Triple

T18897003
Position Surface form Disambiguated ID Type / Status
Subject Cassels–Fröhlich: Algebraic Number Theory E462233 entity
Predicate topic P261 FINISHED
Object Dirichlet unit 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: Dirichlet unit theorem | Statement: [Cassels–Fröhlich: Algebraic Number Theory, topic, Dirichlet unit theorem]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Dirichlet unit theorem
Context triple: [Cassels–Fröhlich: Algebraic Number Theory, topic, Dirichlet unit theorem]
  • A. Dirichlet unit theorem chosen
    The Dirichlet unit theorem is a fundamental result in algebraic number theory that describes the structure of the unit group of the ring of integers in a number field as a finitely generated abelian group of a specific rank determined by the field’s real and complex embeddings.
  • B. Kronecker–Weber theorem
    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.
  • C. Hermite–Minkowski theorem
    The Hermite–Minkowski theorem is a fundamental result in algebraic number theory that gives a finiteness bound on the number of number fields of a given degree and discriminant.
  • D. 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.
  • E. 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.
  • 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.