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.