Triple

T7833156
Position Surface form Disambiguated ID Type / Status
Subject Lyapunov exponents E181623 entity
Predicate relatedTo P37 FINISHED
Object Lyapunov dimension
The Lyapunov dimension is a fractal dimension used in dynamical systems theory to quantify the effective number of degrees of freedom of a chaotic attractor based on its Lyapunov exponents.
 E695938 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 dimension | Statement: [Lyapunov exponents, relatedTo, Lyapunov dimension]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Lyapunov dimension
Context triple: [Lyapunov exponents, relatedTo, Lyapunov dimension]
  • A. 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.
  • B. Hausdorff dimension
    The Hausdorff dimension is a mathematical concept in fractal geometry and measure theory that generalizes the notion of dimension to capture the scaling complexity of irregular sets.
  • C. 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.
  • D. Lyapunov fractal
    The Lyapunov fractal is a complex, self-similar pattern arising from iterating logistic maps with periodically varying parameters, used to visualize stability and chaos in dynamical systems.
  • E. Lyapunov time
    Lyapunov time is a measure in dynamical systems theory that quantifies how long it takes for small differences in initial conditions to grow exponentially and significantly affect a system’s future behavior, indicating the timescale of predictability.
  • 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 dimension
Triple: [Lyapunov exponents, relatedTo, Lyapunov dimension]
Generated description
The Lyapunov dimension is a fractal dimension used in dynamical systems theory to quantify the effective number of degrees of freedom of a chaotic attractor based on its Lyapunov exponents.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07 
Target entity: Lyapunov dimension
Target entity description: The Lyapunov dimension is a fractal dimension used in dynamical systems theory to quantify the effective number of degrees of freedom of a chaotic attractor based on its Lyapunov exponents.
  • A. 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.
  • B. Hausdorff dimension
    The Hausdorff dimension is a mathematical concept in fractal geometry and measure theory that generalizes the notion of dimension to capture the scaling complexity of irregular sets.
  • C. 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.
  • D. Lyapunov fractal
    The Lyapunov fractal is a complex, self-similar pattern arising from iterating logistic maps with periodically varying parameters, used to visualize stability and chaos in dynamical systems.
  • E. Lyapunov time
    Lyapunov time is a measure in dynamical systems theory that quantifies how long it takes for small differences in initial conditions to grow exponentially and significantly affect a system’s future behavior, indicating the timescale of predictability.
  • 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.