Triple

T18792975
Position Surface form Disambiguated ID Type / Status
Subject global class field theory E459561 entity
Predicate typicalReference P33736 FINISHED
Object Artin–Tate: Class Field Theory
Artin–Tate: Class Field Theory is a classic textbook that provides a rigorous and accessible introduction to global and local class field theory in algebraic number theory.
E1343407 NE FINISHED

How this triple was built (5 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: Artin–Tate: Class Field Theory | Statement: [global class field theory, typicalReference, Artin–Tate: Class Field Theory]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Artin–Tate: Class Field Theory
Context triple: [global class field theory, typicalReference, Artin–Tate: Class Field Theory]
  • A. Furtwängler’s theorem in class field theory
    Furtwängler’s theorem in class field theory is a fundamental result in algebraic number theory that refines the principal ideal theorem by describing how ideal classes capitulate (become principal) in certain abelian extensions of number fields.
  • B. Cassels–Fröhlich: Algebraic Number Theory
    Cassels–Fröhlich: Algebraic Number Theory is a classic graduate-level textbook that provides a comprehensive and rigorous introduction to algebraic number theory and its foundational results.
  • C. 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.
  • D. Neukirch: Algebraic Number Theory
    "Neukirch: Algebraic Number Theory" is a widely respected graduate-level textbook that provides a rigorous, modern introduction to algebraic number theory, including class field theory and foundational results such as the Kronecker–Weber theorem.
  • E. Artin reciprocity law
    The Artin reciprocity law is a fundamental theorem in class field theory that generalizes quadratic reciprocity by describing abelian extensions of number fields in terms of characters of their idele class groups.
  • 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: Artin–Tate: Class Field Theory
Triple: [global class field theory, typicalReference, Artin–Tate: Class Field Theory]
Generated description
Artin–Tate: Class Field Theory is a classic textbook that provides a rigorous and accessible introduction to global and local class field theory in algebraic number theory.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Artin–Tate: Class Field Theory
Target entity description: Artin–Tate: Class Field Theory is a classic textbook that provides a rigorous and accessible introduction to global and local class field theory in algebraic number theory.
  • A. Furtwängler’s theorem in class field theory
    Furtwängler’s theorem in class field theory is a fundamental result in algebraic number theory that refines the principal ideal theorem by describing how ideal classes capitulate (become principal) in certain abelian extensions of number fields.
  • B. Cassels–Fröhlich: Algebraic Number Theory
    Cassels–Fröhlich: Algebraic Number Theory is a classic graduate-level textbook that provides a comprehensive and rigorous introduction to algebraic number theory and its foundational results.
  • C. 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.
  • D. Neukirch: Algebraic Number Theory
    "Neukirch: Algebraic Number Theory" is a widely respected graduate-level textbook that provides a rigorous, modern introduction to algebraic number theory, including class field theory and foundational results such as the Kronecker–Weber theorem.
  • E. Artin reciprocity law
    The Artin reciprocity law is a fundamental theorem in class field theory that generalizes quadratic reciprocity by describing abelian extensions of number fields in terms of characters of their idele class groups.
  • F. None of above. chosen
PD Predicate disambiguation gpt-5-mini-2025-08-07
Target predicate: typicalReference
Context triple: [global class field theory, typicalReference, Artin–Tate: Class Field Theory]
  • A. typicalIn
    Indicates that something commonly occurs, appears, or is found within a given context, category, or environment.
  • B. standardReference chosen
    Indicates that one entity serves as the authoritative or canonical reference or benchmark for interpreting, validating, or comparing another entity.
  • C. typicalBase
    Indicates that one entity serves as the standard or most representative base or foundation for another entity in typical or common cases.
  • D. referenceType
    Indicates the specific kind or category of reference relationship that one entity has to another.
  • E. typicalCoreType
    Indicates that something is a standard or characteristic core type within a given classification or system.
  • F. None of above.

Provenance (6 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_69d8d396f54c8190ba49db31e8743842 completed April 10, 2026, 10:40 a.m.
NER Named-entity recognition batch_69e59787e5988190883ed575ab4b6dec completed April 20, 2026, 3:03 a.m.
NED1 Entity disambiguation (via context triple) batch_6a05471e942c81908de4ec52f4c0bb6f completed May 14, 2026, 3:53 a.m.
NEDg Description generation batch_6a0548414b188190bf64dc5a0673b9cd completed May 14, 2026, 3:57 a.m.
NED2 Entity disambiguation (via description) batch_6a0548d472bc81909d874e0b27ca3736 completed May 14, 2026, 4 a.m.
PD Predicate disambiguation batch_69e48d16dd34819096e096d0c0e4c15c completed April 19, 2026, 8:06 a.m.
Created at: April 10, 2026, 11:53 a.m.