process, machine, manufacture, or composition of matter, or any new and useful improvement thereof
A claim should fail 101 if it claims something that isn't one of the above.
The were not claiming to invent a machine (the computer)
They were not claiming to invent the process (hedging)
Actually, they were. It's the second word in the claim - a "method". They were claiming they invented a specific method of maintaining shadow accounts.
Now, I should stipulate, I don't think they did invent anything, and that this was either known under 102 or obvious under 103 given the existence of double-margin bookkeeping. But they were certainly claiming to have invented a process, which is a statutory category under 101.
Instead their claim was using a machine to solve a problem. That doesn't fall under 101 unless it falls under a patentable process.
Exactly.
SCOTUS said that the 2 step process of (take exising process) and (apply it on a computer) is just a drafting trick to get a patent on old things. If you remove the drafting trick then you have a process with no steps. So they rejected it under 101.
If you remove the drafting trick, you'd have a process with known steps, not no steps. For example, say I had a claim of:
A method for adding two integers, comprising:
inputting a first integer to a computer;
inputting a second integer to the computer;
calculating a sum of the first integer and second integer, with the computer; and
outputting the calculated sum, on a display of the computer.
Now, that's clearly "a process". And if you remove the "drafting trick" of applying it on a computer, you end up with:
A method for adding two integers, comprising:
inputting a first integer;
inputting a second integer;
calculating a sum of the first integer and second integer; and
outputting the calculated sum.
You still have the exact same number of steps, and it's still a process. Now, sure, it's well known and has been for thousands upon thousands of years, but that doesn't suddenly make it not a process, or an "abstract idea", or anything else... It's a claim directed to statutory subject matter under 101 that is not new under 102 and therefore is not a valid patent claim.