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.