Exact diameter of the 4×4×4 Rubik’s Cube in the quarter-turn metric

Determine the exact diameter of the Cayley graph of the 4×4×4 Rubik’s Cube group in the quarter-turn metric, defined as the minimal number of allowed moves (only 90° turns on any of the three layer indices for each axis and their inverses) required to solve the Cube from any configuration. This establishes the precise “God’s number” for the 4×4×4 Cube in the quarter-turn metric, which remains unknown; current work provides only probabilistic estimates (48 turns).

Background

Using the same probabilistic logic, the authors estimate the diameter for the 4×4×4 Cube under the quarter-turn metric, where only 90° turns (and their inverses) are permitted. They infer a predicted diameter of 48.

Despite this prediction, the exact diameter has not been determined. The paper emphasizes that computing it exactly is currently beyond reach, similar to the half-turn case.