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: Lusternik–Schnirelmann theory | Statement: [Lazar Lyusternik, knownFor, Lusternik–Schnirelmann theory]

Target entity: Lusternik–Schnirelmann theory
Context triple: [Lazar Lyusternik, knownFor, Lusternik–Schnirelmann theory]

• A. Lusternik–Schnirelmann category chosen
  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.
• B. Morse Theory
  Morse Theory is a branch of differential topology that studies the relationship between the topology of manifolds and the critical points of smooth real-valued functions defined on them.
• C. Leray–Schauder degree
  The Leray–Schauder degree is a topological invariant that generalizes the Brouwer degree to compact perturbations of the identity in infinite-dimensional Banach spaces, providing a powerful tool for proving existence of solutions to nonlinear equations.
• D. Poincaré–Hopf theorem
  The Poincaré–Hopf theorem is a fundamental result in differential topology that relates the sum of the indices of a vector field’s isolated zeros on a compact manifold to the manifold’s Euler characteristic.
• E. Arnold conjecture
  The Arnold conjecture is a central statement in symplectic geometry predicting a lower bound on the number of fixed points of Hamiltonian diffeomorphisms in terms of the topology of the underlying manifold.
• F. None of above.
• G. Unsure - the case is ambiguous/there is not enough information to decide.