noumpere

It's a reasonably common term (this is from MW, but other dictionaries give similar definitions): piping noun pip·ing | \ ˈpī-piŋ Definition of piping (Entry 1 of 2) 1a : a sound, note, or call like that of a pipe b : the music of a pipe 2 : a quantity or system of pipes 3 : trimming stitched in seams or along edges (as of clothing, slipcovers, or curtains)

Yes.

The same as any other play where two umpires have different calls: UIC (usually, but not always, PU) decides.

If there's a missed tag and a missed base at home, no call is the proper mechanic.

I had a play like this in the state finals. R2 stopped at third. I left him there -- F7 was charging and made a strong throw right to the plate. Change those last two facts and I might have awarded home.

I understand the logic if R2 stopped at third and you had to decide whether to award home -- in your judgement / viewing he would not have reached home. We are allowed to consider post obstruction evidence to help with the decision -- and in the OP we have it.

Why only to third? (Just trying to understand, not trying to argue or suggest that you are wrong)

If R2 was slowed down by more than the amount he was thrown out, then you should award him home. If he was thrown out by more than he was slowed down, then the out stands.

The run does not score when the batter makes the third out before reaching first base. (In a very weird play where R3 scores before F1 starts his motion, the run would count.)

Only in some local rules.

Even if the runner does not retouch home, he's safe at third until the defense appeals the missed base.

Specified right in the rule book (which I don't have handy at the moment). Something like "when announced. If not announced, when the ball is made live." Some specific differences for pitchers and batters, iirc

As long as there's an illegal sub on base, the defense can appeal. When the illegal sub leaves the bases (in this example, scores), NOW the defense must appeal before the next pitch.

And I had multiple plays where as BU I was hung out on a swipe tag at first and PU could have helped. It's as I've said -- the mechanics on this go back-and-forth because whoever is in charge at some particular time has had one play or the other.

I should add that my answer above is what we did in my state (which never used pure FED mechanics), in my college group (I forget whether that was the standard at the time), and in all our OBR games. I still think it's better than having PU go to third on this play -- but nobody asked me.