Triple
T3325855
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | control theory |
E69912
|
entity |
| Predicate | usesConcept |
P531
|
FINISHED |
| Object | Lyapunov stability |
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 | Statement: [control theory, usesConcept, Lyapunov stability]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Lyapunov stability Context triple: [control theory, usesConcept, Lyapunov stability]
-
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.
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.
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.
-
D.
Ulam stability
Ulam stability is a concept in the theory of functional equations that studies when approximate solutions imply the existence of exact solutions nearby, forming the basis of what is now called Hyers–Ulam stability.
-
E.
Lyapunov exponents
Lyapunov exponents are quantitative measures in dynamical systems theory that characterize the rates at which nearby trajectories diverge or converge, indicating the presence and strength of chaos.
- 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_69ad85a1829881908942c14075644d0d |
completed | March 8, 2026, 2:20 p.m. |
| NER | Named-entity recognition | batch_69adb16ca13c8190aea8caed8ccd9b88 |
completed | March 8, 2026, 5:27 p.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69b31a7b26248190b9bf159982d7d19e |
completed | March 12, 2026, 7:56 p.m. |
Created at: March 8, 2026, 3:12 p.m.