Triple
T7833245
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Lyapunov equation |
E181625
|
entity |
| Predicate | hasType |
P0
|
FINISHED |
| Object | continuous-time Lyapunov equation |
E181625
|
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: continuous-time Lyapunov equation | Statement: [Lyapunov equation, hasType, continuous-time Lyapunov equation]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: continuous-time Lyapunov equation Context triple: [Lyapunov equation, hasType, continuous-time Lyapunov equation]
-
A.
Lyapunov equation
chosen
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.
-
B.
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.
-
C.
Lyapunov stability theory
Lyapunov stability theory is a fundamental framework in dynamical systems and control theory that uses energy-like functions to assess the stability of equilibrium points without explicitly solving differential equations.
-
D.
Lyapunov vector
A Lyapunov vector is a mathematical construct in dynamical systems theory that characterizes the directions in phase space associated with exponential growth or decay rates quantified by Lyapunov exponents.
-
E.
Stability of Linear Systems
"Stability of Linear Systems" is a foundational book by Eliahu I. Jury that systematically develops the theory and criteria for determining the stability of linear dynamical and control systems.
- 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_69ca8284a25c8190a1a20afad30da792 |
completed | March 30, 2026, 2:02 p.m. |
| NER | Named-entity recognition | batch_69cb064a47648190af2ca2b336584a92 |
completed | March 30, 2026, 11:24 p.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69cbdef32d4c8190a2e5c76d2db6c45f |
completed | March 31, 2026, 2:49 p.m. |
Created at: March 30, 2026, 4:45 p.m.