Triple

T9297060
Position Surface form Disambiguated ID Type / Status
Subject Chebotarev density theorem E223663 entity
Predicate hasVariant P455 FINISHED
Object effective Chebotarev density theorem E223663 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: effective Chebotarev density theorem | Statement: [Chebotarev density theorem, hasVariant, effective Chebotarev density theorem]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: effective Chebotarev density theorem
Context triple: [Chebotarev density theorem, hasVariant, effective Chebotarev density theorem]
  • A. Chebotarev density theorem chosen
    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.
  • B. Sato–Tate distribution (for families of elliptic curves)
    The Sato–Tate distribution (for families of elliptic curves) is a probabilistic law describing how the normalized Frobenius traces (or equivalently, the angles in the Hasse bound) of elliptic curves are distributed, typically following a specific sine-squared measure on the interval [0, π].
  • C. Hilbert’s irreducibility theorem
    Hilbert’s irreducibility theorem is a fundamental result in number theory and algebraic geometry that ensures many polynomial equations with parameterized coefficients retain irreducibility for infinitely many specializations of those parameters.
  • D. Faltings' theorem
    Faltings' theorem is a landmark result in arithmetic geometry that proves every algebraic curve of genus greater than one over a number field has only finitely many rational points.
  • 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 (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_69ca8423edb08190bc0c91287a484768 completed March 30, 2026, 2:09 p.m.
NER Named-entity recognition batch_69cd089c9c588190967404c9eb938dfb completed April 1, 2026, 11:59 a.m.
NED1 Entity disambiguation (via context triple) batch_69d0b251c4148190a94fafdc23a601d6 completed April 4, 2026, 6:40 a.m.
Created at: March 30, 2026, 7:36 p.m.