Triple
T11411707
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Gelfand–Kirillov dimension |
E270385
|
entity |
| Predicate | relatedTo |
P37
|
FINISHED |
| Object | Krull dimension |
E157401
|
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: Krull dimension | Statement: [Gelfand–Kirillov dimension, relatedTo, Krull dimension]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Krull dimension Context triple: [Gelfand–Kirillov dimension, relatedTo, Krull dimension]
-
A.
Krull dimension
chosen
Krull dimension is a fundamental invariant in commutative algebra that measures the "size" of a ring by the maximum length of chains of its prime ideals.
-
B.
Krull–Gabriel dimension
Krull–Gabriel dimension is a refinement of Krull dimension used in the representation theory of rings and abelian categories to measure the complexity of their subobject lattices and module categories.
-
C.
Gelfand–Kirillov dimension
The Gelfand–Kirillov dimension is an invariant in noncommutative algebra that measures the growth rate of algebras and modules, serving as an analogue of Krull dimension for noncommutative settings.
-
D.
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.
-
E.
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.
- 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_69d6aaddeaa8819088b30ef7b50598c9 |
completed | April 8, 2026, 7:22 p.m. |
| NER | Named-entity recognition | batch_69d8015017d08190b4020c76545556d6 |
completed | April 9, 2026, 7:43 p.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69e5b855f0508190a2e57ef9407ddb1a |
completed | April 20, 2026, 5:23 a.m. |
Created at: April 8, 2026, 9:34 p.m.