Triple

T20439486
Position Surface form Disambiguated ID Type / Status
Subject Edmund Landau E501345 entity
Predicate notableWork P4 FINISHED
Object Darstellung und Begründung einiger neuerer Ergebnisse der Funktionentheorie
Darstellung und Begründung einiger neuerer Ergebnisse der Funktionentheorie is a mathematical work by Edmund Landau that presents and justifies several then-recent advances in complex function theory.
E1430744 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: Darstellung und Begründung einiger neuerer Ergebnisse der Funktionentheorie | Statement: [Edmund Landau, notableWork, Darstellung und Begründung einiger neuerer Ergebnisse der Funktionentheorie]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Darstellung und Begründung einiger neuerer Ergebnisse der Funktionentheorie
Context triple: [Edmund Landau, notableWork, Darstellung und Begründung einiger neuerer Ergebnisse der Funktionentheorie]
  • A. Harmonic Integrals in the Theory of Analytic Functions
    "Harmonic Integrals in the Theory of Analytic Functions" is a foundational mathematical work by Kunihiko Kodaira that develops the theory of harmonic integrals and lays groundwork for modern complex analysis and complex geometry.
  • B. Théorie des fonctions analytiques
    Théorie des fonctions analytiques is a foundational mathematical treatise by Joseph-Louis Lagrange that systematically develops calculus using power series and analytic functions instead of geometric or infinitesimal arguments.
  • C. 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.
  • D. 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.
  • E. Le calcul des résidus et ses applications à la théorie des fonctions
    *Le calcul des résidus et ses applications à la théorie des fonctions* is a mathematical treatise on the theory of residues in complex analysis and its applications to the study of analytic 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: Darstellung und Begründung einiger neuerer Ergebnisse der Funktionentheorie
Triple: [Edmund Landau, notableWork, Darstellung und Begründung einiger neuerer Ergebnisse der Funktionentheorie]
Generated description
Darstellung und Begründung einiger neuerer Ergebnisse der Funktionentheorie is a mathematical work by Edmund Landau that presents and justifies several then-recent advances in complex function theory.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Darstellung und Begründung einiger neuerer Ergebnisse der Funktionentheorie
Target entity description: Darstellung und Begründung einiger neuerer Ergebnisse der Funktionentheorie is a mathematical work by Edmund Landau that presents and justifies several then-recent advances in complex function theory.
  • A. Harmonic Integrals in the Theory of Analytic Functions
    "Harmonic Integrals in the Theory of Analytic Functions" is a foundational mathematical work by Kunihiko Kodaira that develops the theory of harmonic integrals and lays groundwork for modern complex analysis and complex geometry.
  • B. Théorie des fonctions analytiques
    Théorie des fonctions analytiques is a foundational mathematical treatise by Joseph-Louis Lagrange that systematically develops calculus using power series and analytic functions instead of geometric or infinitesimal arguments.
  • C. 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.
  • D. 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.
  • E. Le calcul des résidus et ses applications à la théorie des fonctions
    *Le calcul des résidus et ses applications à la théorie des fonctions* is a mathematical treatise on the theory of residues in complex analysis and its applications to the study of analytic 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_69e0b4ab3cfc8190ac9bf32e932316b1 completed April 16, 2026, 10:06 a.m.
NER Named-entity recognition batch_69e685f20fe08190b9370b523a20153d completed April 20, 2026, 8 p.m.
NED1 Entity disambiguation (via context triple) batch_6a0883fd1af88190a34aef615ec3a23e completed May 16, 2026, 2:49 p.m.
NEDg Description generation batch_6a0884d316148190b1fe155fc2dfbb7b completed May 16, 2026, 2:53 p.m.
NED2 Entity disambiguation (via description) batch_6a088565cbcc81909b4bbc286d272ef6 completed May 16, 2026, 2:55 p.m.
Created at: April 16, 2026, 11:31 a.m.