Triple
T26971137
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Hopf invariant |
E679320
|
entity |
| Predicate | instanceOf |
P0
|
FINISHED |
| Object | integer-valued invariant |
C52317
|
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: integer-valued invariant Context triple: [Hopf invariant, instanceOf, integer-valued invariant]
-
A.
quantum invariant
A quantum invariant is a quantity associated with a quantum system or topological object that remains unchanged under specified transformations, often used to distinguish or classify quantum states, knots, or manifolds.
-
B.
Laurent polynomial-valued invariant
A Laurent polynomial-valued invariant is a quantity assigned to mathematical objects (such as knots, links, or manifolds) that remains unchanged under specified transformations and takes the form of a Laurent polynomial in one or more variables.
-
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.
object in invariant theory
An object in invariant theory is a mathematical entity, such as a vector space, polynomial ring, or group action, whose structure and symmetries are studied through the functions or quantities that remain unchanged under a specified group of transformations.
-
E.
homological invariant
A homological invariant is a quantity or structure derived from homology theory that remains unchanged under specified transformations, used to distinguish and classify mathematical objects up to an appropriate notion of equivalence.
- F. None of above. chosen
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.