Triple

T9843485
Position Surface form Disambiguated ID Type / Status
Subject Augustin-Louis Cauchy E239282 entity
Predicate notableFor P22 FINISHED
Object Cauchy’s theorem in group theory E620659 NE FINISHED

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: Cauchy’s theorem in group theory | Statement: [Augustin-Louis Cauchy, notableFor, Cauchy’s theorem in group theory]

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: Cauchy’s theorem in group theory
Context triple: [Augustin-Louis Cauchy, notableFor, Cauchy’s theorem in group theory]
  • A. Cauchy's theorem in group theory chosen
    Cauchy's theorem in group theory is a fundamental result stating that if a finite group’s order is divisible by a prime p, then the group contains an element (and hence a subgroup) of order p.
  • B. Lagrange's theorem in group theory
    Lagrange's theorem in group theory is a fundamental result stating that the order of any subgroup of a finite group divides the order of the group.
  • C. Theorie der Gruppen von endlicher Ordnung
    "Theorie der Gruppen von endlicher Ordnung" is a foundational mathematical monograph on finite group theory that helped shape the modern development of abstract algebra.
  • D. Chevalley–Warning theorem
    The Chevalley–Warning theorem is a result in number theory and algebraic geometry that gives conditions under which systems of polynomial equations over finite fields must have nontrivial solutions.
  • E. Sylow theorems
    The Sylow theorems are fundamental results in finite group theory that describe the existence, conjugacy, and number of subgroups whose orders are powers of a prime dividing the group order.
  • F. None of above.
  • G. Unsure - the case is ambiguous/there is not enough information to decide.

Provenance (3 batches)

Stage Batch ID Job type Status
creating batch_69ca84e3f0c48190ada72a65ebd50efd elicitation completed
NER batch_69cdb35c8e348190aa090c71bf6f30eb ner completed
NED1 batch_69d1d5dda4b0819092703270e87bee5a ned_source_triple completed
Created at: March 30, 2026, 8:33 p.m.