Triple

T7420293
Position Surface form Disambiguated ID Type / Status
Subject Swan constructed counterexamples over the rational numbers E171228 entity
Predicate relatedTo P37 FINISHED
Object Noether's problem for finite groups 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: Noether's problem for finite groups | Statement: [Swan constructed counterexamples over the rational numbers, relatedTo, Noether's problem for finite groups]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Noether's problem for finite groups
Context triple: [Swan constructed counterexamples over the rational numbers, relatedTo, Noether's problem for finite groups]
  • 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 fourteenth problem
    Hilbert’s fourteenth problem is one of David Hilbert’s famous list of 23 problems, concerning the finite generation of certain algebras of invariants in algebraic geometry and invariant theory.
  • 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. Noether’s theorem in algebraic geometry (Noether’s AF+BG theorem)
    Noether’s AF+BG theorem is a foundational result in algebraic geometry that provides conditions under which a polynomial vanishing on the intersection of two plane curves can be expressed as a linear combination of their defining equations.
  • E. 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.
  • 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_69c68a625d048190af70eb8b63bec5a0 completed March 27, 2026, 1:47 p.m.
NER Named-entity recognition batch_69c6f2ea61248190886e8e55b42ba5f1 completed March 27, 2026, 9:13 p.m.
NED1 Entity disambiguation (via context triple) batch_69c8344541308190af8d90633cd92645 completed March 28, 2026, 8:04 p.m.
Created at: March 27, 2026, 3:11 p.m.