> I'm very curious to learn more about 1cm, what is the math behind it?

So I actually got that from a cool math talk I attended about 20 years ago. At the end the professor had a cool demonstration where he glued paper strips of various sizes radially on the CD, and exactly as the math he spend an hour explaining predicted, the CD player could cope with up to a 1cm width strip, but no more.

Let me try to find some written material.

https://en.wikipedia.org/wiki/Cross-interleaved_Reed%E2%80%9... is a good start, but doesn't go into the details. https://en.wikipedia.org/wiki/Reed%E2%80%93Solomon_error_cor... might also be worth a read.

In a nutshell, you arrive at the 1cm like this: you can look up what proportion of 'wrong' bits the CD's coding can correct and other overhead. Then you look up the circumference of a CD (about 28 cm), then you do some multiplication, and figure out that you can lose about 1cm out of every 28cm, and still be able to correct.

Most of the interesting math happens at the first step of 'what proportion of errors can the music CD correct?' and more interestingly 'how does the CD player do that?'

> I was always fascinating by ability of old super scratched optical disks still functioning without problems.

Keep in mind that CD-ROMs have one additional layer of coding on top of what music CDs have. That's because if a bit error slips through the error correction chances are it still won't be audible to the human ear for music, but software might still crash with a single wrong bit.

> Do you speak about classical music CD with ±700mb of capacity?

Yes, that's because that's what I heard the talk about. I am sure more modern formats also have interesting error correction, but I don't know what they use and how much you could cover up.