Triple

T11812508
Position Surface form Disambiguated ID Type / Status
Subject Elwin Bruno Christoffel E280907 entity
Predicate notableWork P4 FINISHED
Object 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.
E947537 NE FINISHED

How this triple was built (4 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: Christoffel–Minkowski problem | Statement: [Elwin Bruno Christoffel, notableWork, Christoffel–Minkowski problem]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Christoffel–Minkowski problem
Context triple: [Elwin Bruno Christoffel, notableWork, Christoffel–Minkowski problem]
  • A. 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.
  • B. 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.
  • C. 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.
  • D. Minkowski’s theorem on convex sets
    Minkowski’s theorem on convex sets is a fundamental result in convex geometry that characterizes lattice points in convex bodies, underpinning much of the theory of convex polytopes and the geometry of numbers.
  • E. Calabi conjecture
    The Calabi conjecture is a fundamental result in complex differential geometry, proved by Shing-Tung Yau, which characterizes when a compact Kähler manifold admits a unique Ricci-flat Kähler metric in a given Kähler class.
  • F. None of above. chosen
  • G. Unsure - the case is ambiguous/there is not enough information to decide.
NEDg Description generation gpt-5.1
Instruction
Generate a one-sentence description of the target entity. 
You are given a context triple in the form (subject, predicate, object), where the object is the target entity. 
# Instructions
Use the triple to infer relevant information about the entity. Describe the entity based on what is most defining, well-known. 
Avoid repeating the information from the triple, unless really essential.
# Response Format
Return only the sentence: "Description: [one-sentence description of the target entity]"
Input
Entity: Christoffel–Minkowski problem
Triple: [Elwin Bruno Christoffel, notableWork, Christoffel–Minkowski problem]
Generated description
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.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Christoffel–Minkowski problem
Target entity description: 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.
  • A. 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.
  • B. 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.
  • C. 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.
  • D. Minkowski’s theorem on convex sets
    Minkowski’s theorem on convex sets is a fundamental result in convex geometry that characterizes lattice points in convex bodies, underpinning much of the theory of convex polytopes and the geometry of numbers.
  • E. Calabi conjecture
    The Calabi conjecture is a fundamental result in complex differential geometry, proved by Shing-Tung Yau, which characterizes when a compact Kähler manifold admits a unique Ricci-flat Kähler metric in a given Kähler class.
  • F. None of above. chosen

Provenance (5 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_69d6ab26aae88190b2489efcb2a24234 completed April 8, 2026, 7:23 p.m.
NER Named-entity recognition batch_69d8a5cba708819097467bb7aca7fc65 completed April 10, 2026, 7:24 a.m.
NED1 Entity disambiguation (via context triple) batch_69f131a01aa48190bf5a70759ac886f6 completed April 28, 2026, 10:16 p.m.
NEDg Description generation batch_69f141b31c9081908f19ff870f5f3c33 completed April 28, 2026, 11:24 p.m.
NED2 Entity disambiguation (via description) batch_69f14fdb39d48190828668fc535d7f6a completed April 29, 2026, 12:24 a.m.
Created at: April 8, 2026, 9:42 p.m.