Triple

T9843849
Position Surface form Disambiguated ID Type / Status
Subject Cauchy–Schwarz inequality E239290 entity
Predicate appliesTo P1129 FINISHED
Object Hilbert spaces E2126 NE FINISHED

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: Hilbert spaces
Context triple: [Cauchy–Schwarz inequality, appliesTo, Hilbert spaces]
  • A. Hilbert spaces chosen
    Hilbert spaces are complete inner product spaces that provide the fundamental framework for modern functional analysis and many areas of mathematical physics.
  • B. Banach spaces
    Banach spaces are complete normed vector spaces that provide a fundamental framework for functional analysis and the study of infinite-dimensional linear phenomena.
  • C. Hilbert–Schmidt operators
    Hilbert–Schmidt operators are a class of compact operators on Hilbert spaces characterized by having finite Hilbert–Schmidt norm, playing a central role in functional analysis and operator theory.
  • D. Foundations of Functional Analysis
    Foundations of Functional Analysis is a seminal mathematical text that systematically develops the core concepts and theorems of functional analysis, particularly in the tradition of the Riesz school.
  • E. Gelfand triples (rigged Hilbert spaces)
    Gelfand triples (rigged Hilbert spaces) are a mathematical framework that extends Hilbert spaces to rigorously handle generalized eigenvectors and distributions, particularly in quantum mechanics and functional analysis.
  • 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_69cdb35dc29c819080203be5b904dc9d ner completed
NED1 batch_69d1d5dda4b0819092703270e87bee5a ned_source_triple completed
Created at: March 30, 2026, 8:33 p.m.