Triple
T36184707
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Arnold cat map |
E1046813
|
entity |
| Predicate | instanceOf |
P0
|
FINISHED |
| Object | toral automorphism |
C29371
|
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: toral automorphism Context triple: [Arnold cat map, instanceOf, toral automorphism]
-
A.
self-homeomorphism of a surface
chosen
A self-homeomorphism of a surface is a continuous bijection from the surface to itself with a continuous inverse, preserving its topological structure.
-
B.
Kleinian group
A Kleinian group is a discrete subgroup of the group of Möbius transformations acting on the Riemann sphere (or equivalently on hyperbolic 3-space), often studied via its geometric and dynamical properties.
-
C.
topological algebra
A topological algebra is an algebra over a field that is also a topological vector space, where the algebraic operations (addition, scalar multiplication, and multiplication) are continuous with respect to the topology.
-
D.
aperiodic tiling
An aperiodic tiling is a way of covering the plane with shapes that fit together without gaps or overlaps but never repeat in a regular, periodic pattern.
-
E.
topological group
A topological group is a group equipped with a topology such that the group operation and inversion are continuous maps with respect to that topology.
- 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.