Triple

T1489785
Position Surface form Disambiguated ID Type / Status
Subject Noether's problem E29549 entity
Predicate knownResult P28576 FINISHED
Object Bogomolov used the unramified Brauer group to produce counterexamples E29549 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: Bogomolov used the unramified Brauer group to produce counterexamples | Statement: [Noether's problem, knownResult, Bogomolov used the unramified Brauer group to produce counterexamples]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Bogomolov used the unramified Brauer group to produce counterexamples
Context triple: [Noether's problem, knownResult, Bogomolov used the unramified Brauer group to produce counterexamples]
  • A. Noether's problem chosen
    Noether's problem is a fundamental question in invariant theory and field theory that asks whether the fixed field of a finite group acting on a rational function field is itself a purely transcendental (rational) extension.
  • B. 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.
  • C. Riemann–Hurwitz formula
    The Riemann–Hurwitz formula is a fundamental result in algebraic geometry and complex analysis that relates the genera of two Riemann surfaces connected by a branched covering map, accounting for the ramification data.
  • D. Hilbert’s syzygy theorem
    Hilbert’s syzygy theorem is a fundamental result in commutative algebra that describes the finite length and structure of free resolutions of modules over polynomial rings.
  • E. Categories for the Working Mathematician
    Categories for the Working Mathematician is a foundational textbook in category theory that systematically develops the subject and its applications for professional mathematicians.
  • 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_69a498da82e08190ba833330d05f380f completed March 1, 2026, 7:51 p.m.
NER Named-entity recognition batch_69a4c9e02c188190b87c0aac939eafdd completed March 1, 2026, 11:21 p.m.
NED1 Entity disambiguation (via context triple) batch_69ad1ca98e64819097916eb7717e6364 completed March 8, 2026, 6:52 a.m.
Created at: March 1, 2026, 8:12 p.m.