Existence of a compact solenoid by holomorphic curves in the complex projective plane

A solenoid by holomorphic curves is a compact solenoid in the complex projective plane whose leaves are holomorphic curves. Holomorphic-solenoid conjecture. There exists a compact solenoid by holomorphic curves in the complex projective plane that contains no algebraic curve. The authors do not have intuition about whether this solenoid is tangent to a holomorphic foliation.