Triple

T14265430
Position Surface form Disambiguated ID Type / Status
Subject Wacław Sierpiński E353630 entity
Predicate notableWork P4 FINISHED
Object Elementary Theory of Numbers
Elementary Theory of Numbers is a classic introductory textbook on number theory by Wacław Sierpiński, covering fundamental properties of integers and related topics in a rigorous yet accessible manner.
E1090233 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: Elementary Theory of Numbers | Statement: [Wacław Sierpiński, notableWork, Elementary Theory of Numbers]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Elementary Theory of Numbers
Context triple: [Wacław Sierpiński, notableWork, Elementary 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. 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.
  • C. 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.
  • D. Essai sur la théorie des nombres
    Essai sur la théorie des nombres is a foundational 18th-century treatise on number theory by Adrien-Marie Legendre that systematically developed many key results in the field.
  • E. 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.
  • 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: Elementary Theory of Numbers
Triple: [Wacław Sierpiński, notableWork, Elementary Theory of Numbers]
Generated description
Elementary Theory of Numbers is a classic introductory textbook on number theory by Wacław Sierpiński, covering fundamental properties of integers and related topics in a rigorous yet accessible manner.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Elementary Theory of Numbers
Target entity description: Elementary Theory of Numbers is a classic introductory textbook on number theory by Wacław Sierpiński, covering fundamental properties of integers and related topics in a rigorous yet accessible manner.
  • 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. 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.
  • C. 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.
  • D. Essai sur la théorie des nombres
    Essai sur la théorie des nombres is a foundational 18th-century treatise on number theory by Adrien-Marie Legendre that systematically developed many key results in the field.
  • E. 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.
  • 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_69d8278c43e08190824146f4632b89a5 completed April 9, 2026, 10:26 p.m.
NER Named-entity recognition batch_69de6357a8188190ba518a486521052b completed April 14, 2026, 3:55 p.m.
NED1 Entity disambiguation (via context triple) batch_69fd326551b08190ae8fe220a6422339 completed May 8, 2026, 12:46 a.m.
NEDg Description generation batch_69fd3417e8e88190b099bfe4ba30f364 completed May 8, 2026, 12:53 a.m.
NED2 Entity disambiguation (via description) batch_69fd37df3dfc8190a594abb2c14e11bb completed May 8, 2026, 1:09 a.m.
Created at: April 10, 2026, 1:09 a.m.