Triple
T5837246
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Kähler form |
E129501
|
entity |
| Predicate | generalizedBy |
P2372
|
FINISHED |
| Object |
Kähler current
A Kähler current is a generalized, possibly singular analogue of a Kähler form, typically realized as a closed positive (1,1)-current on a complex manifold.
|
E129501
|
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: Kähler current | Statement: [Kähler form, generalizedBy, Kähler current]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Kähler current Context triple: [Kähler form, generalizedBy, Kähler current]
-
A.
Kähler–Ricci flow
Kähler–Ricci flow is a geometric evolution equation that deforms Kähler metrics on complex manifolds according to their Ricci curvature, playing a central role in complex differential geometry and the study of canonical metrics.
-
B.
Kähler manifold
A Kähler manifold is a complex manifold equipped with a Hermitian metric whose associated symplectic form is closed, making it simultaneously a complex, Riemannian, and symplectic manifold in a compatible way.
-
C.
Kähler form
A Kähler form is a closed, positive-definite (1,1)-form that defines the compatible symplectic and Hermitian structure on a Kähler manifold.
-
D.
Monge–Ampère equation
The Monge–Ampère equation is a fully nonlinear partial differential equation central to differential geometry, optimal transport, and several complex variables, often used to study curvature and geometric structures.
-
E.
Differential Analysis on Complex Manifolds
"Differential Analysis on Complex Manifolds" is a foundational mathematical monograph that systematically develops the theory of differential and complex geometry on complex manifolds.
- 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: Kähler current Triple: [Kähler form, generalizedBy, Kähler current]
Generated description
A Kähler current is a generalized, possibly singular analogue of a Kähler form, typically realized as a closed positive (1,1)-current on a complex manifold.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Kähler current Target entity description: A Kähler current is a generalized, possibly singular analogue of a Kähler form, typically realized as a closed positive (1,1)-current on a complex manifold.
-
A.
Kähler–Ricci flow
Kähler–Ricci flow is a geometric evolution equation that deforms Kähler metrics on complex manifolds according to their Ricci curvature, playing a central role in complex differential geometry and the study of canonical metrics.
-
B.
Kähler manifold
A Kähler manifold is a complex manifold equipped with a Hermitian metric whose associated symplectic form is closed, making it simultaneously a complex, Riemannian, and symplectic manifold in a compatible way.
-
C.
Kähler form
chosen
A Kähler form is a closed, positive-definite (1,1)-form that defines the compatible symplectic and Hermitian structure on a Kähler manifold.
-
D.
Monge–Ampère equation
The Monge–Ampère equation is a fully nonlinear partial differential equation central to differential geometry, optimal transport, and several complex variables, often used to study curvature and geometric structures.
-
E.
Differential Analysis on Complex Manifolds
"Differential Analysis on Complex Manifolds" is a foundational mathematical monograph that systematically develops the theory of differential and complex geometry on complex manifolds.
- F. None of above.
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_69c0084af79c81908af128ccc29983d0 |
completed | March 22, 2026, 3:18 p.m. |
| NER | Named-entity recognition | batch_69c034a48750819099ae917ae2b54e6d |
completed | March 22, 2026, 6:27 p.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69c0a19a6554819086cdae499f4d2247 |
completed | March 23, 2026, 2:12 a.m. |
| NEDg | Description generation | batch_69c0a5ce005c8190a7da8d337caa089c |
completed | March 23, 2026, 2:30 a.m. |
| NED2 | Entity disambiguation (via description) | batch_69c0a62cadf481909007a2a16cd36dbf |
completed | March 23, 2026, 2:32 a.m. |
Created at: March 22, 2026, 3:54 p.m.