Triple

T29464944

Position	Surface form	Disambiguated ID	Type / Status
Subject	Riesz rearrangement inequality	`E747350`	entity
Predicate	usesConcept	`P531`	FINISHED
Object	Hardy–Littlewood rearrangement inequality The Hardy–Littlewood rearrangement inequality is a fundamental result in real analysis that compares integrals of products of functions with those of their symmetric decreasing rearrangements, providing powerful bounds in measure theory and functional analysis.	`E1868409`	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: Hardy–Littlewood rearrangement inequality | Statement: [Riesz rearrangement inequality, usesConcept, Hardy–Littlewood rearrangement inequality]

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: Hardy–Littlewood rearrangement inequality
Triple: [Riesz rearrangement inequality, usesConcept, Hardy–Littlewood rearrangement inequality]

Generated description

The Hardy–Littlewood rearrangement inequality is a fundamental result in real analysis that compares integrals of products of functions with those of their symmetric decreasing rearrangements, providing powerful bounds in measure theory and functional analysis.

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_69f0bd4125f88190b56104591351619c`	completed	April 28, 2026, 1:59 p.m.
NER	Named-entity recognition	`batch_69f66ba6316c8190a84523b9bd642e9a`	completed	May 2, 2026, 9:24 p.m.
NED1	Entity disambiguation (via context triple)	`batch_6a25f115d4788190b7604baf3d9f84ec`	completed	June 7, 2026, 10:30 p.m.
NEDg	Description generation	`batch_6a25f6362f6081909a04ef3fbd5bb67f`	completed	June 7, 2026, 10:52 p.m.
NED2	Entity disambiguation (via description)	`batch_6a25fa9d98d08190aef6fb0a1779f501`	completed	June 7, 2026, 11:11 p.m.

Created at: April 28, 2026, 3:52 p.m.