Triple
T18897014
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Cassels–Fröhlich: Algebraic Number Theory |
E462233
|
entity |
| Predicate | topic |
P261
|
FINISHED |
| Object | Kronecker–Weber theorem |
—
|
NE NERFINISHED |
How this triple was built (2 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: Kronecker–Weber theorem | Statement: [Cassels–Fröhlich: Algebraic Number Theory, topic, Kronecker–Weber theorem]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Kronecker–Weber theorem Context triple: [Cassels–Fröhlich: Algebraic Number Theory, topic, Kronecker–Weber theorem]
-
A.
Kronecker–Weber theorem
chosen
The Kronecker–Weber theorem is a fundamental result in algebraic number theory stating that every finite abelian extension of the rational numbers is contained in a cyclotomic field generated by roots of unity.
-
B.
Kummer theory
Kummer theory is a branch of algebraic number theory that studies abelian extensions of fields, especially cyclotomic and radical extensions, using properties of roots of unity and ideal class groups.
-
C.
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.
-
D.
Artin–Schreier theory
Artin–Schreier theory is a branch of algebraic number theory and field theory that characterizes cyclic extensions of prime degree in fields of characteristic p using additive polynomials.
-
E.
Chebotarev density theorem
The Chebotarev density theorem is a fundamental result in algebraic number theory that generalizes the prime number theorem to describe how often primes in a number field have a given Frobenius conjugacy class in its Galois group.
- F. None of above.
- G. Unsure - the case is ambiguous/there is not enough information to decide.
Provenance (2 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_69d8dcfd05bc819088903cca13cc2846 |
completed | April 10, 2026, 11:20 a.m. |
| NER | Named-entity recognition | batch_69e5c47f6c948190918ade08bb88f1fd |
completed | April 20, 2026, 6:15 a.m. |
Created at: April 10, 2026, 11:58 a.m.