Triple

T1428731
Position Surface form Disambiguated ID Type / Status
Subject Harold Davenport E30393 entity
Predicate notableWork P4 FINISHED
Object Multiplicative Number Theory
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.
E163262 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: Multiplicative Number Theory | Statement: [Harold Davenport, notableWork, Multiplicative Number Theory]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Multiplicative Number Theory
Context triple: [Harold Davenport, notableWork, Multiplicative Number Theory]
  • 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. 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.
  • C. 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.
  • D. Dyson’s transform in number theory
    Dyson’s transform in number theory is a combinatorial technique introduced by Freeman Dyson to manipulate and relate integer partitions, particularly in the study of partition identities and congruences.
  • E. Statistical Independence in Probability, Analysis and Number Theory
    "Statistical Independence in Probability, Analysis and Number Theory" is a mathematical monograph by Mark Kac that explores the concept of independence across probability theory, real analysis, and number theory.
  • 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: Multiplicative Number Theory
Triple: [Harold Davenport, notableWork, Multiplicative Number Theory]
Generated description
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.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Multiplicative Number Theory
Target entity description: 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.
  • 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. 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.
  • C. 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.
  • D. Dyson’s transform in number theory
    Dyson’s transform in number theory is a combinatorial technique introduced by Freeman Dyson to manipulate and relate integer partitions, particularly in the study of partition identities and congruences.
  • E. Statistical Independence in Probability, Analysis and Number Theory
    "Statistical Independence in Probability, Analysis and Number Theory" is a mathematical monograph by Mark Kac that explores the concept of independence across probability theory, real analysis, and number theory.
  • 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_69a498fb823c8190a67ce4c4837e641a completed March 1, 2026, 7:52 p.m.
NER Named-entity recognition batch_69a4c4d9575881908bb58598e5a80590 completed March 1, 2026, 10:59 p.m.
NED1 Entity disambiguation (via context triple) batch_69ad016930ec8190ab3900d6f40c4aa0 completed March 8, 2026, 4:56 a.m.
NEDg Description generation batch_69ad01d1c01c81908917c4837ed2b393 completed March 8, 2026, 4:57 a.m.
NED2 Entity disambiguation (via description) batch_69ad0265f610819085a2dd293abd4812 completed March 8, 2026, 5 a.m.
Created at: March 1, 2026, 8 p.m.