Triple

T13894041
Position Surface form Disambiguated ID Type / Status
Subject Hadamard inequality E334041 entity
Predicate proofTechnique P7024 FINISHED
Object Cauchy–Schwarz inequality E239290 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–Schwarz inequality | Statement: [Hadamard inequality, proofTechnique, Cauchy–Schwarz inequality]

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–Schwarz inequality
Context triple: [Hadamard inequality, proofTechnique, Cauchy–Schwarz inequality]
  • A. Cauchy–Schwarz inequality chosen
    The Cauchy–Schwarz inequality is a fundamental result in linear algebra and analysis that bounds the inner product of two vectors by the product of their magnitudes, underpinning many concepts in geometry, probability, and functional analysis.
  • B. Minkowski inequality
    The Minkowski inequality is a fundamental result in functional analysis and measure theory that generalizes the triangle inequality to L^p spaces, providing a key tool for studying norms and integrable functions.
  • C. Hölder inequality
    Hölder inequality is a fundamental result in mathematical analysis that generalizes the Cauchy–Schwarz inequality and provides bounds for integrals or sums of products in Lᵖ spaces.
  • D. Bessel inequality
    Bessel inequality is a fundamental result in functional analysis that bounds the sum of squared Fourier coefficients of a vector in an inner product space by the square of its norm.
  • E. Hadamard inequality
    The Hadamard inequality is a fundamental result in linear algebra and analysis that bounds the absolute value of a determinant by the product of the Euclidean norms of its row or column vectors.
  • 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_69d81c5dd2d48190b7a5fc1e009de936 elicitation completed
NER batch_69de23a741908190bdf46d76c5f1411a ner completed
NED1 batch_69f7ce7419cc81909488871c16d6b356 ned_source_triple completed
Created at: April 9, 2026, 10:15 p.m.