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.