Sorry K4u,
That was critical of me and this is a very constructive thread. I negatively responded to the dismissive statement that 'a Cow is not sufficiently secure for this list', and that was wrong of me.
The Cow hitch requires a fairly high CF cord in order to function and just about all modern plastic braids are just too slick for it to even remotely hold.
The problem with making a definition (especially the one you are considering), is that in this instance you will instantly eliminate a whole range of cordages and applications. Your given example of a Girth hitch for example has to be replaced, because it is not around the defined 1" pipe unless the pipe is just to define security.
Manila cordage is still widely used and it has a massive CF even just against itself. Consequently, the Cow hitch is quite adequate in any number of applications, even where the anchor point is slick.
So although I am not offering a 'succinct definition', perhaps I could offer up the insight that a knot be included, but if it has functionality limitations, then we describe those. Much as most of our present knots it seems would probably simply pull through in the new utra slick HMPE cordages of increasing availability, so we could include the Cow hitch with the comment that it needs high CF cordage in order not to simply slide through at the slightest load.
Once again, thank you for reminding me not to be an arse...
Derek