Triple

T13589840
Position Surface form Disambiguated ID Type / Status
Subject Optimal Transport: Old and New E324664 entity
Predicate subject P450 FINISHED
Object Monge–Kantorovich problem E1020368 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: Monge–Kantorovich problem | Statement: [Optimal Transport: Old and New, subject, Monge–Kantorovich problem]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Monge–Kantorovich problem
Context triple: [Optimal Transport: Old and New, subject, Monge–Kantorovich problem]
  • A. Kantorovich problem in optimal transport chosen
    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.
  • 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. 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.
  • D. Kantorovich duality
    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.
  • 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.