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: Betti numbers | Statement: [Castelnuovo–Mumford regularity, relatedTo, Betti numbers]

Target entity: Betti numbers
Context triple: [Castelnuovo–Mumford regularity, relatedTo, Betti numbers]

• A. Poincaré duality
  Poincaré duality is a fundamental theorem in algebraic topology that relates the homology and cohomology groups of an oriented closed manifold in complementary dimensions.
• B. Milnor number
  The Milnor number is an invariant in singularity theory that measures the complexity of an isolated critical point of a complex hypersurface or function.
• C. Lusternik–Schnirelmann category
  The Lusternik–Schnirelmann category is a numerical homotopy invariant of a topological space that measures the minimal number of contractible open sets needed to cover it, playing a key role in critical point theory and algebraic topology.
• D. Alexander–Spanier cohomology
  Alexander–Spanier cohomology is a cohomology theory in algebraic topology defined using cochains on all finite subsets of a space, notable for its generality and close relationship to Čech and singular cohomology.
• E. Pontryagin classes
  Pontryagin classes are characteristic classes associated with real vector bundles that capture topological information about the bundle’s curvature and play a central role in differential topology and geometry.
• 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: Betti numbers
Triple: [Castelnuovo–Mumford regularity, relatedTo, Betti numbers]

Betti numbers are topological invariants that count the number of independent cycles or holes in each dimension of a topological space, reflecting its underlying shape and structure.

Target entity: Betti numbers
Target entity description: Betti numbers are topological invariants that count the number of independent cycles or holes in each dimension of a topological space, reflecting its underlying shape and structure.

• A. Poincaré duality
  Poincaré duality is a fundamental theorem in algebraic topology that relates the homology and cohomology groups of an oriented closed manifold in complementary dimensions.
• B. Milnor number
  The Milnor number is an invariant in singularity theory that measures the complexity of an isolated critical point of a complex hypersurface or function.
• C. Lusternik–Schnirelmann category
  The Lusternik–Schnirelmann category is a numerical homotopy invariant of a topological space that measures the minimal number of contractible open sets needed to cover it, playing a key role in critical point theory and algebraic topology.
• D. Alexander–Spanier cohomology
  Alexander–Spanier cohomology is a cohomology theory in algebraic topology defined using cochains on all finite subsets of a space, notable for its generality and close relationship to Čech and singular cohomology.
• E. Pontryagin classes
  Pontryagin classes are characteristic classes associated with real vector bundles that capture topological information about the bundle’s curvature and play a central role in differential topology and geometry.
• F. None of above. chosen