We need t measure the case in come to a reasonable conclusion on screen size.
I'm not sure if we're talking about the same case here:
http://www.iphone4life.nl/Thread-Nieuws-iPhone-5-Case-bevestigt-4-inch-scherm--1563
In this article, the actual phone size was estimated to be 4.7x2.6, as compared to iPhone 4's size of 4.5x2.31 and screen size of 2.9x1.95.
If we assume the same edge edge, same top and bottom bezel width, the extra 0.2 inch in screen high and .29 inch in screen width will bring the new screen size to 3.1 inch x 2.24 inch. The diagonal length will work out to be 3.825 and dpi will work out to be 301.6dpi, which is still retina if they use the exiting 960x640 screen resolution.
I know the article that I linked mentioned that it's at least 4 inch, but that's mathematically incorrect.
Perhaps Apple has worked backward, starting with the goal of retaining the retina marketing term, and come to the demension that fits exactly into the case in my link?
Edit again:
I forgot to take aspect ratio into account. Here is my recalculation:
If we take the side bezel width to be the same between iPhone 4 and 5 then the width of the new screen would be 2.24 inch like I calculated before. However, the height of the screen would not be increased by a mere 0.2 inch, but should be by 0.435 inch, in order to retain the same aspect ratio of 3:2. That means the new screen height would be 3.335 inches instead of just 3.1 inch in my former calculation. A screen that is 2.24 inch wide and 3.335 inch high will give a screen size of 4 inches, as mentioned by the article. This obviously mean that the bezel at either the top or bottom would have to be trimmed.
A four inch screen has been confirmed by a Chinese poster, whose friend is a Foxconn worker working on iPhone manufacturing.