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.