That sign is a little off. In Google Earth I get latitude and longitude of 46 40 30 S and 169 00 07 E . Well, who knows, right?
But I also measured the distances and got 5171 and 4831, vs.
5140 and 4803 on the sign. The polar circumference is 40008, which I hit on the nose with Google Earth, finding 10002 for one quarter of it. Honestly, I did not have this number in mind when I made the measurements! The sign values add to 9943, of course.
Only after I looked it up did I recall that the original definition of the meter was the distance from the north pole to the equator, through Paris, of course!
BTW, this latitude corresponds almost exactly to Duluth, MN, mutatis mutandis.
Also BTW, when I was dragging the GE “ruler” to the south pole, I went directly through New Zealand’s Scott Base, adjacent to McMurdo Station.
I was trying to account for this discrepancy, and I did find that if the correct values in miles were converted to kilometers using a factor of 1.6 instead of the more correct 1.60934, we should recover the correct sum in kilometers by multiplying 9943 by 1.60934/1.6, and in fact this comes to 10001.04, so I'm gonna say that's it and call it a day.