Triple
T27176514
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | SL(2,R) |
E683056
|
entity |
| Predicate | IwasawaDecomposition |
P160159
|
FINISHED |
| Object | KAN decomposition with K=SO(2) |
—
|
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 decomposition with K=SO(2) | Statement: [SL(2,R), IwasawaDecomposition, KAN decomposition with K=SO(2)]
PD
Predicate disambiguation
gpt-5-mini-2025-08-07
Target predicate: IwasawaDecomposition Context triple: [SL(2,R), IwasawaDecomposition, KAN decomposition with K=SO(2)]
-
A.
IwasawaDecomposition
chosen
Indicates that a group element is expressed as a product of elements from its Iwasawa components (typically a maximal compact subgroup, a maximal abelian subgroup, and a nilpotent subgroup) according to the Iwasawa decomposition.
-
B.
CartanDecomposition
Indicates a decomposition of a Lie group or Lie algebra element into a product (or sum) of components from a maximal compact subalgebra and its complementary subspace, as specified by the Cartan decomposition.
-
C.
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.
-
D.
hasMaximalCompactSubgroupOf
Indicates that one mathematical group is the maximal compact subgroup contained within another group.
-
E.
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.
- 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_69eefad086808190ab89816c0c300476 |
completed | April 27, 2026, 5:57 a.m. |
| NER | Named-entity recognition | batch_69f6257a5ae881908db3032511378836 |
completed | May 2, 2026, 4:25 p.m. |
| PD | Predicate disambiguation | batch_69f61b41f3848190bd38e697cf189a87 |
completed | May 2, 2026, 3:41 p.m. |
Created at: April 27, 2026, 9:26 a.m.