Triple
T5425705
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Cartan structure equations |
E121356
|
entity |
| Predicate | relatedTo |
P37
|
FINISHED |
| Object | Levi-Civita connection |
E22817
|
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: Levi-Civita connection | Statement: [Cartan structure equations, relatedTo, Levi-Civita connection]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Levi-Civita connection Context triple: [Cartan structure equations, relatedTo, Levi-Civita connection]
-
A.
Levi-Civita connection
chosen
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.
-
B.
Christoffel symbols
Christoffel symbols are mathematical objects in differential geometry that represent how coordinate bases change from point to point on a curved space or spacetime, and are used to define covariant derivatives and geodesics.
-
C.
Cartan connections
Cartan connections are a geometric framework generalizing affine and Riemannian connections that model curved spaces on homogeneous spaces, developed by Élie Cartan.
-
D.
Ricci calculus
Ricci calculus is a mathematical framework for tensor analysis on manifolds that underpins much of modern differential geometry and general relativity.
-
E.
Riemann curvature tensor
The Riemann curvature tensor is a fundamental geometric object in differential geometry that measures how much a Riemannian manifold deviates from being flat by encoding the intrinsic curvature of the space.
- 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_69bd463b58d88190b258261573de9e91 |
completed | March 20, 2026, 1:06 p.m. |
| NER | Named-entity recognition | batch_69bd881598448190a9bb456dee36004b |
completed | March 20, 2026, 5:47 p.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69bf3abfc7e88190b8f0a31b61c33973 |
completed | March 22, 2026, 12:41 a.m. |
Created at: March 20, 2026, 2:06 p.m.