Triple
T6908917
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Zariski topology |
E159881
|
entity |
| Predicate | isNoetherianOn |
P27197
|
FINISHED |
| Object | Spec(R) when R is Noetherian |
—
|
LITERAL FINISHED |
How this triple was built (2 steps)
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.
NER
Named-entity recognition
gpt-5-mini
Instruction
Given a phrase, classify it is english named entity (e.g., persons, organizations, works of art) in Latin script, or not (e.g., literals, dates, URLs, verbose phrases). For disambiguation, the statement where the phrase occurs as object is also given. Please return a JSON object with `phrase` (string, the phrase being analyzed) and `is_ne` (boolean, indicating whether the phrase is a Named Entity).
Input
Phrase: Spec(R) when R is Noetherian | Statement: [Zariski topology, isNoetherianOn, Spec(R) when R is Noetherian]
PD
Predicate disambiguation
gpt-5-mini-2025-08-07
Target predicate: isNoetherianOn Context triple: [Zariski topology, isNoetherianOn, Spec(R) when R is Noetherian]
-
A.
isNoetherianRing
chosen
Indicates that the ring satisfies the ascending chain condition on ideals, equivalently that every ideal is finitely generated.
-
B.
isIntegrallyClosed
Indicates that a ring (or similar algebraic structure) contains all elements of its field of fractions that are integral over it, i.e., it has no proper integral extension within its field of fractions.
-
C.
overArtinianRing
Indicates that the relevant algebraic structure (such as a module or algebra) is defined over, or considered with respect to, a base ring that is Artinian.
-
D.
hasKrullDimension
Indicates that a mathematical structure (typically a ring or scheme) is associated with a specific Krull dimension, measuring the maximal length of chains of its prime ideals.
-
E.
isDedekindDomain
Indicates that a ring is a Dedekind domain, meaning it is a Noetherian, integrally closed integral domain of Krull dimension one in which every nonzero ideal factors uniquely into prime ideals.
- F. None of above.
Provenance (3 batches)
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_69c68839ccb88190b4aa5cc1aca3448f |
completed | March 27, 2026, 1:38 p.m. |
| NER | Named-entity recognition | batch_69c6d9be98748190b5cb698e66e3aa42 |
completed | March 27, 2026, 7:25 p.m. |
| PD | Predicate disambiguation | batch_69c6d7b93d688190a297244ce81b67ac |
completed | March 27, 2026, 7:17 p.m. |
Created at: March 27, 2026, 2:25 p.m.