Triple
T13589853
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Optimal Transport: Old and New |
E324664
|
entity |
| Predicate | subject |
P450
|
FINISHED |
| Object | Kantorovich duality |
E1017918
|
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: Kantorovich duality | Statement: [Optimal Transport: Old and New, subject, Kantorovich duality]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Kantorovich duality Context triple: [Optimal Transport: Old and New, subject, Kantorovich duality]
-
A.
Kantorovich duality
chosen
Kantorovich duality is a fundamental result in optimal transport theory that characterizes the optimal transport cost as the supremum of a dual variational problem over suitable test functions.
-
B.
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.
-
C.
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.
-
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.
Karush–Kuhn–Tucker conditions
The Karush–Kuhn–Tucker conditions are fundamental optimality criteria in nonlinear programming that generalize Lagrange multipliers to handle inequality constraints.
- 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.