Triple

T2306399
Position Surface form Disambiguated ID Type / Status
Subject Jean-Pierre Serre E51848 entity
Predicate notableWork P4 FINISHED
Object A Course in Arithmetic
A Course in Arithmetic is a classic introductory text in number theory by Jean-Pierre Serre, renowned for its concise and elegant treatment of fundamental arithmetic and algebraic concepts.
E253120 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: A Course in Arithmetic | Statement: [Jean-Pierre Serre, notableWork, A Course in Arithmetic]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: A Course in Arithmetic
Context triple: [Jean-Pierre Serre, notableWork, A Course in Arithmetic]
  • 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. 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.
  • C. 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.
  • 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. Gauss’s lemma in number theory
    Gauss’s lemma in number theory is a result that relates the Legendre symbol to the number of sign changes in a certain sequence of multiples, providing a practical criterion for determining quadratic residues modulo an odd prime.
  • 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: A Course in Arithmetic
Triple: [Jean-Pierre Serre, notableWork, A Course in Arithmetic]
Generated description
A Course in Arithmetic is a classic introductory text in number theory by Jean-Pierre Serre, renowned for its concise and elegant treatment of fundamental arithmetic and algebraic concepts.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: A Course in Arithmetic
Target entity description: A Course in Arithmetic is a classic introductory text in number theory by Jean-Pierre Serre, renowned for its concise and elegant treatment of fundamental arithmetic and algebraic concepts.
  • 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. 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.
  • C. 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.
  • 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. Gauss’s lemma in number theory
    Gauss’s lemma in number theory is a result that relates the Legendre symbol to the number of sign changes in a certain sequence of multiples, providing a practical criterion for determining quadratic residues modulo an odd prime.
  • 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_69a88b0bb30c81908ded03b006d29387 completed March 4, 2026, 7:42 p.m.
NER Named-entity recognition batch_69abc60489c881908b0ba76d2075bc89 completed March 7, 2026, 6:30 a.m.
NED1 Entity disambiguation (via context triple) batch_69ae7f379bbc8190b085b82e2e16401e completed March 9, 2026, 8:05 a.m.
NEDg Description generation batch_69ae8004fb6c81908f9fb1678f608419 completed March 9, 2026, 8:08 a.m.
NED2 Entity disambiguation (via description) batch_69ae809ebfdc8190ae404d5711a58b59 completed March 9, 2026, 8:11 a.m.
Created at: March 4, 2026, 7:49 p.m.