Here's your first reference source:
http://www.vamworld.com/1879s+rev+78First thing with PAF 1879-S is defining the shape of the "r" in "trust." On some examples, this letter was "broken," losing detail in the right knob, like so (image courtesy of Heritage Auctions):

Your coin has a full "r," which eliminates 11 of the 21 possibilities right off. Now it gets more difficult, and labor-intensive. We keep the remaining 10 from that list, and proceed to the next reference:
http://www.vamworld.com/1879+S+Reve...t+By+ReverseIt's now necessary to look at each sub-listing which involves a full "r", to see if details called out on that page can help narrow things down for us. The alternative is looking at each
VAM listing separately, meaning a detail page like this one is an enormous help which I wish existed for every year and type. Not so, unfortunately.

First listing is "Full r, open 9, pitted." Your images do not clearly enough show the 9 to determine if it's Open (bottom knob doesn't touch upper loop) or Closed (bottom knob touches). No help there. But "pitted...." Well, this refers (as the images show) to the area just under where the eagle's left (viewer's right) wing meets the body. Some of these had rust pitting in that area, which show on the struck coin as raised dots. In your images, I see some "business" in that area which makes me think this coin has that pitting, certainly a strong-enough indication to start looking closely at the varieties in this category.
Once I've reached this point in an attribution process - where I'm forced to look at a series of individual varieties for little clues because I'm all out of help

- I first go through the list of possibilities quickly, looking for what we refer to as a "smoking gun" attribute. These are attributes of a given variety which are not only fairly easy to find, but also unique to that die pair, not shared with any other and therefore definitive for that
VAM.
When I do that with your coin, there's a hit. Look at the back of the cap, inward from the UN of UNUM. See that line in the cap extending up and down?
Bang. That's the "smoking gun" unique to VAM-56, and there's no need to look further.
There is a Census published on VAMworld of the 1879-S Rev. '78 varieties. In that census, there are 1612 individuals noted in
TPG slabs with an attribution on the slab.
Only 10 of them are VAM-56.
Now, that is purely an advisory number. The VAMming project, even though it's been ongoing for over half a century, is still by no means anywhere near complete. New VAMs are being named regularly, and new examples of given varieties are being uncovered every day. Indeed, for this family in particular (1879-S Rev. '78), there are enough examples of dies being paired with multiple dies from the other face that it's almost certain we haven't seen all the die pairings yet. So absolute numbers mean little, except in comparative fashion.
Compared to the rest, yours is kind of a biggie.

Not the rarest of the bunch, but
among the rarest, and a pretty big score for the bulk price which you paid. It is, in my opinion, worth putting into an attributed slab at some point down the road, to maximize resale value.