Triple

T20627433
Position Surface form Disambiguated ID Type / Status
Subject Nevanlinna–Pick interpolation E506854 entity
Predicate involves P1256 FINISHED
Object Nevanlinna–Pick kernels NE NERFINISHED

How this triple was built (3 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: Nevanlinna–Pick kernels | Statement: [Nevanlinna–Pick interpolation, involves, Nevanlinna–Pick kernels]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Nevanlinna–Pick kernels
Context triple: [Nevanlinna–Pick interpolation, involves, Nevanlinna–Pick kernels]
  • A. Nevanlinna–Pick interpolation
    Nevanlinna–Pick interpolation is a classical problem in complex analysis and operator theory that seeks analytic functions, typically bounded by one in the unit disk, which match prescribed values at given points.
  • B. 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.
  • C. Blaschke products
    Blaschke products are bounded analytic functions on the unit disk formed as (finite or infinite) products of Möbius transformations that map the disk to itself, playing a central role in complex analysis and function theory.
  • D. Szegő polynomials
    Szegő polynomials are a fundamental family of orthogonal polynomials on the unit circle that play a key role in complex analysis, approximation theory, and spectral theory.
  • E. 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.
  • F. None of above. chosen
  • G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Nevanlinna–Pick kernels
Target entity description: 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.
  • A. Nevanlinna–Pick interpolation
    Nevanlinna–Pick interpolation is a classical problem in complex analysis and operator theory that seeks analytic functions, typically bounded by one in the unit disk, which match prescribed values at given points.
  • B. 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.
  • C. Blaschke products
    Blaschke products are bounded analytic functions on the unit disk formed as (finite or infinite) products of Möbius transformations that map the disk to itself, playing a central role in complex analysis and function theory.
  • D. Szegő polynomials
    Szegő polynomials are a fundamental family of orthogonal polynomials on the unit circle that play a key role in complex analysis, approximation theory, and spectral theory.
  • E. 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.
  • F. None of above. chosen

Provenance (2 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_69e0b4bd4a0081908d4e97a590a33fb2 completed April 16, 2026, 10:06 a.m.
NER Named-entity recognition batch_69e6abe645888190b639ebedc5b3041a completed April 20, 2026, 10:42 p.m.
Created at: April 16, 2026, 11:42 a.m.