I don't mean to be cheeky, but it would be between 12 and 20.
SO, let me expand a bit.
Frame size is a function, at minimum, and I am speaking of SxS's here, of the measure between the cartridge primers, plus 2x the minimum chamber thickness the material requires. The shoulders can't be more narrow than that. So, it's also a function of barrel material.
Starting there, you cannot go narrower, because with the first cartridge the chamber would blow.
Moving backward, the width of the action has to contain all the parts, and give enough room for them to move.
Some actions are fantastic gems, so miniaturized.
I am fiddling with a Crescent 16 right now, a simple back action sidelock, crude in all respects, that functions perfectly with an action width of 1.40" and 2 1/16 across the shoulders.
In the hand it is very tiny.
And a set of Ithaca Flues model 12's, of the earliest derivation, that are scandalously light. Being box locks measuring 1.32" across the action, and 2.30 across the shoulders.
Point being, that they can only be so small and compact. It is a great expense creating an optimized action only a few Thou narrower than the 12, or larger than the 20.
You still need the lock work to deliver enough punch at the right spot to fire the cartridges, so some pieces need the same rotational mass.
And the volume produced doesn't always merit making parts a few thou narrower.
I can attest that the webs on these Fluesies are very thin.
And on some small 16's, the trigger work ends up so close it is hard to get your finger to the front trigger, or one with a glove, to the rear. You need a minimum length there that changes the trigger function.
Some day, I'd like to flush out Don Amos's database with some spin data pertaining to these American hardware store guns.
