Triple
T7833335
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Lyapunov inequality |
E181627
|
entity |
| Predicate | usedIn |
P98
|
FINISHED |
| Object | Lyapunov stability theory |
E181622
|
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: Lyapunov stability theory | Statement: [Lyapunov inequality, usedIn, Lyapunov stability theory]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Lyapunov stability theory Context triple: [Lyapunov inequality, usedIn, Lyapunov stability theory]
-
A.
Lyapunov stability theory
chosen
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.
-
B.
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.
-
C.
Inners and Stability of Dynamic Systems
"Inners and Stability of Dynamic Systems" is a seminal work in control theory by Eliahu I. Jury that analyzes the role of inner functions in determining the stability properties of dynamic systems.
-
D.
LaSalle’s invariance principle
LaSalle’s invariance principle is a fundamental result in dynamical systems theory that extends Lyapunov’s direct method by characterizing the asymptotic behavior of trajectories through invariant sets where a Lyapunov function’s derivative vanishes.
-
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 (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_69cc639916b48190b0dd4adbd323703a |
completed | April 1, 2026, 12:15 a.m. |
Created at: March 30, 2026, 4:45 p.m.