Triple
T5256420
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Carathéodory–Fejér interpolation |
E118709
|
entity |
| Predicate | uses |
P98
|
FINISHED |
| Object | Toeplitz matrices |
E451536
|
NE FINISHED |
How this triple was built (2 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: Toeplitz matrices | Statement: [Carathéodory–Fejér interpolation, uses, Toeplitz matrices]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Toeplitz matrices Context triple: [Carathéodory–Fejér interpolation, uses, Toeplitz matrices]
-
A.
Toeplitz matrices
chosen
Toeplitz matrices are structured matrices whose entries are constant along each diagonal, playing a central role in operator theory, numerical analysis, and signal processing.
-
B.
Hadamard matrices
Hadamard matrices are square matrices with entries ±1 whose rows are mutually orthogonal, playing a key role in combinatorics, coding theory, and signal processing.
-
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.
Cauchy matrix
A Cauchy matrix is a structured matrix whose entries are defined by the reciprocals of pairwise differences of two sequences, widely used in numerical analysis, interpolation, and algebra.
- F. None of above.
- G. Unsure - the case is ambiguous/there is not enough information to decide.
Provenance (3 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. |
Created at: March 20, 2026, 1:50 p.m.