Yep, the back of it looks like it was straight off a rock wall, the sides have that sawn look.
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IME the older Escher labels, with the 4 men, are stuck on there hard. Usually leave residue if they wear off. Almost impossible to remove in routine honing. OTOH, the later labels with & Sohn and 2 men, will come off easily just from normal honing/getting wet. Might very well be a Escher. Congrats.
Looking at the small white scratches on the surface, the color and shining from the pictures, the rough back that you said which is typical and the quite typical size, there is quite a good chance that this is a thuringian!
Congrats.