Triple

T7625144
Position Surface form Disambiguated ID Type / Status
Subject Edward M. Wright E172608 entity
Predicate coWrote P7732 FINISHED
Object An Introduction to the Theory of Numbers
An Introduction to the Theory of Numbers is a classic, widely used textbook in number theory that provides a rigorous yet accessible treatment of fundamental topics such as divisibility, Diophantine equations, prime numbers, and quadratic forms.
E120387 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 Introduction to the Theory of Numbers | Statement: [Edward M. Wright, coWrote, An Introduction to the Theory of Numbers]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: An Introduction to the Theory of Numbers
Context triple: [Edward M. Wright, coWrote, An Introduction to 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. 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.
  • D. 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.
  • E. Number Theory: An Approach through History from Hammurapi to Legendre
    "Number Theory: An Approach through History from Hammurapi to Legendre" is a historical and expository book by André Weil that traces the development of number theory from ancient Mesopotamia to the early 19th century.
  • 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 Introduction to the Theory of Numbers
Triple: [Edward M. Wright, coWrote, An Introduction to the Theory of Numbers]
Generated description
An Introduction to the Theory of Numbers is a classic, widely used textbook in number theory that provides a rigorous yet accessible treatment of fundamental topics such as divisibility, Diophantine equations, prime numbers, and quadratic forms.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: An Introduction to the Theory of Numbers
Target entity description: An Introduction to the Theory of Numbers is a classic, widely used textbook in number theory that provides a rigorous yet accessible treatment of fundamental topics such as divisibility, Diophantine equations, prime numbers, and quadratic forms.
  • A. An Introduction to the Theory of Numbers chosen
    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. 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.
  • D. 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.
  • E. Number Theory: An Approach through History from Hammurapi to Legendre
    "Number Theory: An Approach through History from Hammurapi to Legendre" is a historical and expository book by André Weil that traces the development of number theory from ancient Mesopotamia to the early 19th century.
  • F. None of above.

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_69c699517e348190bd3348b6889200f2 completed March 27, 2026, 2:50 p.m.
NER Named-entity recognition batch_69c6fa6648608190a9203b98b76209aa completed March 27, 2026, 9:45 p.m.
NED1 Entity disambiguation (via context triple) batch_69c89ab1132481909e525e90764df041 completed March 29, 2026, 3:21 a.m.
NEDg Description generation batch_69c89b9d22e88190b08543c975ce7898 completed March 29, 2026, 3:25 a.m.
NED2 Entity disambiguation (via description) batch_69c89c2e62848190a5339707ba401772 completed March 29, 2026, 3:27 a.m.
Created at: March 27, 2026, 3:56 p.m.