Triple

T27562979
Position Surface form Disambiguated ID Type / Status
Subject Legendre transformation E695821 entity
Predicate relatedConcept P37 FINISHED
Object Legendre–Fenchel transform
The Legendre–Fenchel transform is a generalization of the classical Legendre transform to convex (possibly non-differentiable) functions, mapping a function to its convex conjugate and playing a central role in convex analysis and optimization.
 E695821 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: Legendre–Fenchel transform | Statement: [Legendre transformation, relatedConcept, Legendre–Fenchel transform]
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: Legendre–Fenchel transform
Triple: [Legendre transformation, relatedConcept, Legendre–Fenchel transform]
Generated description
The Legendre–Fenchel transform is a generalization of the classical Legendre transform to convex (possibly non-differentiable) functions, mapping a function to its convex conjugate and playing a central role in convex analysis and optimization.

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_69ef53891af88190a193c5e2a1dac9b1 completed April 27, 2026, 12:16 p.m.
NER Named-entity recognition batch_69f62fbbc4408190b9afd456a429f61b completed May 2, 2026, 5:09 p.m.
NED1 Entity disambiguation (via context triple) batch_6a12d0cf04108190a88e56bf8b2c0af2 completed May 24, 2026, 10:19 a.m.
NEDg Description generation batch_6a12d169e8888190bf3c8e7f0718a3a5 completed May 24, 2026, 10:22 a.m.
NED2 Entity disambiguation (via description) batch_6a12d2747f6881909aa2a5b0c389a494 completed May 24, 2026, 10:27 a.m.
Created at: April 27, 2026, 1:40 p.m.