Per British proof charts;
4 Ga = 1.052"
5 Ga = 0.976"
6 Ga = 0.919"
8 Ga = 0.835"

Now this is what I seem to recall hearing. If anyone has other info do jump in with it.
The "4-Bore" originated as a muzzle loader with a bore size of 1.052" ± the makers ideas or tolerance. The earliest 4-Bore breech loaders were rifles & used the 1.052" bore diameter with thin brass cases.When paper cases with their thicker case walls were introduced it was not desirable to change the chamber size so the bores were reduced to accommodate the paper hulls. Consequently 4-Bore guns built for paper hulls will normally carry bores of about .935" & will thus be proofed as a 6. The few 4-bore guns I have seen I had neither opportunity to check bore diameters or proof marks, but I understand the 4 is most often found with this 6-bore proof.
A late 4 gauge paper new empty I have head-stamped Gevelot 4
Paris only measures 1.040" at the head. The paper on this hull is quite rigid so can get a pretty accurate reading of the mouth diameters, which amazingly seems to have the same 1.040" od as at the head. ID checks to about .930".
An 8 gauge "Fired" Remington industrial measures .920" "Ahead" of the enlarged band.
Hope this helps you a bit but true 4 gauge is 1.052" based on the weight of a pure lead ball which fits. It just would appear that very few "True" 4's were actually built.


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