Triple

T19370504
Position Surface form Disambiguated ID Type / Status
Subject Oka coherence theorem E484522 entity
Predicate relatedTo P37 FINISHED
Object Oka–Cartan theory
Oka–Cartan theory is a foundational area of complex analysis that studies the structure and properties of holomorphic functions and coherent analytic sheaves on complex manifolds, particularly Stein spaces.
E1372643 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: Oka–Cartan theory | Statement: [Oka coherence theorem, relatedTo, Oka–Cartan theory]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Oka–Cartan theory
Context triple: [Oka coherence theorem, relatedTo, Oka–Cartan theory]
  • 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. 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.
  • C. Chern–Weil theory
    Chern–Weil theory is a framework in differential geometry that constructs characteristic classes of vector bundles from curvature forms, linking topology and geometry through invariant polynomials.
  • D. 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.
  • E. Chern–Simons forms
    Chern–Simons forms are secondary characteristic classes in differential geometry that arise from connections on principal bundles and play a central role in topological quantum field theories.
  • 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: Oka–Cartan theory
Triple: [Oka coherence theorem, relatedTo, Oka–Cartan theory]
Generated description
Oka–Cartan theory is a foundational area of complex analysis that studies the structure and properties of holomorphic functions and coherent analytic sheaves on complex manifolds, particularly Stein spaces.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Oka–Cartan theory
Target entity description: Oka–Cartan theory is a foundational area of complex analysis that studies the structure and properties of holomorphic functions and coherent analytic sheaves on complex manifolds, particularly Stein spaces.
  • 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. 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.
  • C. Chern–Weil theory
    Chern–Weil theory is a framework in differential geometry that constructs characteristic classes of vector bundles from curvature forms, linking topology and geometry through invariant polynomials.
  • D. 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.
  • E. Chern–Simons forms
    Chern–Simons forms are secondary characteristic classes in differential geometry that arise from connections on principal bundles and play a central role in topological quantum field theories.
  • 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_69d8e8d305088190ad13571532aa454c completed April 10, 2026, 12:10 p.m.
NER Named-entity recognition batch_69e619af33e481908643f8beb2f498dc completed April 20, 2026, 12:18 p.m.
NED1 Entity disambiguation (via context triple) batch_6a072419c4ec8190931c1918450f2a83 completed May 15, 2026, 1:48 p.m.
NEDg Description generation batch_6a0725c32c4c8190bb29a764695cd245 completed May 15, 2026, 1:55 p.m.
NED2 Entity disambiguation (via description) batch_6a0726ea260c8190b97e2b18fde36272 completed May 15, 2026, 2 p.m.
Created at: April 10, 2026, 1:35 p.m.