Triple
T34585687
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Nil geometry |
E888037
|
entity |
| Predicate | instanceOf |
P0
|
FINISHED |
| Object | left-invariant Riemannian geometry |
C3506
|
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: left-invariant Riemannian geometry Context triple: [Nil geometry, instanceOf, left-invariant Riemannian geometry]
-
A.
pseudo-Riemannian manifold
A pseudo-Riemannian manifold is a smooth manifold equipped with a nondegenerate, symmetric metric tensor of arbitrary signature that allows measurement of lengths and angles, including those with indefinite sign as in spacetime geometry.
-
B.
geometric invariant
A geometric invariant is a property of a geometric object that remains unchanged under a specified group of transformations, such as rotations, translations, or more general symmetries.
-
C.
branch of differential geometry
A branch of differential geometry is a specialized area of study within differential geometry that focuses on analyzing smooth manifolds and related geometric structures using differential and integral calculus techniques.
-
D.
infinite-dimensional Lie group
An infinite-dimensional Lie group is a group that is also a smooth manifold modeled on an infinite-dimensional topological vector space, such that the group operations (multiplication and inversion) are smooth maps.
-
E.
differential geometric object
chosen
A differential geometric object is a mathematical entity, such as a manifold, tensor, or connection, defined on smooth spaces and characterized by properties that are invariant under smooth coordinate transformations.
- 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_69f349d25cbc8190869998de5915886b |
completed | April 30, 2026, 12:23 p.m. |
Created at: May 1, 2026, 2:03 a.m.