A JVC RC-EX30 manual claims that discs need to be cleaned by moving a soft towel from inside to outside and reversed, not on circles.
I tried both and there was no readability difference.
When you clean a disc, the disc can get mini scratches. If you clean it in circles, the scratches can occur in exact the positions of the tracks and the error correction has harder work to do.
Concentric scratches affect continuous stream of data and in theory are much harder to be handled by the error correction system. Radial scratches are considered not that harmful.
Maybe this is useful if you plan to clean your disc with sandpaper
Is it documented online somewhere?
Mine does not, when using cosmetic towels or micro fibre, except if I push with nails, CQ CDs get tiny scratches, DVDs not.
Why would I use sandpaper?
But yes, horizontal scratches are really horrible for error correction.