Triple

T8850258
Position Surface form Disambiguated ID Type / Status
Subject Hilbert’s seventeenth problem E210619 entity
Predicate solutionMethod P859 FINISHED
Object Artin–Schreier theory E537780 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–Schreier theory | Statement: [Hilbert’s seventeenth problem, solutionMethod, Artin–Schreier theory]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Artin–Schreier theory
Context triple: [Hilbert’s seventeenth problem, solutionMethod, Artin–Schreier theory]
  • A. Artin–Schreier theory chosen
    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.
  • B. Kummer theory
    Kummer theory is a branch of algebraic number theory that studies abelian extensions of fields, especially cyclotomic and radical extensions, using properties of roots of unity and ideal class groups.
  • C. Algebraic Groups and Class Fields
    "Algebraic Groups and Class Fields" is a influential mathematical monograph that develops the deep connections between algebraic group theory and class field theory within number theory and arithmetic geometry.
  • D. Artin reciprocity law
    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.
  • E. Galois theory
    Galois theory is a branch of abstract algebra that studies field extensions and polynomial equations through the structure of their associated symmetry groups.
  • 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_69ca838a424c8190b1ecac115c2927e7 completed March 30, 2026, 2:07 p.m.
NER Named-entity recognition batch_69cc60abb0748190af41d4e1f419e39c completed April 1, 2026, 12:02 a.m.
NED1 Entity disambiguation (via context triple) batch_69cf89cb853c8190a7664f2e7de0de87 completed April 3, 2026, 9:35 a.m.
Created at: March 30, 2026, 6:49 p.m.