Well, with coticules, and I'm assuming Thuris are the same, they must be water stones, never used with oil. And they need to be free of cracks and imperfections that might absorb blood from the animal being butchered. They need to have a very pure and consistent colour. There may be other requirements I don't know of. Ardennes has, or had a seperate line of coticules they sold that met all the specifications.
The knives used need to be kosher as well, and there are a whole bunch of rules there too.
tough-standards-knife-sharpening-new-york