"Bitcoin is a payment network based on triple-entry crowd accounting. A crowd of computers - run by ordinary Bitcoin users - observes the transactions, produces a single common ledger, and keeps everyone honest. The magic that came from Bitcoin's inventor - the thread that holds the whole thing together - is a process by which the entire crowd can always agree on what transactions it observed, despite differences in timing and perspective, and even despite varying levels of honesty among participants. Bitcoin's design ensures that no matter how big the crowd, its collective efforts always produce exactly one transaction ledger."
Replace "magic" with "technology" and you've got my vote. I know you want to capture the magic of bitcoin, but if I were a banker, I'd stay the hell away from anything that "magically worked".
I would address this concern by calling it a magic
documented process, as documented magic is more appealing than "technology". Magic "just works" and is scary, but documented magic not only "just works", it just works for a reason. I updated the OP just to see how it looks.
I say that because people throw around the word "technology" nowadays to mean the most trivial things. It seems anyone who buys gadget X and puts it in place Y where it has never been before, is said to have invented a new technology. Anyone with a soldering iron can produce technology. Apple soared to where it's at by selling magic.
And as long as we're renaming anyway:
Please, please rename "mining" to "securing". As far as I can tell, people are saying "What, computers do some calculation, and then mine bitcoins out of nothing? Lol, what a joke!"
By naming it securing, or maybe "verifying", it signifies useful work being done.
The word that comes to mind for me to describe the process as I visualize it, is "recording", "hardening", or "memorializing" the transactions to the public ledger. I think of it as the same thing the local County Recorder does, to make a real estate transaction permanent on public records.