Triple

T3072660
Position Surface form Disambiguated ID Type / Status
Subject Annals of Mathematics Studies E64059 entity
Predicate hasNotableWork P4 FINISHED
Object Algebraic Groups and Class Fields
"Algebraic Groups and Class Fields" is a influential mathematical monograph that develops the deep connections between algebraic group theory and class field theory within number theory and arithmetic geometry.
E325282 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: Algebraic Groups and Class Fields | Statement: [Annals of Mathematics Studies, hasNotableWork, Algebraic Groups and Class Fields]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Algebraic Groups and Class Fields
Context triple: [Annals of Mathematics Studies, hasNotableWork, Algebraic Groups and Class Fields]
  • A. Adeles and Algebraic Groups
    "Adeles and Algebraic Groups" is a foundational mathematical work by André Weil that develops the theory of adeles and its deep connections with algebraic groups and number theory.
  • B. Hilbert’s twelfth problem
    Hilbert’s twelfth problem is one of David Hilbert’s famous list of 23 problems, asking for a general explicit class field theory that would generate all abelian extensions of a given number field using special values of analytic functions.
  • C. Deligne–Lusztig theory
    Deligne–Lusztig theory is a framework in algebraic geometry and representation theory that constructs and studies representations of finite groups of Lie type using varieties defined over finite fields.
  • D. 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.
  • E. Cohomologie Galoisienne
    Cohomologie Galoisienne is a foundational monograph by Jean-Pierre Serre that systematically develops Galois cohomology and its deep applications in number theory and algebraic geometry.
  • 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: Algebraic Groups and Class Fields
Triple: [Annals of Mathematics Studies, hasNotableWork, Algebraic Groups and Class Fields]
Generated description
"Algebraic Groups and Class Fields" is a influential mathematical monograph that develops the deep connections between algebraic group theory and class field theory within number theory and arithmetic geometry.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Algebraic Groups and Class Fields
Target entity description: "Algebraic Groups and Class Fields" is a influential mathematical monograph that develops the deep connections between algebraic group theory and class field theory within number theory and arithmetic geometry.
  • A. Adeles and Algebraic Groups
    "Adeles and Algebraic Groups" is a foundational mathematical work by André Weil that develops the theory of adeles and its deep connections with algebraic groups and number theory.
  • B. Hilbert’s twelfth problem
    Hilbert’s twelfth problem is one of David Hilbert’s famous list of 23 problems, asking for a general explicit class field theory that would generate all abelian extensions of a given number field using special values of analytic functions.
  • C. Deligne–Lusztig theory
    Deligne–Lusztig theory is a framework in algebraic geometry and representation theory that constructs and studies representations of finite groups of Lie type using varieties defined over finite fields.
  • D. 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.
  • E. Cohomologie Galoisienne
    Cohomologie Galoisienne is a foundational monograph by Jean-Pierre Serre that systematically develops Galois cohomology and its deep applications in number theory and algebraic geometry.
  • 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_69ad857a8aec8190bfdfd9c14554ac5a completed March 8, 2026, 2:19 p.m.
NER Named-entity recognition batch_69ada14e372c81908c25c7f3e7e0c864 completed March 8, 2026, 4:18 p.m.
NED1 Entity disambiguation (via context triple) batch_69b1f8828c488190877902a6c2dfcb5e completed March 11, 2026, 11:19 p.m.
NEDg Description generation batch_69b1f930321081908f98aa5f9b8ba611 completed March 11, 2026, 11:22 p.m.
NED2 Entity disambiguation (via description) batch_69b1f9ad0b148190b98f93699598dd1e completed March 11, 2026, 11:24 p.m.
Created at: March 8, 2026, 3:02 p.m.