Triple

T21047160
Position Surface form Disambiguated ID Type / Status
Subject Baire category theorem E518477 entity
Predicate hasConsequence P812 FINISHED
Object Closed graph theorem — 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: Closed graph theorem | Statement: [Baire category theorem, hasConsequence, Closed graph theorem]

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: Closed graph theorem
Context triple: [Baire category theorem, hasConsequence, Closed graph theorem]
  • A. Closed Graph Theorem chosen
    The Closed Graph Theorem is a fundamental result in functional analysis stating that a linear operator between Banach spaces is bounded (and hence continuous) if its graph is closed in the product space.
  • B. Banach–Steinhaus theorem
    The Banach–Steinhaus theorem is a fundamental result in functional analysis that characterizes when a family of continuous linear operators is uniformly bounded, with major implications for the behavior of sequences of operators on Banach spaces.
  • C. Banach inverse mapping theorem
    The Banach inverse mapping theorem is a fundamental result in functional analysis stating that a bijective bounded linear operator between Banach spaces has a bounded linear inverse.
  • D. Banach–Alaoglu theorem
    The Banach–Alaoglu theorem is a fundamental result in functional analysis stating that the closed unit ball in the dual of a normed space is compact in the weak-* topology.
  • E. Hahn–Banach theorem
    The Hahn–Banach theorem is a fundamental result in functional analysis that guarantees the extension of bounded linear functionals from a subspace to the whole space without increasing their norm.
  • 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_69e0b50438e08190917e2538bb8bc034 elicitation completed
NER batch_69e6fcf4d26481908b639996500a8319 ner completed
Created at: April 16, 2026, 2:34 p.m.