We've all heard the Super-X story in precis form and probably not a bad idea to hear more about the historical moment for the emergence of SAAMI. In the meantime, here's my old school testament about chamber pressure, recoil, and certainly "causal" relationships.
1) Pressure has no place in the calculation of recoil force. Knowing the wgt. of payload plus ephemera (wadding and powder charge), velocity of payload, and wgt of gun allows the predictive calculation of recoil of the gun.
2) Expanding gas CAN impart energy to the components of a pressure containment vessel (pressure relief valve, walls of the vessel). A shotgun at moment of firing is very much like a tank with a pressure relief valve. Expanding gas is held in containment by a piston or valve whose inertial or mechanical resistance to movement (or release) is also the condition for the creation of pressure. You could say that the vessel of containment "causes" pressure and not be much further from enlightenment than if you said pressure "causes" metal deformation and looseness in shotguns. Obviously, there is correlation of apparatus and chemical phoenomena which make possible events as disparate as: a) triggering a valve, b) overcoming the inertia of a plug or piston, c) rupturing the walls of a container, d) static maintenance of pressure in the container (in the case of hot gas, pressure in containment would decrease by dissipation of heat but would still be the classic extreme case of pressure which "causes" absolutely nothing cf. to the dramatic work done by shotguns and engines).
3) In past discussions, the mathheads and strict Newtonians have beat me about the head and shoulders until I have at least absorbed the idea that predicability of the resultant of chemical and physical events is vastly more important than which necessary pre-conditions may be termed in the vernacular "causational".
4) I still want to see the math in which peak (or durational) chamber pressure is incorporated in an equivalency of ratios to predict a single unknown (recoil force) one side of Mr. Equal Sign. Until then, I'll stick with the older vernacular that recoil of the gun as a whole and as parts (think freight cars slamming together on coupling) "causes" temporary frame deformation, barrel whip, radial and torque force around the axis of the hingepin, splaying of breech balls away from extension slots, battering of the stockhead, flexing of the stock wrist, general "Deacon's Shay" looseness, and ultimately the staggering flinch.
jack
