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.