So back in the day when I researched this there was the uncertainty in the median one can derive from the sample size n (which is that extra column). This was done back in GMT 4 so I cannot recall what the source was, but googling now it says the notch half-length is

1.57 * IQR / sqrt(n)

while it looks like the GMT code has

1.7 * ((1.25 * IQR) / (1.35 * n));

which must be the original source I used. But this simplifies to

1.57 * IQR / n);

IQR is inter-quartile range. I cannot see we take the sort of n anywhere so that seems to be a bug. Of course, we have no tests using +n which is good and bad. Maybe if you can find an example we can add a test, possibly adding a sort to lines 243 and 286 in psxy.c

So the “notch” is the “waist”?
But there is nothing to sort because -EY already requires the data to be provided as quartiles. My julia example accepts the raw data and computes them.

OK, I will see if I have time after dinner. Life is hectic up north these days. Can you please make a PR for that change since it is clearly a bug regardless of further work.