No back. But the uprights will extend to the floor, and i will be affixing it to the wall. I figure I will start by getting a single upright completely plumb and level, then attach that to the wall for a stable reference. Whatever looseness is built in to ease assembly can be stabilized by wall anchoring. At least that's the plan...
Another question, will the ends of the shelves fit between walls or be free range?
The uprights not only need to be plumb and level (slots) but also the same height. Which means the bottoms of the uprights will need to be scribed to the floor. Which means the slots will not be the same heights if pre-made.
How will these deep but narrow uprights be anchored to the wall? Side mounted cleats or hardware? Is it necessary or even possible to anchor into studs?
I think it will be easier and more successful (if only because everything else I can think of is even harder) to scribe, fit, and temporarily install (tape etc.) each upright, then use a laser level to mark the shelf cuts, then take out the uprights and make the cuts. If the uprights are reinstalled in exactly the same places and the slots are sufficiently accommodating then the shelves should go in nicely. Also, the fronts of the scribed uprights will also need to be rip/trimed to restore them to plumb.
But how to keep it all from falling forward? If the uprights are well scribed to the floor gravity will take care of a stable load but what if a kid climbs on the shelves? I haven’t thought of a secure way to anchor the uprights that isn’t unsightly except to put very long screws through the back of the slots into…what? Would be fine if the wall is made of wood.
The best I’ve thought of is to capture the tops of the uprights with a slotted cleat that spans the width of the installation (and a couple inches longer to lap both sides of the flanking uprights) which is screwed/anchored to the ceiling (oops, I’m assuming they reach the ceiling, minus the half inch or so removed to scribe the bottom to the floor). It should be easy to make a secure connection to the ceiling and from there down gravity is sufficient. Just add a discrete fastener at the bottom of each upright to keep it from moving until some weight is added to the shelves.