Triple
T23589656
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Cartan formula |
E582440
|
entity |
| Predicate | instanceOf |
P0
|
FINISHED |
| Object | formula in differential geometry |
C1718
|
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: formula in differential geometry Context triple: [Cartan formula, instanceOf, formula in differential geometry]
-
A.
differential geometric object
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.
-
B.
mathematical formula
chosen
A mathematical formula is a concise symbolic expression that defines a relationship between quantities using numbers, variables, and mathematical operators.
-
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.
curvature tensor
A curvature tensor is a multilinear mathematical object in differential geometry that measures how much a space (or manifold) deviates from being flat by quantifying the failure of vectors to return to their original direction after parallel transport around infinitesimal loops.
-
E.
tensor calculus
Tensor calculus is a branch of mathematics that generalizes vector calculus to tensors, providing coordinate-independent tools for analyzing multidimensional quantities and their transformations, especially in physics and differential geometry.
- 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_69e248f9e0a08190814772847003b1ff |
completed | April 17, 2026, 2:51 p.m. |
Created at: April 17, 2026, 6:41 p.m.