From the SAAMI Technical Data Sheet: Maximum Average Pressure--is the recommended maximum pressure for loading commercial sporting ammunition. Slightly different words, but it's the same thing the CIP refers to as their standard service pressure.
Completely misleading. The Maximum Probable Sample Mean (MPSM) is, the maximum expected average pressure that may be observed in the testing of product subsequent to its manufacture .
The MAP is the intention; the MPSM is the acceptable reality when a lot is tested prior to release for public sale.
Your problem, gun rag writer, is that you want things to be simple. When they arent you just start ignoring facts until its simple enough for you.
Anyone who is truly interested in this subject doesnt need to take my word or Larrys. The actual facts are published by SAAMI.
Found any of those pre-WWI Spanish guns yet, Kyrie? Photos maybe? To include details? I find it interesting that Spain did not even adopt obligatory proof until 1924. And that before things became more "standardized", Spanish makers were in the habit of copying proofmarks from other nations. Might explain why not many of those guns made it out of the country.
Asked and answered. Apparently you didnt like the answer and would like to pretend the answer never happened. Shrug.
Actually, to begin at the end . . . no, you disappeared when I asked for photos, details, etc of those pre-WWI Spanish guns. If you answered, please refer us to that answer. In a previous life, I had to deal with secret writing on occasion. ("Invisible ink".) Maybe that's what you were using, and I just didn't know the formula to use to make it appear.

Likewise, another Spanish gun fan (in addition to the above) also raised the 7 pin 578 point.
As for the Maximum Probable Sample Mean . . . you forgot the second half of the sentence to which you referred from the SAAMI technical sheet: " . . . and is NOT intended for use as a loading control point." (Emphasis SAAMI.) Might some loads exceed the target for service pressure? Sure. Also true under CIP rules. But the point is, they're both aiming for a service pressure standard. Which, in the case of the 12ga, is 11,500 psi under SAAMI guidelines--whether it's 2 3/4" or 3". That figure is one that is also the upper limit of pressure figures I find when I look at the Alliant Powder reloading guide. Especially in the case of 2 3/4" reloads, there are very few listed above 11,000 psi. And the reason that proof pressure exceeds service pressure by several thousand psi is to provide an additional safety cushion.
As far as being a "gun rag writer", if you have valuable information to provide to the shooting public, maybe you should try getting yourself published in a gun rag. If you can do a better job backing up your facts than you demonstrate here.