Triple

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).

Phrase: Levi-Civita connection | Statement: [Hodge Laplacian, localExpressionDependsOn, Levi-Civita connection]

Target entity: Levi-Civita connection
Context triple: [Hodge Laplacian, localExpressionDependsOn, 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. Ehresmann connection
  An Ehresmann connection is a geometric structure on a fiber bundle that specifies a way to consistently split tangent spaces into vertical and horizontal parts, enabling the definition of parallel transport.
• C. 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.
• D. Cartan connections
  Cartan connections are a geometric framework generalizing affine and Riemannian connections that model curved spaces on homogeneous spaces, developed by Élie Cartan.
• E. Ricci calculus
  Ricci calculus is a mathematical framework for tensor analysis on manifolds that underpins much of modern differential geometry and general relativity.
• F. None of above.
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target predicate: localExpressionDependsOn
Context triple: [Hodge Laplacian, localExpressionDependsOn, Levi-Civita connection]

• A. hasLocalExpression
  Indicates that something has a specific form, representation, or manifestation that is valid or defined only within a particular local context or region.
• B. hasExpressionIn
  Indicates that one entity is manifested, represented, or realized within another entity, typically as a specific form, version, or expression.
• C. hasExpression
  Indicates that an entity displays or possesses a particular facial or emotional expression.
• D. usedInExpression
  Indicates that one entity (typically a term, symbol, or construct) is employed as a component within another entity that represents an expression.
• E. coreExpression
  Indicates that something is the primary or central expression or representation of another thing.
• F. None of above. chosen