Triple

T9843478
Position Surface form Disambiguated ID Type / Status
Subject Augustin-Louis Cauchy E239282 entity
Predicate notableFor P22 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: [Augustin-Louis Cauchy, notableFor, 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: [Augustin-Louis Cauchy, notableFor, 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. 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.
  • E. Young's inequality
    Young's inequality is a fundamental result in mathematical analysis that provides an upper bound for the product of two nonnegative numbers in terms of their powers, playing a key role in convex analysis and functional inequalities.
  • 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.