Triple

T18480215
Position Surface form Disambiguated ID Type / Status
Subject Toeplitz matrix E451536 entity
Predicate hasAlgorithm P37563 FINISHED
Object Levinson recursion 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: Levinson recursion | Statement: [Toeplitz matrix, hasAlgorithm, Levinson recursion]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Levinson recursion
Context triple: [Toeplitz matrix, hasAlgorithm, Levinson recursion]
  • A. 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.
  • B. Berlekamp–Massey algorithm
    The Berlekamp–Massey algorithm is a key algorithm in coding theory and cryptography used to efficiently determine the shortest linear feedback shift register that generates a given binary sequence.
  • C. Kailath factorization in linear systems
    Kailath factorization in linear systems is a matrix factorization technique used in control and signal processing to efficiently analyze and solve linear dynamical systems.
  • D. 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.
  • E. Cooley–Tukey Fast Fourier Transform algorithm
    The Cooley–Tukey Fast Fourier Transform algorithm is a widely used, efficient method for computing the discrete Fourier transform that revolutionized digital signal processing and numerical analysis.
  • 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: Levinson recursion
Target entity description: Levinson recursion is a fast, recursive algorithm for solving linear systems with Toeplitz structure, widely used in signal processing and time-series analysis.
  • A. 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.
  • B. Berlekamp–Massey algorithm
    The Berlekamp–Massey algorithm is a key algorithm in coding theory and cryptography used to efficiently determine the shortest linear feedback shift register that generates a given binary sequence.
  • C. Kailath factorization in linear systems
    Kailath factorization in linear systems is a matrix factorization technique used in control and signal processing to efficiently analyze and solve linear dynamical systems.
  • D. 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.
  • E. Cooley–Tukey Fast Fourier Transform algorithm
    The Cooley–Tukey Fast Fourier Transform algorithm is a widely used, efficient method for computing the discrete Fourier transform that revolutionized digital signal processing and numerical analysis.
  • 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_69d8d38465a0819099b9b42d2a662ac1 completed April 10, 2026, 10:40 a.m.
NER Named-entity recognition batch_69e53066a7108190a50eda9b489c90ca completed April 19, 2026, 7:43 p.m.
Created at: April 10, 2026, 11:35 a.m.