Triple
T10772751
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Éléments de Géométrie Algébrique |
E254120
|
entity |
| Predicate | defines |
P264
|
FINISHED |
| Object | Noetherian scheme |
E29919
|
NE 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: Noetherian scheme | Statement: [Éléments de Géométrie Algébrique, defines, Noetherian scheme]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Noetherian scheme Context triple: [Éléments de Géométrie Algébrique, defines, Noetherian scheme]
-
A.
Noetherian space
chosen
A Noetherian space is a topological space in which every descending chain of closed subsets stabilizes, mirroring the finiteness conditions of Noetherian rings in algebra.
-
B.
Noetherian rings
Noetherian rings are a fundamental class of rings in commutative algebra characterized by the property that every ascending chain of ideals stabilizes, ensuring that all ideals are finitely generated.
-
C.
Cohen–Macaulay ring
A Cohen–Macaulay ring is a commutative Noetherian ring whose depth equals its Krull dimension, giving it especially well-behaved homological and geometric properties.
-
D.
Noetherian module
A Noetherian module is an algebraic structure in which every ascending chain of submodules stabilizes, ensuring that all submodules are finitely generated and enabling powerful finiteness arguments in ring and module theory.
-
E.
Zariski topology
The Zariski topology is a fundamental topology in algebraic geometry, defined on the spectrum of a ring or an algebraic variety, whose closed sets correspond to solution sets of polynomial equations.
- F. None of above.
- G. Unsure - the case is ambiguous/there is not enough information to decide.
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_69d6aa5f54f4819082d0bbcb6f8797e6 |
completed | April 8, 2026, 7:19 p.m. |
| NER | Named-entity recognition | batch_69d7329b27748190bd0e2569c7972fd1 |
completed | April 9, 2026, 5:01 a.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69de238559b48190abc759e744ab0f8e |
completed | April 14, 2026, 11:22 a.m. |
Created at: April 8, 2026, 9:16 p.m.