Triple

T38260733

Position	Surface form	Disambiguated ID	Type / Status
Subject	Brenier map	`E1017920`	entity
Predicate	isGuaranteedBy	`P190217`	FINISHED
Object	Brenier’s polar factorization theorem Brenier’s polar factorization theorem is a fundamental result in optimal transport theory that decomposes any suitable map between probability measures into a measure-preserving transformation followed by a gradient of a convex function, yielding the so-called Brenier map.	`E1017920`	NE FINISHED

How this triple was built (3 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: Brenier’s polar factorization theorem | Statement: [Brenier map, isGuaranteedBy, Brenier’s polar factorization 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: Brenier’s polar factorization theorem
Triple: [Brenier map, isGuaranteedBy, Brenier’s polar factorization theorem]

Generated description

Brenier’s polar factorization theorem is a fundamental result in optimal transport theory that decomposes any suitable map between probability measures into a measure-preserving transformation followed by a gradient of a convex function, yielding the so-called Brenier map.

PD Predicate disambiguation gpt-5-mini-2025-08-07

Target predicate: isGuaranteedBy
Context triple: [Brenier map, isGuaranteedBy, Brenier’s polar factorization theorem]

A. guaranteedFor
Indicates that one entity provides an assurance or warranty that remains valid for another entity over a specified period or under certain conditions.
B. aimsToGuarantee
Indicates an intention or effort by one entity to ensure that a particular condition, outcome, or state is reliably achieved or maintained for another.
C. guaranteeStatus
Indicates the current state or condition of a guarantee associated with an entity or agreement.
D. guaranteeProvider
Indicates that one entity serves as the party that provides or issues a guarantee for another entity or obligation.
E. mayGuarantee
Indicates that one entity has the potential or authority to provide a guarantee for another entity or outcome.
F. None of above. chosen

Provenance (7 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_69f76de33e4481909099fa812709bd42`	completed	May 3, 2026, 3:46 p.m.
NER	Named-entity recognition	`batch_69fcc3321ef081908023590ba70ba0cf`	completed	May 7, 2026, 4:52 p.m.
NED1	Entity disambiguation (via context triple)	`batch_6a4193d4e2408190bd8893fc769eaaa2`	completed	June 28, 2026, 9:36 p.m.
NEDg	Description generation	`batch_6a41947a2f608190aba9f20c7e4cd8d6`	completed	June 28, 2026, 9:39 p.m.
NED2	Entity disambiguation (via description)	`batch_6a4195210170819086828d7780a6e407`	completed	June 28, 2026, 9:41 p.m.
PD	Predicate disambiguation	`batch_69fcb0fdc6e08190b05e894c59481a0d`	completed	May 7, 2026, 3:34 p.m.
PDg	Predicate description generation	`batch_69fcc330b4288190858b49d986160706`	completed	May 7, 2026, 4:52 p.m.

Created at: May 3, 2026, 4:30 p.m.