Triple
T27176515
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | SL(2,R) |
E683056
|
entity |
| Predicate | CartanDecomposition |
P160160
|
FINISHED |
| Object | KAK 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: KAK decomposition with K=SO(2) | Statement: [SL(2,R), CartanDecomposition, KAK decomposition with K=SO(2)]
PD
Predicate disambiguation
gpt-5-mini-2025-08-07
Target predicate: CartanDecomposition Context triple: [SL(2,R), CartanDecomposition, KAK decomposition with K=SO(2)]
-
A.
CartanDecomposition
chosen
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.
-
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.
CartanFormula
Indicates how a derivation or differential operator acts on a product, expressing the result as a graded Leibniz rule that distributes over the product with appropriate signs.
-
D.
IwasawaDecomposition
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.
-
E.
hasCartanSubalgebraDimension
Indicates that an algebraic or Lie algebraic structure has a Cartan subalgebra whose dimension equals a specified value.
- 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_69f620e38aec8190bb184edcdbd6da64 |
completed | May 2, 2026, 4:05 p.m. |
Created at: April 27, 2026, 9:26 a.m.