> A software program running exists.
What is "a software program" in your concept?
You can't put "a software program" into a wheelbarrow. You can print out code and put that in a wheelbarrow, or write it to a disc or USB key or whatever, and each of those things exist, but they are not the program. Patterns in real things exist. The pattern of the bits is real (even in the brain) but the "a software program" is imaginary: it "exists" only in your mind.
Bucky Fuller had a great demo: he would take a length of rope that was made of three smaller lengths of rope spliced together, jute, cotton, and silk. He would tie a loose granny knot in the jute end, hook his finger into the loop, and draw the knot along the length through the jute, into the cotton, then into the silk and then off the end. As with all great demos there is the inner and the outer meaning.
The outer meaning should be obvious: self-referential pattern (the knot) has or can have it's own stable existence in a proper medium (the rope). Both exist, the knot and the rope, but in very different ways.
Are you familiar with Meta-II? The same software program has been translated to many different languages, each translation exists (can be printed out) but none of them are the Meta-II software program. That is just a concept in a human mind.
> the details of the hardware ... are irrelevant.
But it still has to exist? The one detail that matters is that the hardware exists.
> Checkers is a game with rules that are independent of the materials that make up its playing peices.
Checkers doesn't exist. It's just an idea. If all the people who know how to play checkers were to somehow vanish, so would checkers, even if the boards and pieces and rule books remained.
(While I'm at it, I'd like to point out that Tuesdays don't exist either. Just as an aside.)
> Minds as systems run, exist, on physical things.
If those physical things are brains, yes, as far as we know. At least it sure seems that way.
> But they can be independent of any substrate in that any substrate that implements the rules they need to operate will support a mind.
How do you know?
That is an interesting speculation but one that has no evidence to support it.
Even if it's so, and we can build machines intricate enough to carry the knot from our meat into silicon, there is no reason to expect that our subjective awareness would go with it. Mind is not self. We can build models of our minds that act like us, just as Babbage had the Silver Lady, an automaton that danced like a ballerina, but they will not be alive anymore than she.
To me it sounds like you are saying that you believe that knot is mind and can be drawn into non-biological media, I'm saying that "you" are not mind, so even if this is possible and you can achieve it, you will only have succeeded in making a sculpture of yourself which can have no more life or being than stone.