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Virtually all compression stops to bathroom sinks are 3/8" OD compression connections
This is the standard size for most braided sink supplies
3/8" compression nut is too small
Then you have a real odd ball shut off. Probably best to just replace it with a standard 3/8" compression stop. The only sink supply sizes available are 3/8" and 1/2"
I've been doing this for 40+ years and I've never seen a compression stop that wasn't 1/2" or 3/8"
I just purchased a7/16" compression braided supply line from Home Depot
It's not even listed on their website
in fact 7/16 isn't even a standard copper tubing size or compression fitting size
you're trying to fit a square peg in a round hole, like I said before just replace the stop with a standard size
you are in the States?