A true 4 gauge bore is 1.052", though most 4 gauge shotgun bores run closer to 6 gauge & will be so proofed. I have ben told, but cannot really verify, that the original 4 gauge guns were built with brass cases. When paper cases began to be used rather than change the chamber they dropped the bore diameter. Makes sense at least. Not positive but 4 gauge rifles may have preceded the shotguns in this size.

Miller/TN
I Didn't Say Everything I Said, Yogi Berra