Triple
T7833302
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Lyapunov vector |
E181626
|
entity |
| Predicate | belongsTo |
P35
|
FINISHED |
| Object |
Oseledec splitting
Oseledec splitting is a mathematical decomposition of a dynamical system’s tangent space into invariant subspaces associated with distinct Lyapunov exponents, characterizing the system’s asymptotic stability properties.
|
E695945
|
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: Oseledec splitting | Statement: [Lyapunov vector, belongsTo, Oseledec splitting]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Oseledec splitting Context triple: [Lyapunov vector, belongsTo, Oseledec splitting]
-
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.
Sylvester’s law of inertia
Sylvester’s law of inertia is a theorem in linear algebra stating that the numbers of positive, negative, and zero eigenvalues (the inertia) of a real symmetric matrix are invariant under change of basis.
-
C.
May–Wigner stability theorem
The May–Wigner stability theorem is a result in theoretical ecology and random matrix theory showing that large, complex systems with many random interactions are generically unstable beyond a critical level of complexity.
-
D.
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.
-
E.
Young tower construction in nonuniformly hyperbolic dynamics
"Young tower construction in nonuniformly hyperbolic dynamics" is a foundational work in dynamical systems that introduced a powerful tower-based method for analyzing statistical properties such as decay of correlations and limit theorems in nonuniformly hyperbolic systems.
- 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: Oseledec splitting Triple: [Lyapunov vector, belongsTo, Oseledec splitting]
Generated description
Oseledec splitting is a mathematical decomposition of a dynamical system’s tangent space into invariant subspaces associated with distinct Lyapunov exponents, characterizing the system’s asymptotic stability properties.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Oseledec splitting Target entity description: Oseledec splitting is a mathematical decomposition of a dynamical system’s tangent space into invariant subspaces associated with distinct Lyapunov exponents, characterizing the system’s asymptotic stability properties.
-
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.
Sylvester’s law of inertia
Sylvester’s law of inertia is a theorem in linear algebra stating that the numbers of positive, negative, and zero eigenvalues (the inertia) of a real symmetric matrix are invariant under change of basis.
-
C.
May–Wigner stability theorem
The May–Wigner stability theorem is a result in theoretical ecology and random matrix theory showing that large, complex systems with many random interactions are generically unstable beyond a critical level of complexity.
-
D.
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.
-
E.
Young tower construction in nonuniformly hyperbolic dynamics
"Young tower construction in nonuniformly hyperbolic dynamics" is a foundational work in dynamical systems that introduced a powerful tower-based method for analyzing statistical properties such as decay of correlations and limit theorems in nonuniformly hyperbolic systems.
- 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_69cb064a47648190af2ca2b336584a92 |
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.