Diversity of Lipschitz-free spaces over countable complete discrete metric spaces

We show that there are uncountably many mutually non-isomorphic Lipschitz-free spaces over countable, complete, discrete metric spaces. Also there is a countable, complete, discrete metric space whose free space does not embed into the free space of any uniformly discrete metric space. This enhanced diversity is a consequence of the fact that the dentability index D presents a highly non-binary behavior when assigned to the free spaces of metric spaces outside of the oppressive confines of compact purely 1-unrectifiable spaces. Indeed, the cardinality of \D (F (M) ): M countable, complete, discrete\ is uncountable while \D (F (M) ): M infinite, compact, purely 1-unrectifiable\=\, ²\. Similar barrier is observed for uniformly discrete metric spaces as higher values of the dentability index are excluded for their free spaces: \D (F (M) ): M infinite, uniformly discrete\=\², ³\.