Triple

T10063336
Position Surface form Disambiguated ID Type / Status
Subject Hasse norm theorem E213039 entity
Predicate relatedTo P37 FINISHED
Object Artin reciprocity law E537778 NE FINISHED

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: Artin reciprocity law | Statement: [Hasse norm theorem, relatedTo, Artin reciprocity law]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Artin reciprocity law
Context triple: [Hasse norm theorem, relatedTo, Artin reciprocity law]
  • A. Artin reciprocity law chosen
    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.
  • B. Artin’s conjecture on L-functions
    Artin’s conjecture on L-functions is a major unproven hypothesis in number theory asserting that nontrivial Artin L-functions associated to Galois representations are entire, with deep implications for the distribution of primes and the structure of number fields.
  • C. 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.
  • D. 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.
  • E. Hilbert’s twelfth problem
    Hilbert’s twelfth problem is one of David Hilbert’s famous list of 23 problems, asking for a general explicit class field theory that would generate all abelian extensions of a given number field using special values of analytic functions.
  • F. None of above.
  • G. Unsure - the case is ambiguous/there is not enough information to decide.

Provenance (3 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_69ca83977128819084084eb7d1d8c52a completed March 30, 2026, 2:07 p.m.
NER Named-entity recognition batch_69cdcfd4e4ac8190a37061b4082caa48 completed April 2, 2026, 2:09 a.m.
NED1 Entity disambiguation (via context triple) batch_69d2b630ca008190a337660ad8c9d57e completed April 5, 2026, 7:21 p.m.
Created at: March 30, 2026, 8:58 p.m.