Triple

T4597205
Position Surface form Disambiguated ID Type / Status
Subject Kronecker–Weber theorem E100232 entity
Predicate isPartOf P10 FINISHED
Object global class field theory
Global class field theory is a branch of algebraic number theory that classifies finite abelian extensions of global fields (such as number fields) in terms of their arithmetic data, particularly via idele class groups and reciprocity maps.
E459561 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: global class field theory | Statement: [Kronecker–Weber theorem, isPartOf, global class field theory]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: global class field theory
Context triple: [Kronecker–Weber theorem, isPartOf, global class field theory]
  • A. 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.
  • B. Levine-Fricke Field
    Levine-Fricke Field is the home softball stadium of the University of California, Berkeley Golden Bears, located on the university’s campus in Berkeley, California.
  • C. Grothendieck topology
    A Grothendieck topology is an abstract framework in category theory that generalizes the notion of open covers in topology to define sheaves on arbitrary categories.
  • D. 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.
  • E. Grothendieck duality
    Grothendieck duality is a foundational theory in algebraic geometry that generalizes classical Serre duality to a broad categorical and sheaf-theoretic framework for studying duality on schemes and morphisms.
  • 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: global class field theory
Triple: [Kronecker–Weber theorem, isPartOf, global class field theory]
Generated description
Global class field theory is a branch of algebraic number theory that classifies finite abelian extensions of global fields (such as number fields) in terms of their arithmetic data, particularly via idele class groups and reciprocity maps.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: global class field theory
Target entity description: Global class field theory is a branch of algebraic number theory that classifies finite abelian extensions of global fields (such as number fields) in terms of their arithmetic data, particularly via idele class groups and reciprocity maps.
  • A. 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.
  • B. Levine-Fricke Field
    Levine-Fricke Field is the home softball stadium of the University of California, Berkeley Golden Bears, located on the university’s campus in Berkeley, California.
  • C. Grothendieck topology
    A Grothendieck topology is an abstract framework in category theory that generalizes the notion of open covers in topology to define sheaves on arbitrary categories.
  • D. 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.
  • E. Grothendieck duality
    Grothendieck duality is a foundational theory in algebraic geometry that generalizes classical Serre duality to a broad categorical and sheaf-theoretic framework for studying duality on schemes and morphisms.
  • 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_69bd43cbc014819098b45f435908f88a completed March 20, 2026, 12:55 p.m.
NER Named-entity recognition batch_69bd594055dc8190a50f1b4be2be1ba0 completed March 20, 2026, 2:27 p.m.
NED1 Entity disambiguation (via context triple) batch_69bdfa4a99c88190b7332fd2e1799b3a completed March 21, 2026, 1:54 a.m.
NEDg Description generation batch_69bdfb83b5d08190b2d8502e763a0841 completed March 21, 2026, 1:59 a.m.
NED2 Entity disambiguation (via description) batch_69bdfc0e456c81908efa3858d981ccc0 completed March 21, 2026, 2:01 a.m.
Created at: March 20, 2026, 1:11 p.m.