Triple
T461781
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Einstein tensor |
E7353
|
entity |
| Predicate | relatedConcept |
P37
|
FINISHED |
| Object |
Bianchi identities
The Bianchi identities are geometric relations in differential geometry and general relativity that express the vanishing covariant divergence of the Riemann curvature tensor, leading to conservation laws such as energy-momentum conservation via the Einstein tensor.
|
E57422
|
NE FINISHED |
How this triple was built (4 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: Bianchi identities | Statement: [Einstein tensor, relatedConcept, Bianchi identities]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Bianchi identities Context triple: [Einstein tensor, relatedConcept, Bianchi identities]
-
A.
Einstein field equations
The Einstein field equations are the core mathematical framework of general relativity, relating the curvature of spacetime to the distribution of matter and energy.
-
B.
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.
-
C.
Einstein tensor
The Einstein tensor is a mathematical object in general relativity that encapsulates how spacetime curvature is related to the distribution of matter and energy.
-
D.
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.
-
E.
Ricci curvature tensor
The Ricci curvature tensor is a geometric object in differential geometry that measures how volumes in a curved space-time deviate from those in flat space, playing a central role in general relativity.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NEDg
Description generation
gpt-5.1
Instruction
Generate a one-sentence description of the target entity. You are given a context triple in the form (subject, predicate, object), where the object is the target entity. # Instructions Use the triple to infer relevant information about the entity. Describe the entity based on what is most defining, well-known. Avoid repeating the information from the triple, unless really essential. # Response Format Return only the sentence: "Description: [one-sentence description of the target entity]"
Input
Entity: Bianchi identities Triple: [Einstein tensor, relatedConcept, Bianchi identities]
Generated description
The Bianchi identities are geometric relations in differential geometry and general relativity that express the vanishing covariant divergence of the Riemann curvature tensor, leading to conservation laws such as energy-momentum conservation via the Einstein tensor.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Bianchi identities Target entity description: The Bianchi identities are geometric relations in differential geometry and general relativity that express the vanishing covariant divergence of the Riemann curvature tensor, leading to conservation laws such as energy-momentum conservation via the Einstein tensor.
-
A.
Einstein field equations
The Einstein field equations are the core mathematical framework of general relativity, relating the curvature of spacetime to the distribution of matter and energy.
-
B.
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.
-
C.
Einstein tensor
The Einstein tensor is a mathematical object in general relativity that encapsulates how spacetime curvature is related to the distribution of matter and energy.
-
D.
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.
-
E.
Ricci curvature tensor
The Ricci curvature tensor is a geometric object in differential geometry that measures how volumes in a curved space-time deviate from those in flat space, playing a central role in general relativity.
- F. None of above. chosen
Provenance (5 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_69a2e7e5c5bc8190a1dc8178218fba40 |
completed | Feb. 28, 2026, 1:04 p.m. |
| NER | Named-entity recognition | batch_69a2efbed5b88190a45716812eb4cfdf |
completed | Feb. 28, 2026, 1:38 p.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69a44f59e9348190a53c1734b95bc2c3 |
completed | March 1, 2026, 2:38 p.m. |
| NEDg | Description generation | batch_69a44fb74a4481908538fa126571f803 |
completed | March 1, 2026, 2:39 p.m. |
| NED2 | Entity disambiguation (via description) | batch_69a45011a750819098d2ce4908439eb1 |
completed | March 1, 2026, 2:41 p.m. |
Created at: Feb. 28, 2026, 1:12 p.m.