Triple

T7871991
Position Surface form Disambiguated ID Type / Status
Subject Jacobi’s four-square theorem E182757 entity
Predicate appearsIn P795 FINISHED
Object Hardy and Wright, An Introduction to the Theory of Numbers E120387 NE FINISHED

How this triple was built (2 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: Hardy and Wright, An Introduction to the Theory of Numbers | Statement: [Jacobi’s four-square theorem, appearsIn, Hardy and Wright, An Introduction to the Theory of Numbers]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Hardy and Wright, An Introduction to the Theory of Numbers
Context triple: [Jacobi’s four-square theorem, appearsIn, Hardy and Wright, An Introduction to the Theory of Numbers]
  • 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. 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. 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.
  • F. None of above.
  • G. Unsure - the case is ambiguous/there is not enough information to decide.

Provenance (3 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_69ca82894d9081908a832bfce71a4714 completed March 30, 2026, 2:02 p.m.
NER Named-entity recognition batch_69cb39a5950481908399211c5dfe2569 completed March 31, 2026, 3:04 a.m.
NED1 Entity disambiguation (via context triple) batch_69cb5b6bc7248190adbf4377c52e16a9 completed March 31, 2026, 5:28 a.m.
Created at: March 30, 2026, 4:56 p.m.