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Hood to muzzle, or breechface to muzzle? Not necessarily the same thing. A reloading caliper may not be 100% accurate. You are only looking for a few thou.
I ran the tail of my caliper down the barrel of the assembled EMPTY pistol, bottomed it out against the slide breechface, and rested the frame-end across the muzzle.
Caliper's a decent one. Same reading, couple of times.
They look for a good 105+, just don't tell them. That is awfully damn close. Take some epoxy and put a light coat on the muzzle that should bring her up
They go by what the manufacturer says it is. The actual measurement doesn't matter. A cleaning rod into a closed action then measured will do, but if the maker says it's a 4" barrel, it won't matter to the CFC. There are no CFC techs in any case. Just clerks.
Do you need to submit this for verification? Or are you just wondering about someting that someone has?
I like the epoxy idea. Make sure the muzzle is good and clean so you get a nice bond.