Triple
T36468720
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Möbius transformation |
E898486
|
entity |
| Predicate | instanceOf |
P0
|
FINISHED |
| Object | bijection of the Riemann sphere |
C29369
|
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: bijection of the Riemann sphere Context triple: [Möbius transformation, instanceOf, bijection of the Riemann sphere]
-
A.
extended complex plane
The extended complex plane is the complex number system augmented with a single point at infinity, forming a compact space often visualized as the Riemann sphere.
-
B.
bounded symmetric domain (up to biholomorphism)
A bounded symmetric domain (up to biholomorphism) is a connected bounded open subset of complex Euclidean space whose biholomorphic automorphism group acts transitively and admits, at each point, an involutive automorphism reversing all geodesics through that point, considered up to biholomorphic equivalence.
-
C.
homeomorphism
chosen
A homeomorphism is a continuous bijective function between topological spaces whose inverse is also continuous, establishing a topological equivalence between them.
-
D.
conformal model of the hyperbolic plane
A conformal model of the hyperbolic plane is a geometric representation (such as the Poincaré disk or upper half-plane) in which hyperbolic lines and distances are depicted so that angles are preserved while the metric differs from the Euclidean one.
-
E.
self-homeomorphism of a surface
A self-homeomorphism of a surface is a continuous bijection from the surface to itself with a continuous inverse, preserving its topological structure.
- 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_69f76e58ebd88190b75d9b169b59d793 |
completed | May 3, 2026, 3:48 p.m. |
Created at: May 3, 2026, 4:10 p.m.