Triple
T10661655
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Levi-Civita symbol |
E251240
|
entity |
| Predicate | instanceOf |
P0
|
FINISHED |
| Object | antisymmetric tensor |
C27995
|
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: antisymmetric tensor Context triple: [Levi-Civita symbol, instanceOf, antisymmetric tensor]
-
A.
symmetric tensor
A symmetric tensor is a multilinear map or multidimensional array whose components remain unchanged under any permutation of its indices.
-
B.
(0,2)-tensor
A (0,2)-tensor is a bilinear map that takes two vectors as input and returns a scalar, often representing objects like metrics or covariant tensor fields on a vector space or manifold.
-
C.
rank-2 tensor
A rank-2 tensor is a mathematical object that can be represented as a matrix whose components transform with two indices under a change of basis, generalizing linear maps and bilinear forms in vector spaces.
-
D.
alternating form
chosen
An alternating form is a multilinear map on a vector space that changes sign whenever two of its arguments are swapped, and hence vanishes whenever any two arguments are equal.
-
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_69d6aa5b0d2881909584b20efc5877f0 |
completed | April 8, 2026, 7:19 p.m. |
Created at: April 8, 2026, 9:08 p.m.