Triple

T7833119
Position Surface form Disambiguated ID Type / Status
Subject Lyapunov stability theory E181622 entity
Predicate relatedTo P37 FINISHED
Object 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.
E695937 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: LaSalle’s invariance principle | Statement: [Lyapunov stability theory, relatedTo, LaSalle’s invariance principle]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: LaSalle’s invariance principle
Context triple: [Lyapunov stability theory, relatedTo, LaSalle’s invariance principle]
  • 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. 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.
  • C. 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.
  • D. Hamilton’s maximum principle
    Hamilton’s maximum principle is a fundamental analytical tool in geometric analysis that extends the classical maximum principle to tensor-valued quantities, playing a key role in studying the behavior of solutions to the Ricci flow and related geometric evolution equations.
  • E. Freidlin–Wentzell theory
    Freidlin–Wentzell theory is a mathematical framework in probability that analyzes the behavior of stochastic dynamical systems under small random perturbations using large deviation principles.
  • 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: LaSalle’s invariance principle
Triple: [Lyapunov stability theory, relatedTo, LaSalle’s invariance principle]
Generated description
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.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: LaSalle’s invariance principle
Target entity description: 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.
  • 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. 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.
  • C. 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.
  • D. Hamilton’s maximum principle
    Hamilton’s maximum principle is a fundamental analytical tool in geometric analysis that extends the classical maximum principle to tensor-valued quantities, playing a key role in studying the behavior of solutions to the Ricci flow and related geometric evolution equations.
  • E. Freidlin–Wentzell theory
    Freidlin–Wentzell theory is a mathematical framework in probability that analyzes the behavior of stochastic dynamical systems under small random perturbations using large deviation principles.
  • 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_69ca8284a25c8190a1a20afad30da792 completed March 30, 2026, 2:02 p.m.
NER Named-entity recognition batch_69cb0648bb308190a34fbcd81ff6fda2 completed March 30, 2026, 11:24 p.m.
NED1 Entity disambiguation (via context triple) batch_69cb5a9b7bb081909d6aa066ee064093 completed March 31, 2026, 5:24 a.m.
NEDg Description generation batch_69cb5ded0284819086c40a379b52a5bd completed March 31, 2026, 5:38 a.m.
NED2 Entity disambiguation (via description) batch_69cb765db28881909ac34071ec6889b3 completed March 31, 2026, 7:23 a.m.
Created at: March 30, 2026, 4:45 p.m.