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.