Triple

T21783941
Position Surface form Disambiguated ID Type / Status
Subject Hellenistic mathematics E537786 entity
Predicate notableWork P4 FINISHED
Object Introduction to Arithmetic
Introduction to Arithmetic is an influential ancient Greek mathematical treatise by Nicomachus of Gerasa that systematically presents number theory and arithmetic within the philosophical tradition of Hellenistic mathematics.
E1501890 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: Introduction to Arithmetic | Statement: [Hellenistic mathematics, notableWork, Introduction to Arithmetic]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Introduction to Arithmetic
Context triple: [Hellenistic mathematics, notableWork, Introduction to Arithmetic]
  • A. Elements of Arithmetic
    Elements of Arithmetic is a foundational 19th-century mathematics textbook by Augustus De Morgan that systematically develops the principles of arithmetic and number theory.
  • B. Key to Arithmetic
    Key to Arithmetic is a foundational 15th-century mathematical treatise by Persian astronomer and mathematician Jamshid al-Kashi, known for its systematic treatment of arithmetic and numerical computation.
  • C. An Introduction to Algebra
    An Introduction to Algebra is a foundational mathematics textbook authored by Jeremiah Day that presents the basic principles and methods of algebra.
  • D. Fundamental Concepts of Algebra
    Fundamental Concepts of Algebra is a foundational mathematics text by Claude Chevalley that systematically develops modern abstract algebra, particularly group, ring, and field theory.
  • E. Grundlagen der Mathematik
    Grundlagen der Mathematik is a foundational two-volume work in mathematical logic and the philosophy of mathematics, co-authored by David Hilbert and Paul Bernays, that systematically develops proof theory and formalizes large parts of mathematics.
  • 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: Introduction to Arithmetic
Triple: [Hellenistic mathematics, notableWork, Introduction to Arithmetic]
Generated description
Introduction to Arithmetic is an influential ancient Greek mathematical treatise by Nicomachus of Gerasa that systematically presents number theory and arithmetic within the philosophical tradition of Hellenistic mathematics.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Introduction to Arithmetic
Target entity description: Introduction to Arithmetic is an influential ancient Greek mathematical treatise by Nicomachus of Gerasa that systematically presents number theory and arithmetic within the philosophical tradition of Hellenistic mathematics.
  • A. Elements of Arithmetic
    Elements of Arithmetic is a foundational 19th-century mathematics textbook by Augustus De Morgan that systematically develops the principles of arithmetic and number theory.
  • B. Key to Arithmetic
    Key to Arithmetic is a foundational 15th-century mathematical treatise by Persian astronomer and mathematician Jamshid al-Kashi, known for its systematic treatment of arithmetic and numerical computation.
  • C. An Introduction to Algebra
    An Introduction to Algebra is a foundational mathematics textbook authored by Jeremiah Day that presents the basic principles and methods of algebra.
  • D. Fundamental Concepts of Algebra
    Fundamental Concepts of Algebra is a foundational mathematics text by Claude Chevalley that systematically develops modern abstract algebra, particularly group, ring, and field theory.
  • E. Grundlagen der Mathematik
    Grundlagen der Mathematik is a foundational two-volume work in mathematical logic and the philosophy of mathematics, co-authored by David Hilbert and Paul Bernays, that systematically develops proof theory and formalizes large parts of mathematics.
  • 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_69e0c47198f881908cb0d237266c10e9 completed April 16, 2026, 11:13 a.m.
NER Named-entity recognition batch_69f046303d54819096b3fab4ab5678e6 completed April 28, 2026, 5:31 a.m.
NED1 Entity disambiguation (via context triple) batch_6a0a3e6f77cc81909ff2ca8b6c8e57e0 completed May 17, 2026, 10:17 p.m.
NEDg Description generation batch_6a0a3f5813a081909f253f04ca218559 completed May 17, 2026, 10:21 p.m.
NED2 Entity disambiguation (via description) batch_6a0a400831d881909631e1accd5618f1 completed May 17, 2026, 10:24 p.m.
Created at: April 16, 2026, 6:52 p.m.