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.