Simson's infinite tame-wild dichotomy conjecture for coalgebras

Let $C$ be a coalgebra. A coalgebra is called tame when, for every fixed dimension vector of finite length, the isomorphism types of finite-dimensional comodules with that dimension vector are parametrized by a finite set of one-parameter families, apart from possibly finitely many isomorphism types. It is called wild when its category of finite-dimensional comodules contains the representation theory of every finite-dimensional algebra via representation embeddings.

Simson's infinite tame-wild dichotomy conjecture. Every coalgebra $C$ is either tame or wild, but not both.

This is the infinite-dimensional analogue of the tame-wild dichotomy for finite-dimensional algebras and is formulated in the setting of coalgebras and their finite-dimensional comodule categories. The source does not provide a resolution status.