Triple
T22666414
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Poisson bracket |
E559803
|
entity |
| Predicate | definesLieAlgebraOn |
P28830
|
FINISHED |
| Object | space of smooth functions on a Poisson manifold |
—
|
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: space of smooth functions on a Poisson manifold | Statement: [Poisson bracket, definesLieAlgebraOn, space of smooth functions on a Poisson manifold]
PD
Predicate disambiguation
gpt-5-mini-2025-08-07
Target predicate: definesLieAlgebraOn Context triple: [Poisson bracket, definesLieAlgebraOn, space of smooth functions on a Poisson manifold]
-
A.
hasLieAlgebra
chosen
Indicates that one mathematical structure is associated with, or gives rise to, a specific Lie algebra capturing its infinitesimal or tangent-level structure.
-
B.
hasLieAlgebraDimension
Indicates that an algebraic structure is associated with a Lie algebra having a specified vector-space dimension.
-
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.
satisfiesJacobiIdentity
Indicates that a given binary operation on elements of an algebraic structure obeys the Jacobi identity, i.e., the specific cyclic sum of nested operations always equals zero.
-
E.
isSimpleAsLieGroup
Indicates that a given Lie group has no nontrivial connected normal subgroups, i.e., it is simple in the sense of Lie group theory.
- 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_69e2454a158c819093b8e35f5045efb6 |
completed | April 17, 2026, 2:35 p.m. |
| NER | Named-entity recognition | batch_69f1781c2c808190baf6964ca1eced6f |
completed | April 29, 2026, 3:16 a.m. |
| PD | Predicate disambiguation | batch_69ee62a6245881909506ff502da14137 |
completed | April 26, 2026, 7:08 p.m. |
Created at: April 17, 2026, 3:09 p.m.