Triple

T1597813
Position Surface form Disambiguated ID Type / Status
Subject Aleksandr Lyapunov E34323 entity
Predicate notableWork P4 FINISHED
Object 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.
E181626 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 vector | Statement: [Aleksandr Lyapunov, notableWork, Lyapunov vector]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Lyapunov vector
Context triple: [Aleksandr Lyapunov, notableWork, Lyapunov vector]
  • 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. Lie derivative
    The Lie derivative is a fundamental differential operator in differential geometry that measures how a tensor field changes along the flow generated by a vector field.
  • C. Laplace operator
    The Laplace operator is a second-order differential operator widely used in mathematics and physics to describe phenomena such as diffusion, heat flow, and wave propagation.
  • D. Ornstein–Uhlenbeck process
    The Ornstein–Uhlenbeck process is a continuous-time stochastic process that models mean-reverting random motion, widely used in physics and quantitative finance to describe systems fluctuating around a long-term equilibrium.
  • E. Poynting vector
    The Poynting vector is a fundamental quantity in electromagnetism that represents the directional energy flux (power per unit area) carried by an electromagnetic field.
  • 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 vector
Triple: [Aleksandr Lyapunov, notableWork, Lyapunov vector]
Generated description
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.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Lyapunov vector
Target entity description: 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.
  • 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. Lie derivative
    The Lie derivative is a fundamental differential operator in differential geometry that measures how a tensor field changes along the flow generated by a vector field.
  • C. Laplace operator
    The Laplace operator is a second-order differential operator widely used in mathematics and physics to describe phenomena such as diffusion, heat flow, and wave propagation.
  • D. Ornstein–Uhlenbeck process
    The Ornstein–Uhlenbeck process is a continuous-time stochastic process that models mean-reverting random motion, widely used in physics and quantitative finance to describe systems fluctuating around a long-term equilibrium.
  • E. Poynting vector
    The Poynting vector is a fundamental quantity in electromagnetism that represents the directional energy flux (power per unit area) carried by an electromagnetic field.
  • 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.