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's theorem in Hamiltonian mechanics | Statement: [Joseph Liouville, notableWork, Liouville's theorem in Hamiltonian mechanics]

Target entity: Liouville's theorem in Hamiltonian mechanics
Context triple: [Joseph Liouville, notableWork, Liouville's theorem in Hamiltonian mechanics]

• A. Liouville's theorem in Hamiltonian mechanics chosen
  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.
• B. Liouville–Arnold theorem
  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.
• C. Liouville's theorem
  Liouville's theorem is a fundamental result in complex analysis stating that any bounded entire function must be constant.
• D. Kolmogorov–Arnold–Moser theory
  Kolmogorov–Arnold–Moser theory is a fundamental result in dynamical systems that explains the persistence of quasi-periodic motions in nearly integrable Hamiltonian systems under small perturbations.
• 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.