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: Allen–Cahn equation | Statement: [Cahn–Hilliard equation, relatedTo, Allen–Cahn equation]

Target entity: Allen–Cahn equation
Context triple: [Cahn–Hilliard equation, relatedTo, Allen–Cahn equation]

• A. Cahn–Hilliard equation
  The Cahn–Hilliard equation is a nonlinear partial differential equation that models phase separation and coarsening in binary mixtures and other systems undergoing spinodal decomposition.
• B. Mullins–Sekerka instability
  The Mullins–Sekerka instability is a morphological instability that occurs during diffusion-limited solidification or crystal growth, leading to pattern formation such as dendrites at moving phase boundaries.
• C. Stefan problem
  The Stefan problem is a classical mathematical model in heat transfer that describes how phase-change boundaries, such as the interface between ice and water, move over time.
• D. Monge–Ampère equation
  The Monge–Ampère equation is a fully nonlinear partial differential equation central to differential geometry, optimal transport, and several complex variables, often used to study curvature and geometric structures.
• E. Kardar–Parisi–Zhang equation
  The Kardar–Parisi–Zhang equation is a fundamental stochastic partial differential equation that models the dynamic scaling and roughening of growing interfaces in nonequilibrium statistical physics.
• F. None of above. chosen
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target entity: Allen–Cahn equation
Target entity description: The Allen–Cahn equation is a reaction–diffusion partial differential equation used to model phase separation and interface motion in multi-phase systems.

• A. Cahn–Hilliard equation
  The Cahn–Hilliard equation is a nonlinear partial differential equation that models phase separation and coarsening in binary mixtures and other systems undergoing spinodal decomposition.
• B. Mullins–Sekerka instability
  The Mullins–Sekerka instability is a morphological instability that occurs during diffusion-limited solidification or crystal growth, leading to pattern formation such as dendrites at moving phase boundaries.
• C. Stefan problem
  The Stefan problem is a classical mathematical model in heat transfer that describes how phase-change boundaries, such as the interface between ice and water, move over time.
• D. Monge–Ampère equation
  The Monge–Ampère equation is a fully nonlinear partial differential equation central to differential geometry, optimal transport, and several complex variables, often used to study curvature and geometric structures.
• E. Kardar–Parisi–Zhang equation
  The Kardar–Parisi–Zhang equation is a fundamental stochastic partial differential equation that models the dynamic scaling and roughening of growing interfaces in nonequilibrium statistical physics.
• F. None of above. chosen