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 | Statement: [Hadamard three-circle theorem, contrastWith, Liouville's theorem]

Target entity: Liouville's theorem
Context triple: [Hadamard three-circle theorem, contrastWith, Liouville's theorem]

• A. Liouville's theorem chosen
  Liouville's theorem is a fundamental result in complex analysis stating that any bounded entire function must be constant.
• 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. Picard theorem
  Picard theorem is a fundamental result in complex analysis stating that entire non-constant functions take on all possible complex values, with at most one exception.
• D. Liouville equation
  The Liouville equation is a fundamental differential equation in statistical mechanics and Hamiltonian dynamics that governs the time evolution of a system’s phase-space probability density.
• E. Mittag-Leffler theorem
  The Mittag-Leffler theorem is a fundamental result in complex analysis that characterizes meromorphic functions by allowing the construction of such functions with prescribed principal parts at given poles.
• F. None of above.
• G. Unsure - the case is ambiguous/there is not enough information to decide.