Triple
T10732780
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Serre duality |
E253115
|
entity |
| Predicate | instanceOf |
P0
|
FINISHED |
| Object | duality theorem |
C716
|
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: duality theorem Context triple: [Serre duality, instanceOf, duality theorem]
-
A.
mathematical theorem
chosen
A mathematical theorem is a rigorously proven statement derived from axioms and previously established results, expressing a fundamental truth within a formal mathematical system.
-
B.
optimality conditions
Optimality conditions are mathematical criteria that must be satisfied by a candidate solution to ensure it is a local or global optimum of an optimization problem.
-
C.
necessary conditions for optimality
Necessary conditions for optimality are criteria that any candidate solution must satisfy in order to be considered a potential optimizer (such as a minimum, maximum, or saddle point) of a given objective function under specified constraints.
-
D.
result in convex analysis
In convex analysis, a result is a formally stated and proven fact—such as a theorem, lemma, or proposition—that characterizes properties or relationships of convex sets, convex functions, or related optimization structures.
-
E.
doctrine of non-one-sidedness
The doctrine of non-one-sidedness is a Jain philosophical principle asserting that reality is many-sided and that any single viewpoint captures only a partial truth.
- 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_69d6aa5d8be481909a43218b2bfdbe95 |
completed | April 8, 2026, 7:19 p.m. |
Created at: April 8, 2026, 9:14 p.m.