Triple

T7705186
Position Surface form Disambiguated ID Type / Status
Subject Lindeberg–Feller central limit theorem E174594 entity
Predicate relatedTo P37 FINISHED
Object Lyapunov condition
The Lyapunov condition is a sufficient moment condition on sums of independent random variables that guarantees convergence in distribution to a normal law in central limit theorems.
E683054 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: Lyapunov condition | Statement: [Lindeberg–Feller central limit theorem, relatedTo, Lyapunov condition]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Lyapunov condition
Context triple: [Lindeberg–Feller central limit theorem, relatedTo, Lyapunov condition]
  • A. Lyapunov vector
    A Lyapunov vector is a mathematical construct in dynamical systems theory that characterizes the directions in phase space associated with exponential growth or decay rates quantified by Lyapunov exponents.
  • B. Lyapunov inequality
    The Lyapunov inequality is a fundamental result in stability theory and analysis that provides bounds relating norms or moments of functions or solutions to differential equations, widely used in studying the stability of dynamical systems.
  • C. 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.
  • D. 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.
  • E. Lipschitz continuity condition
    The Lipschitz continuity condition is a mathematical regularity criterion that bounds how fast a function can change, ensuring controlled variation and playing a key role in analysis and differential equations.
  • 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: Lyapunov condition
Triple: [Lindeberg–Feller central limit theorem, relatedTo, Lyapunov condition]
Generated description
The Lyapunov condition is a sufficient moment condition on sums of independent random variables that guarantees convergence in distribution to a normal law in central limit theorems.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Lyapunov condition
Target entity description: The Lyapunov condition is a sufficient moment condition on sums of independent random variables that guarantees convergence in distribution to a normal law in central limit theorems.
  • A. Lyapunov vector
    A Lyapunov vector is a mathematical construct in dynamical systems theory that characterizes the directions in phase space associated with exponential growth or decay rates quantified by Lyapunov exponents.
  • B. Lyapunov inequality
    The Lyapunov inequality is a fundamental result in stability theory and analysis that provides bounds relating norms or moments of functions or solutions to differential equations, widely used in studying the stability of dynamical systems.
  • C. 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.
  • D. 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.
  • E. Lipschitz continuity condition
    The Lipschitz continuity condition is a mathematical regularity criterion that bounds how fast a function can change, ensuring controlled variation and playing a key role in analysis and differential equations.
  • 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_69c6995b3e8c8190833108f883d5f53c completed March 27, 2026, 2:51 p.m.
NER Named-entity recognition batch_69c7028f17f0819081686ac146750d3a completed March 27, 2026, 10:19 p.m.
NED1 Entity disambiguation (via context triple) batch_69c8acc088148190ba5ba07e4ad2284c completed March 29, 2026, 4:38 a.m.
NEDg Description generation batch_69c8ae313d4c8190964be233c0651f3a completed March 29, 2026, 4:44 a.m.
NED2 Entity disambiguation (via description) batch_69c8aea55c0081909aa0f6c96c8d6a03 completed March 29, 2026, 4:46 a.m.
Created at: March 27, 2026, 4:03 p.m.