Triple
T36184710
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Arnold cat map |
E1046813
|
entity |
| Predicate | instanceOf |
P0
|
FINISHED |
| Object | ergodic transformation |
C3058
|
CONCEPT FINISHED |
How this triple was built (1 step)
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.
CD
Concept disambiguation
gpt-5-mini-2025-08-07
Target class: ergodic transformation Context triple: [Arnold cat map, instanceOf, ergodic transformation]
-
A.
equivalence relation in ergodic theory
An equivalence relation in ergodic theory is a measurable partition of a probability space into orbits of a measure-preserving transformation or group action, studied up to measure-theoretic properties such as ergodicity, hyperfiniteness, and orbit structure.
-
B.
theory of dynamical systems
The theory of dynamical systems studies how points in a mathematical space evolve over time under repeated application of rules or equations, revealing patterns such as stability, chaos, and long-term behavior.
-
C.
tool in dynamical systems theory
A tool in dynamical systems theory is a conceptual or computational method—such as phase portraits, Lyapunov functions, or Poincaré maps—used to analyze, visualize, and understand the qualitative and quantitative behavior of dynamical systems over time.
-
D.
mathematical transformation
chosen
A mathematical transformation is a function or operation that systematically maps elements from one set or space to another, often altering their position, scale, orientation, or form while following defined rules.
-
E.
asymmetric transformation
An asymmetric transformation is a process or operation that changes an object, system, or data in a way that is not identical or easily reversible in the opposite direction, often producing different outcomes depending on the direction of application.
- F. None of above.
Provenance (1 batch)
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_69f76e3d4fbc81908c159c7beeb4ce00 |
completed | May 3, 2026, 3:48 p.m. |
Created at: May 3, 2026, 4:08 p.m.