I wish I could give you an academic answer, but I was going off of a similar design and thought if it works there, it should work here.

Honestly I'm a bit worried about the corners, but they feel stable enough.

I used pocket screws and wood glue at each shelf attachment to the frame. The shelf slats are all glued edge grain to edge grain, so in theory the entire shelf should act like a solid board.

Every shelve is a square supported on 3 corners. The weight in the "free" triangle holds because of the opposite corner.

I hope I explain it clear enough.