Triple
T5256423
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Carathéodory–Fejér interpolation |
E118709
|
entity |
| Predicate | relatedTo |
P37
|
FINISHED |
| Object |
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.
|
E506854
|
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: Nevanlinna–Pick interpolation | Statement: [Carathéodory–Fejér interpolation, relatedTo, Nevanlinna–Pick interpolation]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Nevanlinna–Pick interpolation Context triple: [Carathéodory–Fejér interpolation, relatedTo, Nevanlinna–Pick interpolation]
-
A.
Carathéodory–Fejér interpolation
Carathéodory–Fejér interpolation is a classical result in complex analysis and approximation theory that concerns constructing analytic functions, typically with bounded or positive real part, that match prescribed initial Taylor coefficients.
-
B.
Runge approximation theorem
The Runge approximation theorem is a fundamental result in complex analysis stating that holomorphic functions on certain domains can be uniformly approximated by rational functions with poles outside those domains.
-
C.
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.
-
D.
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.
-
E.
Hermite–Biehler theorem
The Hermite–Biehler theorem is a result in complex analysis and control theory that characterizes when a complex polynomial has all its zeros in the open upper half-plane in terms of the interlacing of zeros of two associated real 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: Nevanlinna–Pick interpolation Triple: [Carathéodory–Fejér interpolation, relatedTo, Nevanlinna–Pick interpolation]
Generated description
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.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Nevanlinna–Pick interpolation Target entity description: 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.
-
A.
Carathéodory–Fejér interpolation
Carathéodory–Fejér interpolation is a classical result in complex analysis and approximation theory that concerns constructing analytic functions, typically with bounded or positive real part, that match prescribed initial Taylor coefficients.
-
B.
Runge approximation theorem
The Runge approximation theorem is a fundamental result in complex analysis stating that holomorphic functions on certain domains can be uniformly approximated by rational functions with poles outside those domains.
-
C.
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.
-
D.
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.
-
E.
Hermite–Biehler theorem
The Hermite–Biehler theorem is a result in complex analysis and control theory that characterizes when a complex polynomial has all its zeros in the open upper half-plane in terms of the interlacing of zeros of two associated real 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_69bd446978108190bb5f9c5c23d93f88 |
completed | March 20, 2026, 12:58 p.m. |
| NER | Named-entity recognition | batch_69bd7ba4ecd88190800b5e4eea3abed5 |
completed | March 20, 2026, 4:53 p.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69befe7a1f448190acfcdfe37c962028 |
completed | March 21, 2026, 8:24 p.m. |
| NEDg | Description generation | batch_69beff55faec8190a75a1b5f339a2c20 |
completed | March 21, 2026, 8:28 p.m. |
| NED2 | Entity disambiguation (via description) | batch_69bf001f0d9c8190a67909a06ea41898 |
completed | March 21, 2026, 8:31 p.m. |
Created at: March 20, 2026, 1:50 p.m.