Triple

T15860262
Position Surface form Disambiguated ID Type / Status
Subject Riesz–Fischer theorem E384563 entity
Predicate relatedTo P37 FINISHED
Object Bessel inequality E825431 NE FINISHED

How this triple was built (2 steps)

Every LLM step that produced this triple, in pipeline order — named-entity classification, the disambiguation choices (the exact options shown, with the pick highlighted), and the generated description. The batch + timestamp of each is in the Provenance table below.

NER Named-entity recognition gpt-5-mini
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: Bessel inequality | Statement: [Riesz–Fischer theorem, relatedTo, Bessel inequality]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Bessel inequality
Context triple: [Riesz–Fischer theorem, relatedTo, Bessel inequality]
  • A. Bessel inequality chosen
    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.
  • B. Cauchy–Schwarz inequality
    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.
  • C. 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.
  • D. 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.
  • 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)

The batch behind each pipeline step, in order, with when it ran. Timestamps are batch-level — stages were processed in waves, so the object chain (NER → NED1 → NEDg → NED2) reads in order, but predicate / elicitation batches can sit in a different wave.

Step Stage Batch ID Status When
creating Elicitation batch_69d86da422088190aac39e32e6c68429 completed April 10, 2026, 3:25 a.m.
NER Named-entity recognition batch_69e1555a1f008190bb3f03b0f35ed8a4 completed April 16, 2026, 9:32 p.m.
NED1 Entity disambiguation (via context triple) batch_69ffa14da7ac8190bbef49a1602a76fe completed May 9, 2026, 9:04 p.m.
Created at: April 10, 2026, 4:50 a.m.