Triple
T9297077
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Castelnuovo–Mumford regularity |
E223664
|
entity |
| Predicate | instanceOf |
P0
|
FINISHED |
| Object | homological invariant |
C27157
|
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: homological invariant Context triple: [Castelnuovo–Mumford regularity, instanceOf, homological invariant]
-
A.
cohomology theory
A cohomology theory is a functorial assignment of graded algebraic invariants to topological spaces (or other mathematical objects) that encodes global structural and obstruction information via axioms such as exactness and homotopy invariance.
-
B.
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.
-
C.
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.
-
D.
algebraic variety
An algebraic variety is a geometric object defined as the set of common solutions to a system of polynomial equations over a field, studied up to algebraic and topological properties.
-
E.
Noetherian ring
A Noetherian ring is a ring in which every ascending chain of ideals stabilizes, equivalently, every ideal is finitely generated.
- 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_69ca8423edb08190bc0c91287a484768 |
completed | March 30, 2026, 2:09 p.m. |
Created at: March 30, 2026, 7:36 p.m.