Triple
T26163332
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Arf invariant |
E654172
|
entity |
| Predicate | instanceOf |
P0
|
FINISHED |
| Object | quadratic form invariant |
C29199
|
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: quadratic form invariant Context triple: [Arf invariant, instanceOf, quadratic form invariant]
-
A.
quadratic form
A quadratic form is a homogeneous polynomial of degree two in several variables, typically expressed as xᵀAx for a symmetric matrix A, that defines a scalar-valued function capturing curvature and geometric properties such as lengths, angles, and conic sections.
-
B.
classical invariant
chosen
A classical invariant is a quantity or property associated with a mathematical object that remains unchanged under a specified group of classical transformations, such as rotations, translations, or linear changes of coordinates.
-
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.
problem in invariant theory
A problem in invariant theory concerns determining and characterizing the algebraic functions (invariants) that remain unchanged under the action of a given group on a vector space or algebraic variety.
- 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_69ee5b44391c81908bdbd8813ba9aa99 |
completed | April 26, 2026, 6:36 p.m. |
Created at: April 26, 2026, 8:31 p.m.