<p>What is the thread pitch of the Ender 3's bed leveling screws? The diameter measures about 4mm. Are they M4 0.7 (coarse) pitch or 0.5 (fine) pitch? I'd like to develop rigorous formulas for the amount to turn the knobs by after measuring (or visually inspecting, since I can see an accurate 0.2 mm first layer decently well) leveling-test patterns in the corners rather than using a closed-loop tune-and-retry approach.</p>

I don't know what the value is, but there are a few ways to find out. It is very hard to measure this with a caliper, but it can be done, mark the upper and bottom of e.g. 10 windings and measure this with a caliper. Alternatively measure how much the screw drops after 10 full turns.
There are special tools that give you the answer directly, they cost a few Euros/bucks but can be very handy; a thread gauge, just place the 0.5 mm and the 0.7 mm beside the screw and you will instantly see which is the correct one.
I bought mine at a typical Chinese vendor site.