Triple
T26255018
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | SL(2,ℤ) |
E656692
|
entity |
| Predicate | PSL2ZIsomorphicTo |
P160549
|
FINISHED |
| Object | free product C₂ * C₃ |
—
|
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: free product C₂ * C₃ | Statement: [SL(2,ℤ), PSL2ZIsomorphicTo, free product C₂ * C₃]
PD
Predicate disambiguation
gpt-5-mini-2025-08-07
Target predicate: PSL2ZIsomorphicTo Context triple: [SL(2,ℤ), PSL2ZIsomorphicTo, free product C₂ * C₃]
-
A.
automorphismGroupIsomorphicTo
Indicates that the automorphism group of one structure is isomorphic, as a group, to the automorphism group of another structure.
-
B.
isAutomorphismGroupOf
Indicates that a group is the full automorphism group consisting of all structure-preserving bijections (automorphisms) of a given mathematical object.
-
C.
hasNonAbelianSylow2Subgroups
Indicates that the Sylow 2-subgroups of a given group are non-abelian, i.e., their group operation is not commutative.
-
D.
congruenceSubgroups
Indicates that there is a relationship between groups where one is a congruence subgroup of the other, typically defined by congruence conditions modulo some integer or ideal.
-
E.
hasAutomorphismGroupContaining
Indicates that the automorphism group of one mathematical structure includes the other group as a subgroup or component.
- F. None of above. chosen
Provenance (4 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_69f602d2ec748190ae95154f34c7878f |
completed | May 2, 2026, 1:57 p.m. |
| PDg | Predicate description generation | batch_69f6037bf7a081908862a8359be80cf8 |
completed | May 2, 2026, 2 p.m. |
Created at: April 26, 2026, 9:08 p.m.