Triple

T79882
Position Surface form Disambiguated ID Type / Status
Subject Einstein field equations E1603 entity
Predicate uses P98 FINISHED
Object 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.
E7353 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: Einstein tensor | Statement: [Einstein field equations, uses, Einstein tensor]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Einstein tensor
Context triple: [Einstein field equations, uses, Einstein tensor]
  • A. Kretschmann scalar
    The Kretschmann scalar is a curvature invariant in general relativity that combines components of the Riemann tensor into a single scalar quantity used to characterize the intensity of spacetime curvature, especially near singularities.
  • B. 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.
  • C. Newtonian gravitational constant G
    The Newtonian gravitational constant G is the fundamental physical constant that quantifies the strength of gravitational attraction between masses in classical and relativistic theories of gravity.
  • D. Schwarzschild black hole
    A Schwarzschild black hole is the simplest theoretical black hole solution in general relativity, describing a static, spherically symmetric, non-rotating, uncharged mass with an event horizon defined by the Schwarzschild radius.
  • E. Nash embedding theorem
    The Nash embedding theorem is a fundamental result in differential geometry that shows any Riemannian manifold can be isometrically embedded into some Euclidean space, thereby realizing abstract curved spaces as concrete subsets of standard Euclidean space.
  • 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: Einstein tensor
Triple: [Einstein field equations, uses, Einstein tensor]
Generated description
The Einstein tensor is a mathematical object in general relativity that encapsulates how spacetime curvature is related to the distribution of matter and energy.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Einstein tensor
Target entity description: The Einstein tensor is a mathematical object in general relativity that encapsulates how spacetime curvature is related to the distribution of matter and energy.
  • A. Kretschmann scalar
    The Kretschmann scalar is a curvature invariant in general relativity that combines components of the Riemann tensor into a single scalar quantity used to characterize the intensity of spacetime curvature, especially near singularities.
  • B. 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.
  • C. Kasner
    Kasner is the birth surname of former German chancellor Angela Merkel, reflecting her family name before marriage.
  • D. Newtonian gravitational constant G
    The Newtonian gravitational constant G is the fundamental physical constant that quantifies the strength of gravitational attraction between masses in classical and relativistic theories of gravity.
  • E. Schwarzschild black hole
    A Schwarzschild black hole is the simplest theoretical black hole solution in general relativity, describing a static, spherically symmetric, non-rotating, uncharged mass with an event horizon defined by the Schwarzschild radius.
  • 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_69a24c60d19c8190a1b6c105ca59ef5b completed Feb. 28, 2026, 2:01 a.m.
NER Named-entity recognition batch_69a24f335b5c8190bf2158d884890ac2 completed Feb. 28, 2026, 2:13 a.m.
NED1 Entity disambiguation (via context triple) batch_69a25abc7b648190b8a83a05f4c76af0 completed Feb. 28, 2026, 3:02 a.m.
NEDg Description generation batch_69a25caa409881909eb7dfe7d038cc39 completed Feb. 28, 2026, 3:10 a.m.
NED2 Entity disambiguation (via description) batch_69a25e287cc88190b2eb5ae02bd2f9d1 completed Feb. 28, 2026, 3:16 a.m.
Created at: Feb. 28, 2026, 2:06 a.m.