The contramodule Bass-flat equivalence conjecture

Let $\mathfrak R$ be a complete, separated topological associative ring with a right linear topology. A Bass flat left $\mathfrak R$-contramodule is a direct limit in the category of left $\mathfrak R$-contramodules of a sequence of free left $\mathfrak R$-contramodules with one generator. The conditions below are compared with the equivalent conditions in the referenced theorem.

Contramodule Bass-flat equivalence conjecture. The following conditions are equivalent to each other and to the conditions listed in the theorem: (i$^\flat$) all Bass flat left $\mathfrak R$-contramodules have projective covers; (iii$^\flat$) all Bass flat left $\mathfrak R$-contramodules are projective; and (v) all discrete right $\mathfrak R$-modules are coperfect.

This conjecture connects projective-cover and projectivity properties of Bass flat contramodules with coperfectness of discrete right modules. The supplied text does not state whether it has been proved or disproved.