# Anisotropic Closest Molecule Models and Their Symmetries

We demonstrate that anisotropic nearest-neighbor anisotropic (NLE) models with a complex $\mathbb{Z}_4$ constant can have a class of non-trivial solutions, which inform the path-integral of the structure of the volume-polynomial density distribution. In particular, we show that some of these complex solutions have even infinite-dimensional solutions, which are integrable near the horizon. These solutions are characterized by the Euclidean algebraic algebra of the logarithmic and logarithmic logarithms, and the differential algebra of the complex and the logarithmic logarithms.