The *hash mark*, #, is a meta-symbol that is neither part of the James notation nor part of the interpretation. # acts like a universal variable standing in place of an *arbitrary base*.
In our interpretation, boundaries can stand in place of exponential and logarithmic expressions. In contrast, transformation within James forms is independent of the concept of a base. In effect, # is a convenience that permits the *interpretation* to remain uncommitted to a value of a base.