@Jozsef Well it’s weird why IrfanView shows lower resolution. Even on info screen - http://temp.kayle.sk/irfanview.jpg
I replicated your small test and yes, letters are not readable, but you have 3456x3456 px for half sphere, only ~12 megapixels.
Here is sample from DSLR with fisheye http://temp.kayle.sk/fisheye.jpg (Samyang 8mm f/3.5 - Google Search)
Resolution is 3456x5184 and for full circle I made 5 shots (maybe 4 was ok, but 5 have larger overlapping) + up and down.
It’s 10-15m from guidepost. Height of those signs is 140mm and letters 15mm.
6912x3456px looks like a lot pixels, but I think it’s not so much for whole sphere.