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: noncommutative local index formula | Statement: [Connes–Moscovici index theorem, relatedTo, noncommutative local index formula]

Target entity: noncommutative local index formula
Context triple: [Connes–Moscovici index theorem, relatedTo, noncommutative local index formula]

• A. Connes–Moscovici index theorem
  The Connes–Moscovici index theorem is a fundamental result in noncommutative geometry that generalizes the classical Atiyah–Singer index theorem to the setting of foliations and noncommutative spaces.
• B. equivariant index theorem
  The equivariant index theorem is a generalization of the Atiyah–Singer index theorem that computes indices of elliptic operators while taking into account the action of a symmetry group.
• C. Atiyah–Singer index theorem
  The Atiyah–Singer index theorem is a fundamental result in mathematics that links the analytical properties of elliptic differential operators to topological invariants of manifolds, unifying analysis, topology, and geometry.
• D. noncommutative geometry
  Noncommutative geometry is a branch of mathematics that generalizes geometric concepts to settings where coordinate algebras do not commute, with deep applications in operator algebras, topology, and theoretical physics.
• E. Atiyah–Bott fixed-point theorem
  The Atiyah–Bott fixed-point theorem is a fundamental result in equivariant cohomology that expresses global invariants, such as indices of elliptic operators, in terms of local data at the fixed points of a group action.
• 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: noncommutative local index formula
Triple: [Connes–Moscovici index theorem, relatedTo, noncommutative local index formula]

The noncommutative local index formula is a result in noncommutative geometry that expresses index-theoretic invariants of operators on noncommutative spaces in terms of local cyclic cocycles and residues, generalizing the classical Atiyah–Singer index theorem.

Target entity: noncommutative local index formula
Target entity description: The noncommutative local index formula is a result in noncommutative geometry that expresses index-theoretic invariants of operators on noncommutative spaces in terms of local cyclic cocycles and residues, generalizing the classical Atiyah–Singer index theorem.

• A. Connes–Moscovici index theorem chosen
  The Connes–Moscovici index theorem is a fundamental result in noncommutative geometry that generalizes the classical Atiyah–Singer index theorem to the setting of foliations and noncommutative spaces.
• B. equivariant index theorem
  The equivariant index theorem is a generalization of the Atiyah–Singer index theorem that computes indices of elliptic operators while taking into account the action of a symmetry group.
• C. Atiyah–Singer index theorem
  The Atiyah–Singer index theorem is a fundamental result in mathematics that links the analytical properties of elliptic differential operators to topological invariants of manifolds, unifying analysis, topology, and geometry.
• D. noncommutative geometry
  Noncommutative geometry is a branch of mathematics that generalizes geometric concepts to settings where coordinate algebras do not commute, with deep applications in operator algebras, topology, and theoretical physics.
• E. Atiyah–Bott fixed-point theorem
  The Atiyah–Bott fixed-point theorem is a fundamental result in equivariant cohomology that expresses global invariants, such as indices of elliptic operators, in terms of local data at the fixed points of a group action.
• F. None of above.