Triple
T1675166
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Nyquist stability criterion |
E36214
|
entity |
| Predicate | relatedConcept |
P37
|
FINISHED |
| Object |
small-gain theorem
The small-gain theorem is a fundamental result in control theory that provides a sufficient condition for the stability of feedback interconnections by requiring the product of system gains to be less than one.
|
E189566
|
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: small-gain theorem | Statement: [Nyquist stability criterion, relatedConcept, small-gain theorem]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: small-gain theorem Context triple: [Nyquist stability criterion, relatedConcept, small-gain theorem]
-
A.
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.
-
B.
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.
-
C.
control theory
Control theory is a branch of engineering and mathematics that studies how to model, analyze, and design systems that regulate their own behavior using feedback.
-
D.
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.
-
E.
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.
- 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: small-gain theorem Triple: [Nyquist stability criterion, relatedConcept, small-gain theorem]
Generated description
The small-gain theorem is a fundamental result in control theory that provides a sufficient condition for the stability of feedback interconnections by requiring the product of system gains to be less than one.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: small-gain theorem Target entity description: The small-gain theorem is a fundamental result in control theory that provides a sufficient condition for the stability of feedback interconnections by requiring the product of system gains to be less than one.
-
A.
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.
-
B.
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.
-
C.
control theory
Control theory is a branch of engineering and mathematics that studies how to model, analyze, and design systems that regulate their own behavior using feedback.
-
D.
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.
-
E.
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.
- 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.