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: Koszul formula | Statement: [Levi-Civita connection, definedByFormula, Koszul formula]

Target entity: Koszul formula
Context triple: [Levi-Civita connection, definedByFormula, Koszul formula]

• A. 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.
• 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. Weyl algebra
  The Weyl algebra is a fundamental noncommutative algebra generated by position and momentum operators satisfying canonical commutation relations, central in quantum mechanics and representation theory.
• D. Carathéodory–Jacobi–Lie theorem
  The Carathéodory–Jacobi–Lie theorem is a fundamental result in symplectic geometry and Hamiltonian mechanics that provides canonical local coordinates adapted to a given set of commuting functions.
• E. Gauss–Bonnet theorem (early form)
  The Gauss–Bonnet theorem (early form) is an early version of the fundamental result in differential geometry that links the total curvature of a surface to its topological characteristics, originally developed by Carl Friedrich Gauss.
• F. None of above. chosen
• G. Unsure - the case is ambiguous/there is not enough information to decide.

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]"

Entity: Koszul formula
Triple: [Levi-Civita connection, definedByFormula, Koszul formula]

The Koszul formula is an explicit expression in Riemannian geometry that uniquely determines the Levi-Civita connection from a given metric by relating covariant derivatives to the metric and Lie brackets of vector fields.

Target entity: Koszul formula
Target entity description: The Koszul formula is an explicit expression in Riemannian geometry that uniquely determines the Levi-Civita connection from a given metric by relating covariant derivatives to the metric and Lie brackets of vector fields.

• 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. Weyl algebra
  The Weyl algebra is a fundamental noncommutative algebra generated by position and momentum operators satisfying canonical commutation relations, central in quantum mechanics and representation theory.
• D. Carathéodory–Jacobi–Lie theorem
  The Carathéodory–Jacobi–Lie theorem is a fundamental result in symplectic geometry and Hamiltonian mechanics that provides canonical local coordinates adapted to a given set of commuting functions.
• E. Gauss–Bonnet theorem (early form)
  The Gauss–Bonnet theorem (early form) is an early version of the fundamental result in differential geometry that links the total curvature of a surface to its topological characteristics, originally developed by Carl Friedrich Gauss.
• F. None of above.

Target predicate: definedByFormula
Context triple: [Levi-Civita connection, definedByFormula, Koszul formula]

• A. mathematicallyExpressedBy
  Indicates that something (such as a concept, quantity, or relationship) is represented or captured using a specific mathematical expression or formulation.
• B. mathematicallyFormulatedBy
  Indicates that something (such as a concept, model, or theory) is expressed or defined using mathematical formulations created by a particular agent.
• C. keyFormula chosen
  Indicates that a formula serves as the primary or defining expression associated with an entity or relationship.
• D. recitesFormula
  Indicates that one entity verbally or mentally repeats a specific formula, such as a set phrase, equation, or ritual wording, typically from memory.
• E. determinedBy
  Indicates that one entity’s state, value, or outcome is decided, controlled, or fully specified by another entity.
• F. None of above.