Triple

T7833157
Position Surface form Disambiguated ID Type / Status
Subject Lyapunov exponents E181623 entity
Predicate relatedTo P37 FINISHED
Object Kolmogorov–Sinai entropy
Kolmogorov–Sinai entropy is a fundamental invariant in dynamical systems theory that quantifies the average rate of information production or unpredictability of a measure-preserving transformation.
E695939 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: Kolmogorov–Sinai entropy | Statement: [Lyapunov exponents, relatedTo, Kolmogorov–Sinai entropy]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Kolmogorov–Sinai entropy
Context triple: [Lyapunov exponents, relatedTo, Kolmogorov–Sinai entropy]
  • A. Rényi entropy
    Rényi entropy is a generalized measure of information and uncertainty that extends Shannon entropy by introducing a tunable order parameter to emphasize different aspects of a probability distribution.
  • B. Lyapunov exponents
    Lyapunov exponents are quantitative measures in dynamical systems theory that characterize the rates at which nearby trajectories diverge or converge, indicating the presence and strength of chaos.
  • C. Shannon entropy
    Shannon entropy is a fundamental measure in information theory that quantifies the average uncertainty or information content in a random variable or message source.
  • D. Khinchin–Kolmogorov theorem
    The Khinchin–Kolmogorov theorem is a fundamental result in probability theory that provides conditions under which series of independent random variables converge almost surely.
  • E. Kakutani equivalence in ergodic theory
    Kakutani equivalence in ergodic theory is a notion of equivalence between measure-preserving dynamical systems based on the isomorphism of their induced transformations on subsets of positive measure.
  • 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: Kolmogorov–Sinai entropy
Triple: [Lyapunov exponents, relatedTo, Kolmogorov–Sinai entropy]
Generated description
Kolmogorov–Sinai entropy is a fundamental invariant in dynamical systems theory that quantifies the average rate of information production or unpredictability of a measure-preserving transformation.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Kolmogorov–Sinai entropy
Target entity description: Kolmogorov–Sinai entropy is a fundamental invariant in dynamical systems theory that quantifies the average rate of information production or unpredictability of a measure-preserving transformation.
  • A. Rényi entropy
    Rényi entropy is a generalized measure of information and uncertainty that extends Shannon entropy by introducing a tunable order parameter to emphasize different aspects of a probability distribution.
  • B. Lyapunov exponents
    Lyapunov exponents are quantitative measures in dynamical systems theory that characterize the rates at which nearby trajectories diverge or converge, indicating the presence and strength of chaos.
  • C. Shannon entropy
    Shannon entropy is a fundamental measure in information theory that quantifies the average uncertainty or information content in a random variable or message source.
  • D. Khinchin–Kolmogorov theorem
    The Khinchin–Kolmogorov theorem is a fundamental result in probability theory that provides conditions under which series of independent random variables converge almost surely.
  • E. Kakutani equivalence in ergodic theory
    Kakutani equivalence in ergodic theory is a notion of equivalence between measure-preserving dynamical systems based on the isomorphism of their induced transformations on subsets of positive measure.
  • 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.