Triple

T13035696
Position Surface form Disambiguated ID Type / Status
Subject Monge–Ampère equation E326554 entity
Predicate relatedTo P37 FINISHED
Object Monge–Kantorovich optimal transport problem E326555 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 optimal transport problem | Statement: [Monge–Ampère equation, relatedTo, Monge–Kantorovich optimal transport problem]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Monge–Kantorovich optimal transport problem
Context triple: [Monge–Ampère equation, relatedTo, Monge–Kantorovich optimal transport problem]
  • A. Monge problem in optimal transport chosen
    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.
  • B. 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.
  • C. 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.
  • D. Wasserstein distance
    Wasserstein distance is a metric from optimal transport theory that measures the minimal “cost” of transforming one probability distribution into another, widely used to compare distributions in statistics and machine learning.
  • E. Carathéodory’s theorem in convex geometry
    Carathéodory’s theorem in convex geometry is a fundamental result stating that any point in the convex hull of a set in ℝⁿ can be expressed as a convex combination of at most n+1 points from that set.
  • 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_69d8076cc45c81908123123f43e69266 completed April 9, 2026, 8:09 p.m.
NER Named-entity recognition batch_69d97effca908190ab89fdb034e02680 completed April 10, 2026, 10:51 p.m.
NED1 Entity disambiguation (via context triple) batch_69f6cbcf11f88190ab1746f973132af1 completed May 3, 2026, 4:15 a.m.
Created at: April 9, 2026, 8:55 p.m.