Characterization of convergence and accessibility in the edgeless case

Characterize convergence over the solved configuration, the accessible configurations, and the associated algebraic structure for edgeless infinitary Rubik’s cubes.

Background

The edged case admits a complete convergence characterization: convergence over the solved configuration, universal convergence, and twist-finiteness coincide. In contrast, convergence over the solved configuration in the edgeless case is weaker than twist-finiteness and is not closed under concatenation, leaving the structure of accessible configurations and their operations unresolved.