Triple
T5705494
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Cartan connection |
E125773
|
entity |
| Predicate | generalizes |
P2372
|
FINISHED |
| Object |
Ehresmann connection
An Ehresmann connection is a geometric structure on a fiber bundle that specifies a way to consistently split tangent spaces into vertical and horizontal parts, enabling the definition of parallel transport.
|
E542125
|
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: Ehresmann connection | Statement: [Cartan connection, generalizes, Ehresmann connection]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Ehresmann connection Context triple: [Cartan connection, generalizes, Ehresmann connection]
-
A.
Cartan connections
Cartan connections are a geometric framework generalizing affine and Riemannian connections that model curved spaces on homogeneous spaces, developed by Élie Cartan.
-
B.
Levi-Civita connection
The Levi-Civita connection is the unique torsion-free affine connection on a Riemannian manifold that is compatible with its metric, enabling the definition of parallel transport and covariant differentiation.
-
C.
Cartan structure equations
Cartan structure equations are fundamental differential geometric relations that express curvature and torsion in terms of connection 1-forms on a manifold.
-
D.
Lie bracket
The Lie bracket is a bilinear, antisymmetric operation on a Lie algebra that measures the noncommutativity of its elements and encodes its infinitesimal structure.
-
E.
theory of G-structures
The theory of G-structures is a framework in differential geometry that studies geometric structures on manifolds defined by reductions of the frame bundle to a Lie group G, encompassing and unifying many classical geometries such as Riemannian, symplectic, and complex structures.
- 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: Ehresmann connection Triple: [Cartan connection, generalizes, Ehresmann connection]
Generated description
An Ehresmann connection is a geometric structure on a fiber bundle that specifies a way to consistently split tangent spaces into vertical and horizontal parts, enabling the definition of parallel transport.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Ehresmann connection Target entity description: An Ehresmann connection is a geometric structure on a fiber bundle that specifies a way to consistently split tangent spaces into vertical and horizontal parts, enabling the definition of parallel transport.
-
A.
Cartan connections
Cartan connections are a geometric framework generalizing affine and Riemannian connections that model curved spaces on homogeneous spaces, developed by Élie Cartan.
-
B.
Levi-Civita connection
The Levi-Civita connection is the unique torsion-free affine connection on a Riemannian manifold that is compatible with its metric, enabling the definition of parallel transport and covariant differentiation.
-
C.
Cartan structure equations
Cartan structure equations are fundamental differential geometric relations that express curvature and torsion in terms of connection 1-forms on a manifold.
-
D.
Lie bracket
The Lie bracket is a bilinear, antisymmetric operation on a Lie algebra that measures the noncommutativity of its elements and encodes its infinitesimal structure.
-
E.
theory of G-structures
The theory of G-structures is a framework in differential geometry that studies geometric structures on manifolds defined by reductions of the frame bundle to a Lie group G, encompassing and unifying many classical geometries such as Riemannian, symplectic, and complex structures.
- 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_69c0082c96988190b3a6a201edce472a |
completed | March 22, 2026, 3:18 p.m. |
| NER | Named-entity recognition | batch_69c02459cd18819080fda0b481d11f08 |
completed | March 22, 2026, 5:18 p.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69c05a666d788190a0f786d12391a44b |
completed | March 22, 2026, 9:08 p.m. |
| NEDg | Description generation | batch_69c05be7f7cc8190bb1f8081289c5e02 |
completed | March 22, 2026, 9:15 p.m. |
| NED2 | Entity disambiguation (via description) | batch_69c0621308588190a0d7a86bb804134d |
completed | March 22, 2026, 9:41 p.m. |
Created at: March 22, 2026, 3:45 p.m.