Triple

T7011060
Position Surface form Disambiguated ID Type / Status
Subject Richard Dedekind E162579 entity
Predicate notableWork P4 FINISHED
Object Vorlesungen über Zahlentheorie (with Dirichlet)
Vorlesungen über Zahlentheorie (with Dirichlet) is a foundational 19th-century textbook on number theory, based on lectures by Peter Gustav Lejeune Dirichlet and edited and expanded by Richard Dedekind.
E634840 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: Vorlesungen über Zahlentheorie (with Dirichlet) | Statement: [Richard Dedekind, notableWork, Vorlesungen über Zahlentheorie (with Dirichlet)]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Vorlesungen über Zahlentheorie (with Dirichlet)
Context triple: [Richard Dedekind, notableWork, Vorlesungen über Zahlentheorie (with Dirichlet)]
  • A. Disquisitiones Arithmeticae
    Disquisitiones Arithmeticae is a foundational 1801 treatise on number theory that systematically developed the subject and introduced many of its central concepts and methods.
  • B. Theorie der algebraischen Zahlen
    "Theorie der algebraischen Zahlen" is Kurt Hensel’s foundational work in algebraic number theory, notable for introducing and developing the concept of p-adic numbers.
  • C. Die Theorie der algebraischen Zahlkörper
    "Die Theorie der algebraischen Zahlkörper" is a foundational mathematical monograph on algebraic number fields, authored by David Hilbert and published as part of his influential Zahlbericht.
  • D. An Introduction to the Theory of Numbers
    An Introduction to the Theory of Numbers is a classic textbook in number theory, co-authored by G. H. Hardy, that systematically develops fundamental concepts such as divisibility, prime numbers, Diophantine equations, and quadratic forms.
  • E. Three Pearls of Number Theory
    Three Pearls of Number Theory is a classic mathematical text that presents three elegant and accessible problems in number theory, illustrating deep ideas through simple, beautifully explained examples.
  • 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: Vorlesungen über Zahlentheorie (with Dirichlet)
Triple: [Richard Dedekind, notableWork, Vorlesungen über Zahlentheorie (with Dirichlet)]
Generated description
Vorlesungen über Zahlentheorie (with Dirichlet) is a foundational 19th-century textbook on number theory, based on lectures by Peter Gustav Lejeune Dirichlet and edited and expanded by Richard Dedekind.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Vorlesungen über Zahlentheorie (with Dirichlet)
Target entity description: Vorlesungen über Zahlentheorie (with Dirichlet) is a foundational 19th-century textbook on number theory, based on lectures by Peter Gustav Lejeune Dirichlet and edited and expanded by Richard Dedekind.
  • A. Disquisitiones Arithmeticae
    Disquisitiones Arithmeticae is a foundational 1801 treatise on number theory that systematically developed the subject and introduced many of its central concepts and methods.
  • B. Theorie der algebraischen Zahlen
    "Theorie der algebraischen Zahlen" is Kurt Hensel’s foundational work in algebraic number theory, notable for introducing and developing the concept of p-adic numbers.
  • C. Die Theorie der algebraischen Zahlkörper
    "Die Theorie der algebraischen Zahlkörper" is a foundational mathematical monograph on algebraic number fields, authored by David Hilbert and published as part of his influential Zahlbericht.
  • D. An Introduction to the Theory of Numbers
    An Introduction to the Theory of Numbers is a classic textbook in number theory, co-authored by G. H. Hardy, that systematically develops fundamental concepts such as divisibility, prime numbers, Diophantine equations, and quadratic forms.
  • E. Three Pearls of Number Theory
    Three Pearls of Number Theory is a classic mathematical text that presents three elegant and accessible problems in number theory, illustrating deep ideas through simple, beautifully explained examples.
  • 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_69c6885a127c8190867b059bdccf13ff completed March 27, 2026, 1:38 p.m.
NER Named-entity recognition batch_69c6dc5729448190af66dbd6f3e8936e completed March 27, 2026, 7:36 p.m.
NED1 Entity disambiguation (via context triple) batch_69c76a4bd424819097e1543ec59979ff completed March 28, 2026, 5:42 a.m.
NEDg Description generation batch_69c76b1ef6f481908f4c4f610328f633 completed March 28, 2026, 5:46 a.m.
NED2 Entity disambiguation (via description) batch_69c76c01679c8190b61f642c23c25ed5 completed March 28, 2026, 5:49 a.m.
Created at: March 27, 2026, 2:34 p.m.