Triple

T17020051
Position Surface form Disambiguated ID Type / Status
Subject Young inequality for convolutions E412923 entity
Predicate relatedTo P37 FINISHED
Object Hausdorff–Young inequality E412923 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: Hausdorff–Young inequality | Statement: [Young inequality for convolutions, relatedTo, Hausdorff–Young inequality]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Hausdorff–Young inequality
Context triple: [Young inequality for convolutions, relatedTo, Hausdorff–Young inequality]
  • A. Riesz–Thorin interpolation theorem
    The Riesz–Thorin interpolation theorem is a fundamental result in functional analysis that provides bounds for linear operators between Lᵖ spaces by interpolating their behavior between two known endpoint estimates.
  • B. 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.
  • C. Young inequality for convolutions chosen
    Young inequality for convolutions is a fundamental result in analysis that provides norm bounds for the convolution of functions in Lebesgue spaces, relating the L^p norms of the factors to the L^r norm of their convolution.
  • D. Friedrichs inequality
    Friedrichs inequality is a fundamental result in functional analysis and partial differential equations that provides bounds on the norms of functions in terms of their derivatives, playing a key role in the theory of Sobolev spaces and boundary value problems.
  • E. Littlewood–Paley theory
    Littlewood–Paley theory is a collection of techniques in harmonic analysis that decompose functions into frequency-localized pieces to study their behavior in L^p spaces and related function spaces.
  • 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.