All matching, great bore, but stock was "sporterized" in the past 60-70 years.
Unless it was sporterized in Switzerland, it probably was sporterized since the mid 1990's. It is my recollection that the first K31 that I saw was a private sale to an American. (Rifles sold to Swiss citizens have a tang stamping.) And that American sold me that rifle at a gun show in 1997. I paid $350 for that rifle, because the things were rare. My timing was impeccable as usual, as shortly afterwards, K31's were selling for as low as $75.00 a rifle, for a scratch and dent version. A bud at work purchased a couple of those. Still I was able to score a couple of very nice ones for less than my first one. Prices have since gone up.
It is my recollection that the earlier models, such as the Swiss M1911's were imported in the US in the 1960's, that is when I remember seeing them. But the K31 was a rare bird until recently.
If you reload, I recommend a 175 grain bullet and any of the 4350 powders. I am using WC852, which is a surplus military ball powder. Accurate Arms makes a copy called AA2700. It is a good powder in this caliber, provides service rifle velocities at mid 40's psia pressures. This round is powerful, my reloads push a 174 at 2550 fps or so, that is the equal of the 308 Win any day.
I took one of my K31's to CMP Talladega, it sort of held the ten ring at 200 yards, held the nine ring at 300 yards. Only after I was done and cleaning the thing did I find that I had not tightened the stock screws. Opps! I loosen the things on rifles I have not glass bedded and am not shooting. There is no good reason to compress the wood. The Range Master had a story of "some cocky kid" who brought one out, and proceeded to show all observers why he was so cocky. Like Dizzy Dean said : "
it ain't bragging if you can do it!" The kid shot well with his rifle all the way out to 600 yards and impressed the Range Master. That's a good recommendation.