After using this saw a few times, I decided that a carrying bag of some sort was needed. So, after seconds and seconds of hard thought, I came up with...
This my version of a folding camp saw, used to cut fire wood or whatever, just don't cut yourself. See the saw used in a test cut video cutting a 3 1/2" walnut log. This is very hard wood and the saw worked very well.
Also see the video showing how to unfold and fold the saw. It took just over 2 minutes to unfold and refold the saw.
I'm not going to claim this idea for my self. I saw different versions of this on Youtube and on this site, this is just the way I did mine.
This saw weighed less than 12.5 oz. and about 20" long. That's small enough to easily fit into any pack. It weighs less than the garden saw that I started with, and it folds.
Again, this is a prototype. It's made of pine scraps that I had in the scrap bin. I plan to make a more durable one out of some walnut or cherry the I have on hand.
The only thing that I had to buy was the garden saw. It was cheaper to buy the whole saw than to buy just the blade online with shipping and everything.