including abelian and related 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_69d8b9f4c22c819093c2680434472894 completed April 10, 2026, 8:51 a.m.
NER Named-entity recognition batch_69e49aa3cd248190a13a8209ba44fd3b completed April 19, 2026, 9:04 a.m.
NED1 Entity disambiguation (via context triple) batch_6a031b1d25e48190a10b72d1658efcad completed May 12, 2026, 12:20 p.m.
NEDg Description generation batch_6a031bc800d081908493949af23dd360 completed May 12, 2026, 12:23 p.m.
NED2 Entity disambiguation (via description) batch_6a031d4bf2dc8190b69eb8f8050b9955 completed May 12, 2026, 12:30 p.m.
Created at: April 10, 2026, 10:18 a.m.