The CDI (black box) needs to be modified. There are a few companies that offer reworked units that will raise your rpm limit, but unless you've got major internal work done to the motor that requires the extra rpms to reach peak hp, you won't benefit by using one. They are also quite expensive.
You may very well be able to find a "U.S. spec" or "U.K. spec" box and install it on your bike for better results.
As it is, the U.S./U.K. spec R1 hits its hp peak before your rev limiter kicks in.
Check out this site for more info
I am doing some experimenting with an R1 engine. Putting 76mm pistons in it (puts the displacement to about 1050cc) and also a new cam. Really think I need the rev limit to be around 12,500. Can you give me the name of a company that could work on my CDI to raise the rev. limit.