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.