Triple
T13589852
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Optimal Transport: Old and New |
E324664
|
entity |
| Predicate | subject |
P450
|
FINISHED |
| Object | Brenier map |
E1017920
|
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: Brenier map | Statement: [Optimal Transport: Old and New, subject, Brenier map]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Brenier map Context triple: [Optimal Transport: Old and New, subject, Brenier map]
-
A.
Brenier map
chosen
The Brenier map is the unique gradient of a convex function that provides the optimal transport between probability measures under a quadratic cost, playing a central role in modern optimal transport theory.
-
B.
Monge problem in optimal transport
The Monge problem in optimal transport is a foundational mathematical formulation that seeks the most efficient way to move mass from one distribution to another, minimizing a given transportation cost.
-
C.
Kantorovich problem in optimal transport
The Kantorovich problem in optimal transport is a relaxed, linear-programming formulation of transporting mass between probability distributions that allows splitting mass and guarantees existence of optimal transport plans.
-
D.
Optimal Transport: Old and New
"Optimal Transport: Old and New" is a comprehensive monograph by Cédric Villani that develops the theory of optimal transport and its applications across analysis, geometry, and probability.
-
E.
Monge–Ampère equation
The Monge–Ampère equation is a fully nonlinear partial differential equation central to differential geometry, optimal transport, and several complex variables, often used to study curvature and geometric structures.
- F. None of above.
- G. Unsure - the case is ambiguous/there is not enough information to decide.
Provenance (3 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_69d80769eaf081909d82f44e484d6113 |
completed | April 9, 2026, 8:09 p.m. |
| NER | Named-entity recognition | batch_69dbb055cc98819091fab597b69e5e3e |
completed | April 12, 2026, 2:46 p.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69f76bc347b881908267455f3bdd50e8 |
completed | May 3, 2026, 3:37 p.m. |
Created at: April 9, 2026, 9:49 p.m.