I still maintain that it is physically impossible to make an F1.0 lens on a PK mount, and so far I have not seen anybody provide information that suggests otherwise.
An F-number is, in basic terms, the degree to which a lens can gather the light that is in front of it onto the focal plane. So, to make things easier to understand, think of an "idealized" lens that exists at the mount plane. Your maximum diameter (D) is going to be the maximum diameter of the mount, and your focal length (F) is going to be the register.
Again
f = F/D
since for PK mount F=45.5mm and D=45mm, an f1.0 lens cannot exist. The point here is that this diagram is as basic and efficient as it gets. There's nothing you can "add" to this simple diagram that will magically make the F-stop smaller, while maintaining the focal distance.
Now, several people mentioned some fast primes with small rear elements. This can easily be explained. What you forget is that rear elements protrude. So you don't need a rear element with a diameter that would be suggested by the simple formula above.
Case in point. Here's the rear element of my fastest lens, Zuiko-S 50mm f1.2
As you can see, the diameter is around 34mm. The OM mount has a register of 46mm, so to get an f1.2 lens, you'd think you need a 46/1.2=38mm rear element, right?
Nope, because the rear element protrudes:
This protrusion is around 6-7mm, making the distance from the rear element to the focal plane around 40mm. What's 40mm divided by 1.2? 33.3mm, just about the diameter of the rear element in the Zuiko.
Do the same calculation with your 31/1.8 (I did), comes out about the same.
So, you may ask, all you need is a rear element that protrudes far back enough without hitting the mirror and maintaining a large diamter, and you should get an F1.0 lens, right? Say, a 40mm rear element that protrudes 5mm behind the PK mount? Hey, what about a mirror-less design? Then you can REALLY have the lens close to your sensor plane! Should make an f1.0 lens a sinch!
The answer is NO, because regardless of how big the rear element is or how close you get it to the sensor plane
at some point during the travel of light, it had to go through the PK mount opening, which has a 45mm diamater, at a distance of 45.5mm from the focal plane. So regardless of whatever voodoo you conduct in front of, or behind the mount,
at the very best, what you are going to get is the idealized "single lens at the mount plane" situation, and because of that, the largest aperture you can get on a PK mount is limited to 45.5/45 = f1.01.
If someone wants to prove me wrong, just give me one example of an F1.0 lens on a mount/system that has a longer register than the mount diameter.
Couple of points:
(1) There is an exception, which is macro lenses. There is, e.g., an M42 Carl Zeiss Jena f0.75 lens, strictly for macro. This is possible, obviously, because the focal distance is, since it's a macro lens, much shorter than the register distance.
(2) Somebody mentioned the Noct-Nikkor. That was a 58/1.2, not an f1.0.