Triple
T23589699
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Cartan magic formula |
E582441
|
entity |
| Predicate | instanceOf |
P0
|
FINISHED |
| Object | identity in differential 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: identity in differential geometry Context triple: [Cartan magic formula, instanceOf, identity in differential geometry]
-
A.
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.
-
B.
symmetry identity
Symmetry identity is the conceptual class describing how an entity’s sense of self is defined, preserved, or transformed through balanced, mirrored, or invariant relationships across changes in form, perspective, or context.
-
C.
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.
-
D.
example in differential topology
An example in differential topology is a specific smooth manifold or smooth map, often constructed to illustrate or test particular concepts such as smooth structures, embeddings, immersions, or invariants.
-
E.
gauge theory identity
A gauge theory identity is a mathematical relation that expresses how physical quantities or fields remain invariant or transform consistently under local gauge symmetry transformations in a gauge theory.
- 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.