Uniform solving method for edged cubes

Construct a uniform method for solving accessible configurations of the edged infinitary Rubik’s cube that does not require knowledge of the scramble, or prove that no such method is possible under an appropriate formalization.

Background

The paper proves solvability in principle for every convergent scramble of the edged cube, but the resulting inverse construction requires the solver to know the entire sequence that produced the scramble. The authors do not provide a procedure depending only on the final configuration and leave open whether such a procedure exists or is impossible.