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.