Triple
T26255068
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | PSL(2,ℝ) |
E656693
|
entity |
| Predicate | IwasawaDecomposition |
P160159
|
FINISHED |
| Object | KAN with K≅SO(2), A≅ℝ, N≅ℝ |
—
|
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: KAN with K≅SO(2), A≅ℝ, N≅ℝ | Statement: [PSL(2,ℝ), IwasawaDecomposition, KAN with K≅SO(2), A≅ℝ, N≅ℝ]
PD
Predicate disambiguation
gpt-5-mini-2025-08-07
Target predicate: IwasawaDecomposition Context triple: [PSL(2,ℝ), IwasawaDecomposition, KAN with K≅SO(2), A≅ℝ, N≅ℝ]
-
A.
hasMaximalCompactSubgroupOf
Indicates that one mathematical group is the maximal compact subgroup contained within another group.
-
B.
hasCartanInvolution
Indicates that one mathematical object (typically a Lie group or Lie algebra) possesses a specific Cartan involution, i.e., an involutive automorphism satisfying the Cartan conditions for that structure.
-
C.
hasParabolicSubgroups
Indicates that one mathematical object (typically a group) possesses parabolic subgroups related to it, usually in the sense of subgroup structures defined by a parabolic construction.
-
D.
maximalTorus
Indicates that one group is a maximal torus inside another group, meaning it is a largest possible connected, abelian, diagonalizable subgroup not properly contained in any larger such torus.
-
E.
hasUniqueIrreducibleUnitaryRepresentationUpToEquivalence
Indicates that there exists exactly one irreducible unitary representation of the entity (up to unitary equivalence), so any two such representations are equivalent.
- 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_69f5f7ff548c8190a23e98c5e66e0bc7 |
completed | May 2, 2026, 1:11 p.m. |
| PDg | Predicate description generation | batch_69f5ffc6268c8190b63f6360ebadab73 |
completed | May 2, 2026, 1:44 p.m. |
Created at: April 26, 2026, 9:08 p.m.