Triple
T7705270
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | SO(3) |
E174596
|
entity |
| Predicate | LieAlgebraIsomorphicTo |
P28830
|
FINISHED |
| Object | ℝ³ with cross product |
—
|
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: ℝ³ with cross product | Statement: [SO(3), LieAlgebraIsomorphicTo, ℝ³ with cross product]
PD
Predicate disambiguation
gpt-5-mini-2025-08-07
Target predicate: LieAlgebraIsomorphicTo Context triple: [SO(3), LieAlgebraIsomorphicTo, ℝ³ with cross product]
-
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.
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.
-
D.
isConformalGroupOf
Indicates that one entity is the conformal symmetry group associated with another entity, typically preserving angles and the conformal structure of that object or space.
-
E.
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.
- 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_69c6995b3e8c8190833108f883d5f53c |
completed | March 27, 2026, 2:51 p.m. |
| NER | Named-entity recognition | batch_69c70402169481909b219dc5f4a64b9b |
completed | March 27, 2026, 10:26 p.m. |
| PD | Predicate disambiguation | batch_69c70165e78c8190bf6b3c34e243cb81 |
completed | March 27, 2026, 10:15 p.m. |
Created at: March 27, 2026, 4:03 p.m.