Triple
T36468731
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Möbius transformation |
E898486
|
entity |
| Predicate | isBiholomorphism |
P160143
|
FINISHED |
| Object | of the Riemann sphere |
—
|
LITERAL 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: of the Riemann sphere | Statement: [Möbius transformation, isBiholomorphism, of the Riemann sphere]
PD
Predicate disambiguation
gpt-5-mini-2025-08-07
Target predicate: isBiholomorphism Context triple: [Möbius transformation, isBiholomorphism, of the Riemann sphere]
-
A.
isBiholomorphismOf
chosen
Indicates that one complex-analytic map is a biholomorphic equivalence between two complex manifolds, i.e., a holomorphic bijection whose inverse is also holomorphic.
-
B.
isHolomorphicOn
Indicates that a complex-valued function is complex differentiable at every point of a specified domain, i.e., holomorphic throughout that region.
-
C.
isHolomorphicallyContractible
Indicates that a space can be continuously shrunk to a point through holomorphic maps, preserving complex-analytic structure throughout the contraction.
-
D.
isDiffeomorphicTo
Indicates that there exists a smooth, bijective map between two spaces whose inverse is also smooth, so the spaces are equivalent in the sense of differential topology.
-
E.
isBijective
Indicates that a function establishes a one-to-one and onto correspondence between elements of its domain and codomain, with each element in both sets paired uniquely.
- F. None of above.
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_69f76e58ebd88190b75d9b169b59d793 |
completed | May 3, 2026, 3:48 p.m. |
| NER | Named-entity recognition | batch_69f7be9d07ac8190adf796cbef60daf6 |
completed | May 3, 2026, 9:31 p.m. |
| PD | Predicate disambiguation | batch_69f7bccf05bc8190b61fdb2b2a315811 |
completed | May 3, 2026, 9:23 p.m. |
Created at: May 3, 2026, 4:10 p.m.