Triple
T7833159
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Lyapunov exponents |
E181623
|
entity |
| Predicate | relatedTo |
P37
|
FINISHED |
| Object |
Pesin theory
Pesin theory is a branch of dynamical systems that studies the statistical and geometric behavior of non-uniformly hyperbolic systems, particularly through the use of Lyapunov exponents and invariant manifolds.
|
E695941
|
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: Pesin theory | Statement: [Lyapunov exponents, relatedTo, Pesin theory]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Pesin theory Context triple: [Lyapunov exponents, relatedTo, Pesin theory]
-
A.
Milnor–Thurston kneading theory
Milnor–Thurston kneading theory is a mathematical framework in one-dimensional dynamical systems that encodes the combinatorial behavior of interval maps to study their dynamics and entropy.
-
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.
Page theorem
The Page theorem is a result in quantum information theory and black hole physics that predicts how the entanglement entropy of a subsystem typically evolves, underpinning the characteristic "Page curve" behavior in discussions of the black hole information paradox.
-
D.
Oblique Function theory
Oblique Function theory is an architectural concept developed by Claude Parent (often with Paul Virilio) that advocates sloping, inclined planes in buildings to disrupt traditional vertical-horizontal spatial organization and transform how people move and inhabit space.
-
E.
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.
- 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: Pesin theory Triple: [Lyapunov exponents, relatedTo, Pesin theory]
Generated description
Pesin theory is a branch of dynamical systems that studies the statistical and geometric behavior of non-uniformly hyperbolic systems, particularly through the use of Lyapunov exponents and invariant manifolds.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Pesin theory Target entity description: Pesin theory is a branch of dynamical systems that studies the statistical and geometric behavior of non-uniformly hyperbolic systems, particularly through the use of Lyapunov exponents and invariant manifolds.
-
A.
Milnor–Thurston kneading theory
Milnor–Thurston kneading theory is a mathematical framework in one-dimensional dynamical systems that encodes the combinatorial behavior of interval maps to study their dynamics and entropy.
-
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.
Page theorem
The Page theorem is a result in quantum information theory and black hole physics that predicts how the entanglement entropy of a subsystem typically evolves, underpinning the characteristic "Page curve" behavior in discussions of the black hole information paradox.
-
D.
Oblique Function theory
Oblique Function theory is an architectural concept developed by Claude Parent (often with Paul Virilio) that advocates sloping, inclined planes in buildings to disrupt traditional vertical-horizontal spatial organization and transform how people move and inhabit space.
-
E.
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.
- 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.