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.