I've been looking into the fountain codes and UR spec for Cashu token transmission over QR codes. I wanted to get a feel for how big in bytes was likely to be a typical payment, and I decided to run some statistics on the number of proofs you need for given payments. The results are interesting so I'm sharing them here.
Here is the distribution of the number of proofs you'll need for a random sample of 10,000 payment amounts between 1 and 1,000,000 satoshis (a payment of 0 to $500 at today's prices).
I was surprised at how a lot of payments can be done with less than 10 proofs, even on pretty big amounts (this makes sense when you think about it but for some reason I had expected a lot more proofs required). Moreover, since the number of proofs required is so nicely distributed, it occurred to me that a simple search "around" a given payment amount that required too many proofs would likely find an amount that