Accessibility of generalized superflip configurations

Determine whether the \(\omega\)-superflip and \(\omega^*\)-superflip configurations of the countable edgeless cube are accessible from the solved configuration by some convergent sequence, despite the failure of the standard finite superflip algorithms to converge in this setting.

Background

The paper constructs two natural infinite analogues of the finite Rubik’s-cube superflip. The usual algorithms generalized from finite cubes do not converge on the countable edgeless cube, but this does not exclude the existence of alternative convergent solving sequences. The authors present these configurations as candidates that may be inaccessible and explicitly state that they do not know how to prove their inaccessibility.