Triple
T26254980
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | PSL(2,ℤ/Nℤ) |
E656691
|
entity |
| Predicate | hasTrivialAbelianizationFor |
P77154
|
FINISHED |
| Object | N = p prime, p ≥ 5 |
—
|
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: N = p prime, p ≥ 5 | Statement: [PSL(2,ℤ/Nℤ), hasTrivialAbelianizationFor, N = p prime, p ≥ 5]
PD
Predicate disambiguation
gpt-5-mini-2025-08-07
Target predicate: hasTrivialAbelianizationFor Context triple: [PSL(2,ℤ/Nℤ), hasTrivialAbelianizationFor, N = p prime, p ≥ 5]
-
A.
hasTrivialAbelianization
chosen
Indicates that the group’s abelianization is trivial, meaning its commutator subgroup is the whole group and it has no nontrivial abelian quotient.
-
B.
hasAbelianization
Indicates that one algebraic structure is related to the abelian group obtained by quotienting it by its commutator subgroup (its abelianization).
-
C.
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.
-
D.
hasTrivialSchurMultiplier
Indicates that the Schur multiplier (second homology group) of a given group is trivial, meaning it is the zero group and there are no nontrivial central extensions detected by this invariant.
-
E.
hasTrivialOuterAutomorphismGroup
Indicates that the outer automorphism group associated with an object is trivial, meaning it contains only the identity element and thus no nontrivial outer automorphisms exist.
- 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_69f72921cf2c8190909bb53f78bcc890 |
completed | May 3, 2026, 10:53 a.m. |
| PD | Predicate disambiguation | batch_69f7283d8cec8190b524c144948bc4ec |
completed | May 3, 2026, 10:49 a.m. |
Created at: April 26, 2026, 9:08 p.m.