application_id is really meant for scenarios where the SQLite database is treated as a document - a file that is intended to be copied around by the user, and opened by the same or another app elsewhere.
According to their mailing list, the way to register your own ID is to submit a patch that adds your ID to the file.
I tried to do that, but maybe the message didn't go through.
Some of the application IDs are made up using hexadecimal (such as Fossil), and some using ASCII (everything else listed in the magic.txt file in the SQLite repository). I have used base thirty-six; I later saw RADIX-50 mentioned, which would be another way.
According to their mailing list, the way to register your own ID is to submit a patch that adds your ID to the file.