I thought I would do a simple test of the properly Permanent blues* I have at hand.
The inks tested were Pilot Blue, Platinum Pigment Blue, Noodler's Aquamarine (for Swishers, now discontinued) and Koh-i-noor Document Blue.
I have selected Blue inks, as there are lots and lots and lots and lots of Permanent Blue-Blacks out there of varying chemistries. I wanted to do Blue.
My exhaustive testing regime consisted of writing samples of all four inks with a FP nib mounted in a pen holder onto Double A Premium copy paper.
After letting the ink dry for at least half an hour I then ran it under a stream of hot water for about 30 seconds.
The first scan is what the sample looked like before the hot water testing.
The second scan is after the hot water testing, and after the paper had dried out. The pencil line shows where the water went.
You can see that the first three inks are totally untouched.
The Pilot Blue leaves enough behind to be readable.
I would not now call Pilot Blue WaterProof, rather WaterResistant.
*Parker Quink 'Permanent' Blue need not apply...