Triple

T13035729
Position Surface form Disambiguated ID Type / Status
Subject Monge problem in optimal transport E326555 entity
Predicate relatedConcept P37 FINISHED
Object Monge–Ampère equation E326554 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–Ampère equation | Statement: [Monge problem in optimal transport, relatedConcept, Monge–Ampère equation]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Monge–Ampère equation
Context triple: [Monge problem in optimal transport, relatedConcept, Monge–Ampère equation]
  • A. Monge–Ampère equation chosen
    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.
  • B. Christoffel–Minkowski problem
    The Christoffel–Minkowski problem is a classical question in convex geometry that seeks to reconstruct a convex body from prescribed curvature or area measure data on the unit sphere.
  • C. Nirenberg problem in differential geometry
    The Nirenberg problem in differential geometry is a classical question about prescribing Gaussian curvature on the 2-sphere via conformal deformations of the metric.
  • D. Yamabe problem
    The Yamabe problem is a fundamental question in differential geometry concerning whether every compact Riemannian manifold admits a metric of constant scalar curvature within a given conformal class.
  • E. 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.
  • 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_69d97f2a71a0819098bb6cf8a4b2208a completed April 10, 2026, 10:52 p.m.
NED1 Entity disambiguation (via context triple) batch_69f6d5fa10fc81908a37b85894f8f849 completed May 3, 2026, 4:58 a.m.
Created at: April 9, 2026, 8:55 p.m.