This is really beautifully done.
Off topic, but barely relevant, I admit I once tried to register http://100000000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000.com thinking I could tell people to “go to my website” – “oh what’s your website?” they’d ask. “google.com” I’d say.
Too many characters is the problem — max is 63 characters. So then I tried http://10^100.com — nope ‘^’ is an invalid character. Then I gave up. Years have passed.
I just checked http://10tothe100th.com is available. I have no interest in it, nor do I expect you to. OK! See you later!

