Triple

T8640760
Position Surface form Disambiguated ID Type / Status
Subject Frigyes Riesz E204639 entity
Predicate knownFor P22 FINISHED
Object Riesz rearrangement inequality
The Riesz rearrangement inequality is a fundamental result in mathematical analysis that provides an optimal bound for integrals of products of functions in terms of their symmetric decreasing rearrangements.
E747350 NE FINISHED

How this triple was built (4 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: Riesz rearrangement inequality | Statement: [Frigyes Riesz, knownFor, Riesz rearrangement inequality]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Riesz rearrangement inequality
Context triple: [Frigyes Riesz, knownFor, Riesz rearrangement inequality]
  • A. Grothendieck inequality
    The Grothendieck inequality is a fundamental result in functional analysis and theoretical computer science that bounds certain bilinear forms and has deep implications for Banach space theory, operator theory, and approximation algorithms.
  • B. Gagliardo–Nirenberg interpolation inequalities
    The Gagliardo–Nirenberg interpolation inequalities are fundamental results in functional analysis and partial differential equations that bound intermediate norms of functions by combinations of lower and higher order norms, playing a key role in regularity theory and nonlinear analysis.
  • C. Korn inequality
    Korn inequality is a fundamental result in functional analysis and the mathematical theory of elasticity that provides bounds relating the full gradient of a vector field to its symmetric part, ensuring control of deformations by their strains.
  • D. Young inequality for convolutions
    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.
  • E. Poincaré inequality
    The Poincaré inequality is a fundamental result in functional analysis and partial differential equations that bounds the average oscillation of a function by the size of its gradient, playing a key role in Sobolev space theory and the study of elliptic problems.
  • F. None of above. chosen
  • G. Unsure - the case is ambiguous/there is not enough information to decide.
NEDg Description generation gpt-5.1
Instruction
Generate a one-sentence description of the target entity. 
You are given a context triple in the form (subject, predicate, object), where the object is the target entity. 
# Instructions
Use the triple to infer relevant information about the entity. Describe the entity based on what is most defining, well-known. 
Avoid repeating the information from the triple, unless really essential.
# Response Format
Return only the sentence: "Description: [one-sentence description of the target entity]"
Input
Entity: Riesz rearrangement inequality
Triple: [Frigyes Riesz, knownFor, Riesz rearrangement inequality]
Generated description
The Riesz rearrangement inequality is a fundamental result in mathematical analysis that provides an optimal bound for integrals of products of functions in terms of their symmetric decreasing rearrangements.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Riesz rearrangement inequality
Target entity description: The Riesz rearrangement inequality is a fundamental result in mathematical analysis that provides an optimal bound for integrals of products of functions in terms of their symmetric decreasing rearrangements.
  • 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. Grothendieck inequality
    The Grothendieck inequality is a fundamental result in functional analysis and theoretical computer science that bounds certain bilinear forms and has deep implications for Banach space theory, operator theory, and approximation algorithms.
  • C. Gagliardo–Nirenberg interpolation inequalities
    The Gagliardo–Nirenberg interpolation inequalities are fundamental results in functional analysis and partial differential equations that bound intermediate norms of functions by combinations of lower and higher order norms, playing a key role in regularity theory and nonlinear analysis.
  • D. Korn inequality
    Korn inequality is a fundamental result in functional analysis and the mathematical theory of elasticity that provides bounds relating the full gradient of a vector field to its symmetric part, ensuring control of deformations by their strains.
  • E. Young inequality for convolutions
    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.
  • F. None of above. chosen

Provenance (5 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_69ca834ca1c88190a11ffb0200342fac completed March 30, 2026, 2:06 p.m.
NER Named-entity recognition batch_69cc47944d1c819081f448f14d04bf9d completed March 31, 2026, 10:15 p.m.
NED1 Entity disambiguation (via context triple) batch_69cebc3b1f508190978df29d995f494c completed April 2, 2026, 6:58 p.m.
NEDg Description generation batch_69cebf12eec081909c40ccced9c1c52b completed April 2, 2026, 7:10 p.m.
NED2 Entity disambiguation (via description) batch_69cebf7302b08190bdfc84aac3147954 completed April 2, 2026, 7:11 p.m.
Created at: March 30, 2026, 6:28 p.m.