Triple
T6295387
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Sophus Lie |
E141118
|
entity |
| Predicate | hasNameInMathematics |
P744
|
FINISHED |
| Object | Lie derivative |
E141121
|
NE 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: Lie derivative | Statement: [Sophus Lie, hasNameInMathematics, Lie derivative]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Lie derivative Context triple: [Sophus Lie, hasNameInMathematics, Lie derivative]
-
A.
Lie derivative
chosen
The Lie derivative is a fundamental differential operator in differential geometry that measures how a tensor field changes along the flow generated by a vector field.
-
B.
Lie bracket
The Lie bracket is a bilinear, antisymmetric operation on a Lie algebra that measures the noncommutativity of its elements and encodes its infinitesimal structure.
-
C.
Levi-Civita connection
The Levi-Civita connection is the unique torsion-free affine connection on a Riemannian manifold that is compatible with its metric, enabling the definition of parallel transport and covariant differentiation.
-
D.
Jacobi bracket
The Jacobi bracket is a bilinear operation generalizing the Poisson bracket in differential geometry, central to the theory of Jacobi manifolds and Hamiltonian systems.
-
E.
Levi-Civita symbol
The Levi-Civita symbol is an antisymmetric tensor used in mathematics and physics to represent orientations, cross products, and determinants in multiple dimensions.
- F. None of above.
- G. Unsure - the case is ambiguous/there is not enough information to decide.
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_69c008cdf2ac8190bb640c94478fb4ed |
completed | March 22, 2026, 3:20 p.m. |
| NER | Named-entity recognition | batch_69c06741fbbc81908d947182b197bf59 |
completed | March 22, 2026, 10:03 p.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69c51988f1388190b36212b0d9756863 |
completed | March 26, 2026, 11:33 a.m. |
Created at: March 22, 2026, 4:27 p.m.