The French Ideal has a dynamic doll's head, with reciprocating wedges rising to engage the barrel extension. The shape is such that the joint is always tight, the parts wear in, keeping contact through the years. Most other doll's heads are kind of delicate affairs with static fit and no provision for wearing in.
The theory is that the doll's head resists the backward bending of the action on firing. Notice that no authority analyses what happens after the action has bent backwards. My guess is that if it does indeed bend, then it springs back to the original position with some force. It becomes a hammer, and so we must ask what is the "work" being hammered and what part becomes the anvil.
The traditionally held belief that the cartridge case pushes on the breech face by itself, and the barrels remain static, is a little suspect. My (unproven as yet) view is that barrel and cartridge become a single unit and both together push against the breech face. Indications that this is so are the imprints left by the barrels on the breech face.
If the barrel and cartridge push back together, then there is no need for any third bite. As people have noted on anothr thread, a double can be fired with no bolting in place, a sign that there are no forces acting to separate barrels from action during firing. And if this turns out to be correct then there is no role for any doll's head, not even the super tight fit one on the Ideal.
