Triple

T17020024
Position Surface form Disambiguated ID Type / Status
Subject Young inequality for convolutions E412923 entity
Predicate involvesConcept P531 FINISHED
Object Hölder inequality E87726 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: Hölder inequality | Statement: [Young inequality for convolutions, involvesConcept, Hölder inequality]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Hölder inequality
Context triple: [Young inequality for convolutions, involvesConcept, Hölder inequality]
  • A. Hölder inequality chosen
    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.
  • 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. 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.
  • D. 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.
  • E. Karamata's inequality
    Karamata's inequality is a fundamental result in majorization theory that generalizes several classical inequalities by comparing sums of convex (or concave) functions over majorized sequences.
  • 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_69d886cc4170819093deddc7b8b4b6a7 completed April 10, 2026, 5:12 a.m.
NER Named-entity recognition batch_69e3d482c3a0819099e6ea4acb0a08ee completed April 18, 2026, 6:59 p.m.
NED1 Entity disambiguation (via context triple) batch_6a011b4f9dfc819085639edb5cda1cca completed May 10, 2026, 11:57 p.m.
Created at: April 10, 2026, 5:33 a.m.