Triple

T7854056
Position Surface form Disambiguated ID Type / Status
Subject Peter Barlow E182126 entity
Predicate notableWork P4 FINISHED
Object An Elementary Investigation of the Theory of Numbers
An Elementary Investigation of the Theory of Numbers is a foundational 19th-century treatise on number theory by mathematician Peter Barlow, covering properties of integers, prime numbers, and related arithmetic topics.
E695718 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: An Elementary Investigation of the Theory of Numbers | Statement: [Peter Barlow, notableWork, An Elementary Investigation of the Theory of Numbers]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: An Elementary Investigation of the Theory of Numbers
Context triple: [Peter Barlow, notableWork, An Elementary Investigation of the Theory of Numbers]
  • A. 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.
  • B. 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.
  • C. The Higher Arithmetic
    The Higher Arithmetic is a classic introductory textbook on number theory, widely regarded for its clear exposition and influence on generations of mathematicians.
  • D. Unsolved Problems in Number Theory
    *Unsolved Problems in Number Theory* is a classic reference book that surveys a wide range of open questions and conjectures in number theory, often with historical context and extensive bibliographic notes.
  • E. 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.
  • 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: An Elementary Investigation of the Theory of Numbers
Triple: [Peter Barlow, notableWork, An Elementary Investigation of the Theory of Numbers]
Generated description
An Elementary Investigation of the Theory of Numbers is a foundational 19th-century treatise on number theory by mathematician Peter Barlow, covering properties of integers, prime numbers, and related arithmetic topics.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: An Elementary Investigation of the Theory of Numbers
Target entity description: An Elementary Investigation of the Theory of Numbers is a foundational 19th-century treatise on number theory by mathematician Peter Barlow, covering properties of integers, prime numbers, and related arithmetic topics.
  • A. 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.
  • B. 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.
  • C. The Higher Arithmetic
    The Higher Arithmetic is a classic introductory textbook on number theory, widely regarded for its clear exposition and influence on generations of mathematicians.
  • D. Unsolved Problems in Number Theory
    *Unsolved Problems in Number Theory* is a classic reference book that surveys a wide range of open questions and conjectures in number theory, often with historical context and extensive bibliographic notes.
  • E. 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.
  • 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_69ca82869ee08190b8f9040dbc2c0467 completed March 30, 2026, 2:02 p.m.
NER Named-entity recognition batch_69cb1a72cfdc8190a3186c4c2894f571 completed March 31, 2026, 12:50 a.m.
NED1 Entity disambiguation (via context triple) batch_69cb5b1e9e808190a0eb2dea5288e743 completed March 31, 2026, 5:26 a.m.
NEDg Description generation batch_69cb5def38e88190864d84abd7959aa3 completed March 31, 2026, 5:38 a.m.
NED2 Entity disambiguation (via description) batch_69cb767b198481909cfc1f7a44e6f0d8 completed March 31, 2026, 7:23 a.m.
Created at: March 30, 2026, 4:51 p.m.