Now that the unit is taking shape, we need to strengthen it and check it for square. We'll use the cabinet's back side to do this.
Cut a piece of 1/4" plywood to 47-1/4" x 18". (Once again, if you're modifying the plans for a different sized case or using 3/4" plywood for the back, you'll need to adjust accordingly.)
Lay the assembly flat onto it's front-side on the table and check it for square. To check for square, measure diagonally from the top-right corner of the cabinet to the lower-left corner and note the distance. Then, measure diagonally between the other two corners and check to see if the distance matches the first measurement. If it matches, the cabinet is square. If not, adjust the carcase appropriately to make the two measurements match.
Now, place the 1/4" plywood onto the back of the assembly. It should fit nicely into the rabbets on the two standards and the rabbet on the bottom shelf. Use some finish nails to affix the back to the carcase.