Bases for upper cluster algebras and tropical points

It is known that many (upper) cluster algebras possess different kinds of good bases which contain the monomials and are parametrized by tropical points Poisson varieties. For a large class upper (injective-reachable ones with full rank coefficients), we describe all its these properties. Moreover, show existence generic basis for them. In addition, prove Bridgeland's representation theoretic formula effective their theta functions (weak genteelness). Our results apply to (almost) well-known arising from theory or higher Teichm\"uller theory, including quantum affine algebras, unipotent cells, double Bruhat skein over surfaces, where change coefficients if necessary so assumption holds.