Triple
T5837247
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Kähler form |
E129501
|
entity |
| Predicate | relatedTo |
P37
|
FINISHED |
| Object |
Fubini–Study form
The Fubini–Study form is the canonical Kähler form on complex projective space, encoding its standard Hermitian and symplectic geometry.
|
E551964
|
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: Fubini–Study form | Statement: [Kähler form, relatedTo, Fubini–Study form]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Fubini–Study form Context triple: [Kähler form, relatedTo, Fubini–Study form]
-
A.
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.
-
B.
Cartan theorems A and B
Cartan theorems A and B are fundamental results in complex analytic geometry that characterize coherent analytic sheaves on Stein spaces by guaranteeing the existence of enough global sections and the vanishing of higher cohomology.
-
C.
Cartan–Killing form
The Cartan–Killing form is a canonical symmetric bilinear form on a Lie algebra that plays a central role in classifying and studying the structure of Lie algebras and Lie groups.
-
D.
Maurer–Cartan form
The Maurer–Cartan form is a canonical Lie algebra-valued 1-form on a Lie group that encodes its infinitesimal structure and underlies many constructions in differential geometry and gauge theory.
-
E.
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.
- 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: Fubini–Study form Triple: [Kähler form, relatedTo, Fubini–Study form]
Generated description
The Fubini–Study form is the canonical Kähler form on complex projective space, encoding its standard Hermitian and symplectic geometry.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Fubini–Study form Target entity description: The Fubini–Study form is the canonical Kähler form on complex projective space, encoding its standard Hermitian and symplectic geometry.
-
A.
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.
-
B.
Cartan theorems A and B
Cartan theorems A and B are fundamental results in complex analytic geometry that characterize coherent analytic sheaves on Stein spaces by guaranteeing the existence of enough global sections and the vanishing of higher cohomology.
-
C.
Cartan–Killing form
The Cartan–Killing form is a canonical symmetric bilinear form on a Lie algebra that plays a central role in classifying and studying the structure of Lie algebras and Lie groups.
-
D.
Maurer–Cartan form
The Maurer–Cartan form is a canonical Lie algebra-valued 1-form on a Lie group that encodes its infinitesimal structure and underlies many constructions in differential geometry and gauge theory.
-
E.
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.
- 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_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.