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.