Triple

T10269883
Position Surface form Disambiguated ID Type / Status
Subject Wilhelm Blaschke E240805 entity
Predicate knownFor P22 FINISHED
Object 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.
E853121 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: Blaschke products | Statement: [Wilhelm Blaschke, knownFor, Blaschke products]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Blaschke products
Context triple: [Wilhelm Blaschke, knownFor, Blaschke products]
  • 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. Lempert function on convex domains
    The Lempert function on convex domains is a complex-analytic invariant that coincides with the Kobayashi distance and provides an extremal characterization of holomorphic mappings between convex domains in several complex variables.
  • C. 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.
  • D. Szegő limit theorem
    The Szegő limit theorem is a fundamental result in analysis and operator theory that describes the asymptotic behavior of determinants of large Toeplitz matrices in terms of the symbol’s integral.
  • E. Inequalities for analytic functions
    "Inequalities for analytic functions" is a mathematical work by Gábor Szegő that develops fundamental bounds and estimates for complex analytic functions, particularly in the context of complex analysis and approximation theory.
  • 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: Blaschke products
Triple: [Wilhelm Blaschke, knownFor, Blaschke products]
Generated description
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.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Blaschke products
Target entity description: 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.
  • 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. Lempert function on convex domains
    The Lempert function on convex domains is a complex-analytic invariant that coincides with the Kobayashi distance and provides an extremal characterization of holomorphic mappings between convex domains in several complex variables.
  • C. 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.
  • D. Szegő limit theorem
    The Szegő limit theorem is a fundamental result in analysis and operator theory that describes the asymptotic behavior of determinants of large Toeplitz matrices in terms of the symbol’s integral.
  • E. Inequalities for analytic functions
    "Inequalities for analytic functions" is a mathematical work by Gábor Szegő that develops fundamental bounds and estimates for complex analytic functions, particularly in the context of complex analysis and approximation theory.
  • 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_69d381a94c1881908fc38fc263d9b9c2 completed April 6, 2026, 9:49 a.m.
NER Named-entity recognition batch_69d4d270fb088190ba43b6f24e881b94 completed April 7, 2026, 9:46 a.m.
NED1 Entity disambiguation (via context triple) batch_69d6f80c25888190a3e8a2c513df7043 completed April 9, 2026, 12:51 a.m.
NEDg Description generation batch_69d6fcaca55c81908a48ac2a0ce24b85 completed April 9, 2026, 1:11 a.m.
NED2 Entity disambiguation (via description) batch_69d6fd772bc08190bf270f5fc767fb29 completed April 9, 2026, 1:14 a.m.
Created at: April 6, 2026, 11:35 a.m.