Triple

T21145357
Position Surface form Disambiguated ID Type / Status
Subject Bergman metric E521039 entity
Predicate constructedFrom P909 FINISHED
Object Bergman kernel
The Bergman kernel is a fundamental object in complex analysis that reproduces holomorphic functions on a domain and encodes its geometric and analytic structure.
E1469578 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: Bergman kernel | Statement: [Bergman metric, constructedFrom, Bergman kernel]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Bergman kernel
Context triple: [Bergman metric, constructedFrom, Bergman kernel]
  • A. Szegő kernel
    The Szegő kernel is a fundamental reproducing kernel in complex analysis and operator theory, associated with Hardy spaces on the boundary of a domain and central to the study of orthogonal polynomials and boundary behavior of analytic functions.
  • B. Nevanlinna–Pick kernels
    Nevanlinna–Pick kernels are special positive-definite kernels that characterize when and how analytic interpolation problems of Nevanlinna–Pick type admit solutions, often serving as the reproducing kernels of associated Hilbert spaces of analytic functions.
  • C. Poisson kernel
    The Poisson kernel is a fundamental function in harmonic analysis and potential theory used to represent harmonic functions inside a domain from their boundary values, especially in the unit disk and upper half-plane.
  • D. Bochner–Martinelli formula
    The Bochner–Martinelli formula is a fundamental integral representation in several complex variables that generalizes the Cauchy integral formula to higher dimensions.
  • E. Bergman metric
    The Bergman metric is a canonical Kähler metric on complex domains derived from the Bergman kernel, widely used in several complex variables and complex differential geometry.
  • 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: Bergman kernel
Triple: [Bergman metric, constructedFrom, Bergman kernel]
Generated description
The Bergman kernel is a fundamental object in complex analysis that reproduces holomorphic functions on a domain and encodes its geometric and analytic structure.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Bergman kernel
Target entity description: The Bergman kernel is a fundamental object in complex analysis that reproduces holomorphic functions on a domain and encodes its geometric and analytic structure.
  • A. Szegő kernel
    The Szegő kernel is a fundamental reproducing kernel in complex analysis and operator theory, associated with Hardy spaces on the boundary of a domain and central to the study of orthogonal polynomials and boundary behavior of analytic functions.
  • B. Nevanlinna–Pick kernels
    Nevanlinna–Pick kernels are special positive-definite kernels that characterize when and how analytic interpolation problems of Nevanlinna–Pick type admit solutions, often serving as the reproducing kernels of associated Hilbert spaces of analytic functions.
  • C. Poisson kernel
    The Poisson kernel is a fundamental function in harmonic analysis and potential theory used to represent harmonic functions inside a domain from their boundary values, especially in the unit disk and upper half-plane.
  • D. Bochner–Martinelli formula
    The Bochner–Martinelli formula is a fundamental integral representation in several complex variables that generalizes the Cauchy integral formula to higher dimensions.
  • E. Bergman metric
    The Bergman metric is a canonical Kähler metric on complex domains derived from the Bergman kernel, widely used in several complex variables and complex differential geometry.
  • 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_69e0b50c6a848190a4e525a77a319b8a completed April 16, 2026, 10:08 a.m.
NER Named-entity recognition batch_69e723fcdb7c8190ae04d6ad9dff3187 completed April 21, 2026, 7:15 a.m.
NED1 Entity disambiguation (via context triple) batch_6a096dc182708190b7311ae0d4bbf2d2 completed May 17, 2026, 7:26 a.m.
NEDg Description generation batch_6a096e6cce748190ba618dfe86f7f6ce completed May 17, 2026, 7:29 a.m.
NED2 Entity disambiguation (via description) batch_6a096f7706448190a1bb61535e0adcd3 completed May 17, 2026, 7:34 a.m.
Created at: April 16, 2026, 2:58 p.m.