Triple
T7449404
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Kakutani equivalence in ergodic theory |
E171967
|
entity |
| Predicate | relatedTo |
P37
|
FINISHED |
| Object |
Kakutani–Rokhlin towers
Kakutani–Rokhlin towers are combinatorial structures in ergodic theory that decompose a measure-preserving transformation into stacked levels (or “towers”) to analyze its dynamical and measure-theoretic properties.
|
E665942
|
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: Kakutani–Rokhlin towers | Statement: [Kakutani equivalence in ergodic theory, relatedTo, Kakutani–Rokhlin towers]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Kakutani–Rokhlin towers Context triple: [Kakutani equivalence in ergodic theory, relatedTo, Kakutani–Rokhlin towers]
-
A.
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.
-
B.
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.
-
C.
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.
-
D.
Kakutani’s random ergodic theorem
Kakutani’s random ergodic theorem is a fundamental result in ergodic theory that extends classical ergodic theorems to sequences of randomly chosen measure-preserving transformations.
-
E.
Lectures on Ergodic Theory
"Lectures on Ergodic Theory" is a classic mathematical monograph that systematically develops the foundations and key results of ergodic theory within dynamical 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: Kakutani–Rokhlin towers Triple: [Kakutani equivalence in ergodic theory, relatedTo, Kakutani–Rokhlin towers]
Generated description
Kakutani–Rokhlin towers are combinatorial structures in ergodic theory that decompose a measure-preserving transformation into stacked levels (or “towers”) to analyze its dynamical and measure-theoretic properties.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Kakutani–Rokhlin towers Target entity description: Kakutani–Rokhlin towers are combinatorial structures in ergodic theory that decompose a measure-preserving transformation into stacked levels (or “towers”) to analyze its dynamical and measure-theoretic properties.
-
A.
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.
-
B.
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.
-
C.
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.
-
D.
Kakutani’s random ergodic theorem
Kakutani’s random ergodic theorem is a fundamental result in ergodic theory that extends classical ergodic theorems to sequences of randomly chosen measure-preserving transformations.
-
E.
Lectures on Ergodic Theory
"Lectures on Ergodic Theory" is a classic mathematical monograph that systematically develops the foundations and key results of ergodic theory within dynamical 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_69c68a65402881908f7869368eb746fb |
completed | March 27, 2026, 1:47 p.m. |
| NER | Named-entity recognition | batch_69c6f389ddd48190a4b8753c67220c4f |
completed | March 27, 2026, 9:15 p.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69c827b0e9848190b28ff10b12b10a33 |
completed | March 28, 2026, 7:10 p.m. |
| NEDg | Description generation | batch_69c8299bb8c08190a5a78b0c1a8cc0fb |
completed | March 28, 2026, 7:18 p.m. |
| NED2 | Entity disambiguation (via description) | batch_69c82ad4384481909616bdfd02624a48 |
completed | March 28, 2026, 7:24 p.m. |
Created at: March 27, 2026, 3:14 p.m.