Triple

T5256424
Position Surface form Disambiguated ID Type / Status
Subject Carathéodory–Fejér interpolation E118709 entity
Predicate relatedTo P37 FINISHED
Object Schur algorithm
The Schur algorithm is a recursive procedure in complex analysis and operator theory used to construct and analyze Schur functions, playing a key role in interpolation problems and system theory.
E506855 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: Schur algorithm | Statement: [Carathéodory–Fejér interpolation, relatedTo, Schur algorithm]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Schur algorithm
Context triple: [Carathéodory–Fejér interpolation, relatedTo, Schur algorithm]
  • 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. 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.
  • C. 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.
  • D. 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.
  • E. Bernstein polynomials
    Bernstein polynomials are a family of polynomials used in approximation theory that provide a constructive proof of the Weierstrass approximation theorem by uniformly approximating continuous functions on a closed interval.
  • 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: Schur algorithm
Triple: [Carathéodory–Fejér interpolation, relatedTo, Schur algorithm]
Generated description
The Schur algorithm is a recursive procedure in complex analysis and operator theory used to construct and analyze Schur functions, playing a key role in interpolation problems and system theory.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Schur algorithm
Target entity description: The Schur algorithm is a recursive procedure in complex analysis and operator theory used to construct and analyze Schur functions, playing a key role in interpolation problems and system theory.
  • 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. 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.
  • C. 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.
  • D. 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.
  • E. Bernstein polynomials
    Bernstein polynomials are a family of polynomials used in approximation theory that provide a constructive proof of the Weierstrass approximation theorem by uniformly approximating continuous functions on a closed interval.
  • 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.