Triple
T26971237
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Hopf–Rinow theorem |
E679322
|
entity |
| Predicate | instanceOf |
P0
|
FINISHED |
| Object | theorem in Riemannian geometry |
C716
|
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: theorem in Riemannian geometry Context triple: [Hopf–Rinow theorem, instanceOf, theorem in Riemannian geometry]
-
A.
problem in differential geometry
A problem in differential geometry involves analyzing and solving questions about the properties of curves, surfaces, and higher-dimensional manifolds using tools from calculus, linear algebra, and topology.
-
B.
mathematical theorem
chosen
A mathematical theorem is a rigorously proven statement derived from axioms and previously established results, expressing a fundamental truth within a formal mathematical system.
-
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.
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.
-
E.
theory in symplectic geometry
A theory in symplectic geometry is a coherent framework of definitions, structures, and results that studies manifolds equipped with a closed, nondegenerate 2-form and the geometric, dynamical, and topological phenomena arising from this 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_69eeeb507a7081909d516e1fa08b7d29 |
completed | April 27, 2026, 4:51 a.m. |
Created at: April 27, 2026, 6:39 a.m.