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.