It is possible that people have been 10,000km into the Rim Continent. However, only a powerful government would have the resources to do this, and none of them are claiming to have done it.
At some point, there is simply too much air between the Sun and the Earth. From that point on, there would be perpetual darkness and the temperatures would drop very quickly. I am only guessing, but I could believe that it might be cold enough for the gases to start to liquefy at that distance from the Sun.
I will try to work on some calculations based on the average temperatures measured at different latitudes as well as the distance in which the Sun's rays may no longer be seen. I'll let you know when I have worked out the details.