Triple
T26255069
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | PSL(2,ℝ) |
E656693
|
entity |
| Predicate | CartanDecomposition |
P160160
|
FINISHED |
| Object | KAK 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 with K≅SO(2) | Statement: [PSL(2,ℝ), CartanDecomposition, KAK with K≅SO(2)]
PD
Predicate disambiguation
gpt-5-mini-2025-08-07
Target predicate: CartanDecomposition Context triple: [PSL(2,ℝ), CartanDecomposition, KAK with K≅SO(2)]
-
A.
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.
-
B.
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.
-
C.
hasCartanSubalgebraDimension
Indicates that an algebraic or Lie algebraic structure has a Cartan subalgebra whose dimension equals a specified value.
-
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.
symmetryAlgebraOf
Indicates that one entity is the symmetry algebra associated with, or governing the symmetries of, the other entity.
- 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.