Triple

T1597809
Position Surface form Disambiguated ID Type / Status
Subject Aleksandr Lyapunov E34323 entity
Predicate notableWork P4 FINISHED
Object 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.
E181623 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 exponents | Statement: [Aleksandr Lyapunov, notableWork, Lyapunov exponents]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Lyapunov exponents
Context triple: [Aleksandr Lyapunov, notableWork, Lyapunov exponents]
  • A. Onsager–Machlup function
    The Onsager–Machlup function is a functional in stochastic process theory that characterizes the most probable paths of fluctuating systems, playing a key role in nonequilibrium statistical mechanics and large deviation theory.
  • B. 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.
  • C. Poincaré map
    The Poincaré map is a mathematical tool in dynamical systems theory that reduces continuous-time dynamics to a discrete map by tracking intersections of trajectories with a lower-dimensional surface.
  • D. Poincaré recurrence theorem
    The Poincaré recurrence theorem is a fundamental result in dynamical systems and ergodic theory stating that certain systems will, after a sufficiently long but finite time, return arbitrarily close to their initial state.
  • E. 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.
  • 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 exponents
Triple: [Aleksandr Lyapunov, notableWork, Lyapunov exponents]
Generated description
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.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Lyapunov exponents
Target entity description: 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.
  • A. Onsager–Machlup function
    The Onsager–Machlup function is a functional in stochastic process theory that characterizes the most probable paths of fluctuating systems, playing a key role in nonequilibrium statistical mechanics and large deviation theory.
  • B. 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.
  • C. Poincaré map
    The Poincaré map is a mathematical tool in dynamical systems theory that reduces continuous-time dynamics to a discrete map by tracking intersections of trajectories with a lower-dimensional surface.
  • D. Poincaré recurrence theorem
    The Poincaré recurrence theorem is a fundamental result in dynamical systems and ergodic theory stating that certain systems will, after a sufficiently long but finite time, return arbitrarily close to their initial state.
  • E. 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.
  • 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_69a885fdcb9c819081ce6f0b8cd477dd completed March 4, 2026, 7:20 p.m.
NER Named-entity recognition batch_69a9092f5f148190b987bc943e89e29c completed March 5, 2026, 4:40 a.m.
NED1 Entity disambiguation (via context triple) batch_69ad46a848ec819085c82be8eaea2044 completed March 8, 2026, 9:51 a.m.
NEDg Description generation batch_69ad4841d278819085507528faeaae3e completed March 8, 2026, 9:58 a.m.
NED2 Entity disambiguation (via description) batch_69ad48ff11d881909fd6e9e40d5f1f38 completed March 8, 2026, 10:01 a.m.
Created at: March 4, 2026, 7:27 p.m.