Triple

T24806754
Position Surface form Disambiguated ID Type / Status
Subject Rellich–Kondrachov compactness theorem E620675 entity
Predicate relatedTo P37 FINISHED
Object Sobolev embedding theorem
The Sobolev embedding theorem is a fundamental result in functional analysis that characterizes when Sobolev spaces continuously or compactly embed into spaces of more regular or integrable functions, such as Lebesgue or Hölder spaces.
E1655423 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: Sobolev embedding theorem | Statement: [Rellich–Kondrachov compactness theorem, relatedTo, Sobolev embedding theorem]
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: Sobolev embedding theorem
Triple: [Rellich–Kondrachov compactness theorem, relatedTo, Sobolev embedding theorem]
Generated description
The Sobolev embedding theorem is a fundamental result in functional analysis that characterizes when Sobolev spaces continuously or compactly embed into spaces of more regular or integrable functions, such as Lebesgue or Hölder spaces.

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_69e2fabf26bc8190b191faac8f67065b completed April 18, 2026, 3:30 a.m.
NER Named-entity recognition batch_69f42206efcc81908d4b512bd4ae899a completed May 1, 2026, 3:46 a.m.
NED1 Entity disambiguation (via context triple) batch_6a10330d50a081908662ae2d550932a7 completed May 22, 2026, 10:42 a.m.
NEDg Description generation batch_6a1033be69f88190988f54e89df5438a completed May 22, 2026, 10:45 a.m.
NED2 Entity disambiguation (via description) batch_6a10346cdcac8190865eb3c1b86c9c2c completed May 22, 2026, 10:48 a.m.
Created at: April 18, 2026, 4:50 a.m.