Triple

T7030755
Position Surface form Disambiguated ID Type / Status
Subject Multiplicative Number Theory E163262 entity
Predicate hasTextbook P5478 FINISHED
Object Multiplicative Number Theory (Harold Davenport) E163262 NE FINISHED

How this triple was built (3 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: Multiplicative Number Theory (Harold Davenport) | Statement: [Multiplicative Number Theory, hasTextbook, Multiplicative Number Theory (Harold Davenport)]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Multiplicative Number Theory (Harold Davenport)
Context triple: [Multiplicative Number Theory, hasTextbook, Multiplicative Number Theory (Harold Davenport)]
  • A. Multiplicative Number Theory chosen
    Multiplicative Number Theory is a branch of analytic number theory that studies arithmetic functions and prime number distributions through their multiplicative properties and associated Dirichlet series.
  • B. 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.
  • 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. Hardy–Littlewood circle method
    The Hardy–Littlewood circle method is a powerful analytic number theory technique that uses complex analysis and Fourier series to study additive problems such as Waring’s problem and the Goldbach conjecture.
  • E. 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.
  • F. None of above.
  • G. Unsure - the case is ambiguous/there is not enough information to decide.
PD Predicate disambiguation gpt-5-mini-2025-08-07
Target predicate: hasTextbook
Context triple: [Multiplicative Number Theory, hasTextbook, Multiplicative Number Theory (Harold Davenport)]
  • A. hasBook
    Indicates that an entity possesses, owns, or is associated with a particular book.
  • B. containsBook chosen
    Indicates that one entity (typically a container or collection) includes a specific book as part of its contents.
  • C. notableTextbook
    Indicates that a textbook is recognized as significant, influential, or widely used within its field or subject area.
  • D. hasEducationalMaterial
    Indicates that an entity provides, contains, or is associated with educational content or learning resources for another entity.
  • E. hasThreeBooksWith
    Indicates that two entities are related by one having exactly three books together with the other (e.g., jointly owned, shared, or associated as a group of three books).
  • F. None of above.

Provenance (4 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_69c6885d691c81908cf7d31083113886 completed March 27, 2026, 1:38 p.m.
NER Named-entity recognition batch_69c6e458ad9c81908c3f492b317ce291 completed March 27, 2026, 8:11 p.m.
NED1 Entity disambiguation (via context triple) batch_69c775980920819081d31b8d2843fb3d completed March 28, 2026, 6:30 a.m.
PD Predicate disambiguation batch_69c6e1b9a2488190aea351d96afa5a12 completed March 27, 2026, 7:59 p.m.
Created at: March 27, 2026, 2:35 p.m.