Urspruch piano music

[JimL]

...the Belgian website mentions the existence of G sharp major.

The leading tone of A-flat is G natural.  In the sharp notation that would have to be notated as F-double sharp.  But in the 24 keys of the circle of 5ths, there are no signatures with double sharps.  So G-sharp Major can exist if notated enharmonically, but not as a key signature.