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.