Triple
T16991699
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Non-Euclidean geometry |
E412207
|
entity |
| Predicate | hasModel |
P2390
|
FINISHED |
| Object |
Beltrami–Klein model
The Beltrami–Klein model is a projective representation of hyperbolic geometry in which the entire hyperbolic plane is mapped inside a disk and geodesics appear as straight line segments.
|
E1245022
|
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: Beltrami–Klein model | Statement: [Non-Euclidean geometry, hasModel, Beltrami–Klein model]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Beltrami–Klein model Context triple: [Non-Euclidean geometry, hasModel, Beltrami–Klein model]
-
A.
Poincaré upper half-plane model
The Poincaré upper half-plane model is a standard representation of the hyperbolic plane using the complex numbers with positive imaginary part, equipped with a specific metric that makes geodesics appear as semicircles and vertical lines.
-
B.
Poincaré metric
The Poincaré metric is the canonical complete Riemannian metric of constant negative curvature on simply connected Riemann surfaces like the unit disk or upper half-plane, fundamental in complex analysis and hyperbolic geometry.
-
C.
Möbius geometry
Möbius geometry is a branch of geometry that studies properties of figures invariant under Möbius (conformal) transformations of the extended complex plane or higher-dimensional spheres.
-
D.
Riemann sphere
The Riemann sphere is the complex plane plus a point at infinity, forming a one-dimensional complex manifold topologically equivalent to a sphere and used to study meromorphic functions and complex analysis.
-
E.
Busemann
Busemann is a surname most notably associated with Herbert Busemann, a German-American mathematician known for his work in geometry.
- 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: Beltrami–Klein model Triple: [Non-Euclidean geometry, hasModel, Beltrami–Klein model]
Generated description
The Beltrami–Klein model is a projective representation of hyperbolic geometry in which the entire hyperbolic plane is mapped inside a disk and geodesics appear as straight line segments.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Beltrami–Klein model Target entity description: The Beltrami–Klein model is a projective representation of hyperbolic geometry in which the entire hyperbolic plane is mapped inside a disk and geodesics appear as straight line segments.
-
A.
Poincaré upper half-plane model
The Poincaré upper half-plane model is a standard representation of the hyperbolic plane using the complex numbers with positive imaginary part, equipped with a specific metric that makes geodesics appear as semicircles and vertical lines.
-
B.
Poincaré metric
The Poincaré metric is the canonical complete Riemannian metric of constant negative curvature on simply connected Riemann surfaces like the unit disk or upper half-plane, fundamental in complex analysis and hyperbolic geometry.
-
C.
Möbius geometry
Möbius geometry is a branch of geometry that studies properties of figures invariant under Möbius (conformal) transformations of the extended complex plane or higher-dimensional spheres.
-
D.
Riemann sphere
The Riemann sphere is the complex plane plus a point at infinity, forming a one-dimensional complex manifold topologically equivalent to a sphere and used to study meromorphic functions and complex analysis.
-
E.
Busemann
Busemann is a surname most notably associated with Herbert Busemann, a German-American mathematician known for his work in geometry.
- 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_69d886cb581c8190ab05f4b429c9cd85 |
completed | April 10, 2026, 5:12 a.m. |
| NER | Named-entity recognition | batch_69e3d280e3348190a27bd5dc7cf87c0e |
completed | April 18, 2026, 6:50 p.m. |
| NED1 | Entity disambiguation (via context triple) | batch_6a00dc14d5688190945f7ae72f724922 |
completed | May 10, 2026, 7:27 p.m. |
| NEDg | Description generation | batch_6a0114d5aeb0819086f1a5d279ac0d0f |
completed | May 10, 2026, 11:29 p.m. |
| NED2 | Entity disambiguation (via description) | batch_6a0115c967b0819088e2335fd45d755b |
completed | May 10, 2026, 11:33 p.m. |
Created at: April 10, 2026, 5:32 a.m.