Triple

T7833303
Position Surface form Disambiguated ID Type / Status
Subject Lyapunov vector E181626 entity
Predicate definedBy P773 FINISHED
Object Oseledec multiplicative ergodic theorem E181623 NE FINISHED

How this triple was built (2 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 multiplicative ergodic theorem | Statement: [Lyapunov vector, definedBy, Oseledec multiplicative ergodic theorem]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Oseledec multiplicative ergodic theorem
Context triple: [Lyapunov vector, definedBy, Oseledec multiplicative ergodic theorem]
  • 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. 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.
  • C. 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.
  • D. Lyapunov exponents chosen
    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.
  • 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.
  • G. Unsure - the case is ambiguous/there is not enough information to decide.

Provenance (3 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.
Created at: March 30, 2026, 4:45 p.m.