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: Liouville integrability theorem | Statement: [Liouville–Arnold theorem, alsoKnownAs, Liouville integrability theorem]

Target entity: Liouville integrability theorem
Context triple: [Liouville–Arnold theorem, alsoKnownAs, Liouville integrability theorem]

• A. Liouville–Arnold theorem chosen
  The Liouville–Arnold theorem is a fundamental result in Hamiltonian mechanics that guarantees the integrability of a system with sufficiently many conserved quantities and describes its motion as quasi-periodic on invariant tori in phase space.
• B. Liouville's theorem in Hamiltonian mechanics
  Liouville's theorem in Hamiltonian mechanics states that the phase-space volume occupied by an ensemble of systems evolving under Hamiltonian dynamics is conserved over time, implying incompressible flow in phase space.
• C. Kovalevskaya integral
  The Kovalevskaya integral is an additional conserved quantity that makes the motion of the Kovalevskaya top exactly integrable in classical rigid body dynamics.
• D. Liouville's theorem
  Liouville's theorem is a fundamental result in complex analysis stating that any bounded entire function must be constant.
• E. 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.
• F. None of above.
• G. Unsure - the case is ambiguous/there is not enough information to decide.