Triple

T19327811
Position Surface form Disambiguated ID Type / Status
Subject Kurt Hensel E483404 entity
Predicate nameGivenTo P63 FINISHED
Object Hensel lemma — NE NERFINISHED

Named-entity recognition

Before disambiguation, gpt-5-mini classified whether the object phrase is a named entity — the step behind the object's NE type shown above.

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: Hensel lemma | Statement: [Kurt Hensel, nameGivenTo, Hensel lemma]

Disambiguation candidates (1 decision)

The exact options the model was shown at each disambiguation step, with the option it chose highlighted — the evidence behind this triple's disambiguated ids.

NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Hensel lemma
Context triple: [Kurt Hensel, nameGivenTo, Hensel lemma]
  • A. Hensel’s lemma chosen
    Hensel’s lemma is a fundamental result in number theory and p-adic analysis that allows one to lift solutions of polynomial congruences modulo a prime power to higher powers, analogous to Newton’s method in the p-adic setting.
  • B. Henselization
    Henselization is a construction in commutative algebra that minimally modifies a local ring to satisfy Hensel’s lemma, making it “Henselian” while preserving much of its original structure.
  • C. Kummer's lemma
    Kummer's lemma is a result in algebraic number theory that provides conditions on ideal factorization in cyclotomic fields, particularly relating to divisibility properties of class numbers and units.
  • D. Hensel
    Hensel is a German surname most notably associated with mathematician Kurt Hensel, known for introducing p-adic numbers.
  • E. Henselian ring
    A Henselian ring is a local ring in which Hensel’s lemma holds, allowing certain types of polynomial factorizations and root liftings from the residue field to the ring itself.
  • F. None of above.
  • G. Unsure - the case is ambiguous/there is not enough information to decide.

Provenance (2 batches)

Stage Batch ID Job type Status
creating batch_69d8e8d13e3c81909d91d1d5ec37c095 elicitation completed
NER batch_69e6163f32f48190be17cccf4e537372 ner completed
Created at: April 10, 2026, 1:33 p.m.