Triple
T9297079
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Castelnuovo–Mumford regularity |
E223664
|
entity |
| Predicate | instanceOf |
P0
|
FINISHED |
| Object | invariant in algebraic geometry |
C10588
|
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: invariant in algebraic geometry Context triple: [Castelnuovo–Mumford regularity, instanceOf, invariant in algebraic geometry]
-
A.
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.
-
B.
geometric invariant
chosen
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.
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.
-
D.
result in arithmetic geometry
A result in arithmetic geometry is a theorem or proposition that connects number-theoretic properties of solutions to polynomial equations with the geometric structure of the varieties they define over arithmetic fields.
-
E.
Weyl algebra
The Weyl algebra is the associative algebra generated by variables and their corresponding differential operators subject to canonical commutation relations, typically modeling the algebraic structure of quantum mechanical observables.
- 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_69ca8423edb08190bc0c91287a484768 |
completed | March 30, 2026, 2:09 p.m. |
Created at: March 30, 2026, 7:36 p.m.