Triple
T7420280
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Swan constructed counterexamples over the rational numbers |
E171228
|
entity |
| Predicate | instanceOf |
P0
|
FINISHED |
| Object | counterexample to Noether's problem |
C7255
|
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: counterexample to Noether's problem Context triple: [Swan constructed counterexamples over the rational numbers, instanceOf, counterexample to Noether's problem]
-
A.
problem in invariant theory
chosen
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.
nonsingular curve
A nonsingular curve is an algebraic curve with no singular points, meaning it is smooth everywhere and has a well-defined tangent line at every point.
-
C.
curve over the rational numbers
A curve over the rational numbers is an algebraic curve defined by polynomial equations with rational coefficients, considered together with its set of rational solutions and their arithmetic properties.
-
D.
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.
-
E.
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.
- 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_69c68a625d048190af70eb8b63bec5a0 |
completed | March 27, 2026, 1:47 p.m. |
Created at: March 27, 2026, 3:11 p.m.