Triple
T1675143
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Nyquist stability criterion |
E36214
|
entity |
| Predicate | comparedWith |
P278
|
FINISHED |
| Object |
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.
|
E189565
|
NE FINISHED |
How this triple was built (4 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: Routh–Hurwitz stability criterion | Statement: [Nyquist stability criterion, comparedWith, Routh–Hurwitz stability criterion]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Routh–Hurwitz stability criterion Context triple: [Nyquist stability criterion, comparedWith, Routh–Hurwitz stability criterion]
-
A.
Nyquist stability criterion
The Nyquist stability criterion is a graphical frequency-domain method in control theory used to determine the stability of feedback systems by analyzing how their open-loop transfer function encircles a critical point in the complex plane.
-
B.
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.
-
C.
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.
-
D.
Poincaré–Bendixson theorem
The Poincaré–Bendixson theorem is a fundamental result in the qualitative theory of dynamical systems that characterizes the possible long-term behaviors of trajectories in two-dimensional continuous flows, ruling out chaotic dynamics in the plane.
-
E.
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.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NEDg
Description generation
gpt-5.1
Instruction
Generate a one-sentence description of the target entity. You are given a context triple in the form (subject, predicate, object), where the object is the target entity. # Instructions Use the triple to infer relevant information about the entity. Describe the entity based on what is most defining, well-known. Avoid repeating the information from the triple, unless really essential. # Response Format Return only the sentence: "Description: [one-sentence description of the target entity]"
Input
Entity: Routh–Hurwitz stability criterion Triple: [Nyquist stability criterion, comparedWith, Routh–Hurwitz stability criterion]
Generated description
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.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Routh–Hurwitz stability criterion Target entity description: 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.
-
A.
Nyquist stability criterion
The Nyquist stability criterion is a graphical frequency-domain method in control theory used to determine the stability of feedback systems by analyzing how their open-loop transfer function encircles a critical point in the complex plane.
-
B.
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.
-
C.
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.
-
D.
Poincaré–Bendixson theorem
The Poincaré–Bendixson theorem is a fundamental result in the qualitative theory of dynamical systems that characterizes the possible long-term behaviors of trajectories in two-dimensional continuous flows, ruling out chaotic dynamics in the plane.
-
E.
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.
- F. None of above. chosen
Provenance (5 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_69a886139ed081909af0940aa9313512 |
completed | March 4, 2026, 7:20 p.m. |
| NER | Named-entity recognition | batch_69aa6247ec408190bc25d694b3238fa4 |
completed | March 6, 2026, 5:12 a.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69ad71b5729c8190b410893d62bedb13 |
completed | March 8, 2026, 12:55 p.m. |
| NEDg | Description generation | batch_69ad728cb27c8190802b30afc5e259e2 |
completed | March 8, 2026, 12:58 p.m. |
| NED2 | Entity disambiguation (via description) | batch_69ad72fa21208190b596bfdfc69043bd |
completed | March 8, 2026, 1 p.m. |
Created at: March 4, 2026, 7:29 p.m.