Triple
T26255024
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | SL(2,ℤ) |
E656692
|
entity |
| Predicate | abelianizationIs |
P77186
|
FINISHED |
| Object | cyclic group of order 12 |
—
|
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: cyclic group of order 12 | Statement: [SL(2,ℤ), abelianizationIs, cyclic group of order 12]
PD
Predicate disambiguation
gpt-5-mini-2025-08-07
Target predicate: abelianizationIs Context triple: [SL(2,ℤ), abelianizationIs, cyclic group of order 12]
-
A.
hasAbelianization
chosen
Indicates that one algebraic structure is related to the abelian group obtained by quotienting it by its commutator subgroup (its abelianization).
-
B.
isAbelianFor
Indicates that the operation or structure associated with the given entity is commutative (i.e., forms an Abelian group) with respect to the specified context or parameters.
-
C.
hasTrivialAbelianization
Indicates that the group’s abelianization is trivial, meaning its commutator subgroup is the whole group and it has no nontrivial abelian quotient.
-
D.
isNonAbelian
Indicates that the operation or structure in question does not satisfy commutativity, so the order of applying the operation matters.
-
E.
associatedGradedIs
Indicates that one mathematical object is the associated graded object (e.g., graded structure derived from a filtration) of another.
- 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_69ee5b4d25ac819086acb51184602576 |
completed | April 26, 2026, 6:37 p.m. |
| NER | Named-entity recognition | batch_69f60dcd2e688190b54e36b0ff0d9187 |
completed | May 2, 2026, 2:44 p.m. |
| PD | Predicate disambiguation | batch_69f5f7ff548c8190a23e98c5e66e0bc7 |
completed | May 2, 2026, 1:11 p.m. |
Created at: April 26, 2026, 9:08 p.m.