Triple
T36184704
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Arnold cat map |
E1046813
|
entity |
| Predicate | instanceOf |
P0
|
FINISHED |
| Object | measure-preserving 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: measure-preserving transformation Context triple: [Arnold cat map, instanceOf, measure-preserving transformation]
-
A.
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.
-
B.
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.
-
C.
measure-theoretic construction
A measure-theoretic construction is a rigorous method of building mathematical objects—such as measures, integrals, or probability spaces—by specifying σ-algebras, set functions, and limiting processes that satisfy the axioms of measure theory.
-
D.
canonical measure
A canonical measure is a mathematically natural, uniquely determined measure associated with a given structure or space, chosen according to its intrinsic symmetries or defining properties.
-
E.
homeomorphism
A homeomorphism is a continuous bijective function between topological spaces whose inverse is also continuous, establishing a topological equivalence between them.
- 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.