Triple

T2228029
Position Surface form Disambiguated ID Type / Status
Subject André Weil E48698 entity
Predicate notableWork P4 FINISHED
Object Basic Number Theory
Basic Number Theory is a foundational graduate-level text by André Weil that systematically develops algebraic number theory and related concepts with exceptional rigor and depth.
E244837 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: Basic Number Theory | Statement: [André Weil, notableWork, Basic Number Theory]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Basic Number Theory
Context triple: [André Weil, notableWork, Basic 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. 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.
  • C. Fermat's little theorem
    Fermat's little theorem is a fundamental result in number theory that characterizes how prime numbers interact with integer powers modulo that prime, forming the basis for many modern cryptographic algorithms.
  • 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. 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. 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: Basic Number Theory
Triple: [André Weil, notableWork, Basic Number Theory]
Generated description
Basic Number Theory is a foundational graduate-level text by André Weil that systematically develops algebraic number theory and related concepts with exceptional rigor and depth.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Basic Number Theory
Target entity description: Basic Number Theory is a foundational graduate-level text by André Weil that systematically develops algebraic number theory and related concepts with exceptional rigor and depth.
  • 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. 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.
  • C. Fermat's little theorem
    Fermat's little theorem is a fundamental result in number theory that characterizes how prime numbers interact with integer powers modulo that prime, forming the basis for many modern cryptographic algorithms.
  • 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. 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. 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_69a88aa51b388190949868ec9766e587 completed March 4, 2026, 7:40 p.m.
NER Named-entity recognition batch_69abc0670ce48190b98814064bff0517 completed March 7, 2026, 6:06 a.m.
NED1 Entity disambiguation (via context triple) batch_69ae6567b64c8190ab718f20bbf033df completed March 9, 2026, 6:15 a.m.
NEDg Description generation batch_69ae666bd32c81909ff15201757a6c76 completed March 9, 2026, 6:19 a.m.
NED2 Entity disambiguation (via description) batch_69ae66d8ba688190a2102c00fc6231c4 completed March 9, 2026, 6:21 a.m.
Created at: March 4, 2026, 7:47 p.m.