Triple
T22964582
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Sylvester matrix |
E571002
|
entity |
| Predicate | relatedTo |
P37
|
FINISHED |
| Object | Sylvester equation |
—
|
NE NERFINISHED |
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: Sylvester equation | Statement: [Sylvester matrix, relatedTo, Sylvester equation]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Sylvester equation Context triple: [Sylvester matrix, relatedTo, Sylvester equation]
-
A.
Sylvester equation
chosen
The Sylvester equation is a matrix equation of the form AX + XB = C that plays a central role in linear algebra, control theory, and numerical analysis for solving systems involving linear transformations.
-
B.
Lyapunov equation
The Lyapunov equation is a fundamental matrix equation in control theory and dynamical systems used to analyze the stability of equilibrium points and design stable controllers.
-
C.
Riccati equation
A Riccati equation is a type of nonlinear differential or difference equation, often quadratic in the unknown function, that plays a central role in control theory, filtering, and various areas of applied mathematics.
-
D.
Bartels–Stewart algorithm
The Bartels–Stewart algorithm is a numerical linear algebra method that efficiently solves certain matrix equations, particularly Sylvester and Lyapunov equations, using Schur decompositions.
-
E.
Routh–Hurwitz stability criterion
The Routh–Hurwitz stability criterion is a mathematical test in control theory that determines whether all roots of a system’s characteristic polynomial lie in the left half of the complex plane, ensuring system stability without explicitly computing the roots.
- F. None of above.
- G. Unsure - the case is ambiguous/there is not enough information to decide.
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_69e245b212a88190b5259caf51606084 |
completed | April 17, 2026, 2:37 p.m. |
| NER | Named-entity recognition | batch_69f181f763688190aab8f444a1a71577 |
completed | April 29, 2026, 3:58 a.m. |
Created at: April 17, 2026, 3:47 p.m.