All,
The book is not accurate.
The double palm is not double proof, but "epreuve superieure".
The triple palm is indeed the double proof which was actually twice the load vs the single proof.
These proofs were for the finished barrels only and used #2 black powder.
The following proof loads are in 12 Ga:
Single palm (standard proof for finished barrels): 10grams of powder and 60 grams of #8 shot for a 1170 kg/cm^2 pressure (16640PSI)
Double palm (superior proof): 14.5 grams of powder and 75 grams of shot with a pressure of 1630 kg (23184PSI)
Triple palm (double proof): 20 grams of powder and 120 grams of shot with a 2150 kg pressure (30580PSI)
Quadruple palm (triple proof): 30 grams of powder and 180 grams of shot for a 3050kg of pressure (43381PSI).

This was quite confusing and many people to this day have been incorrectly calling the double palm proof "double proof".

This gun was proved in the finished state with the load described on the flat. God knows what that pressure was, but for sure much smaller than the barrel proof.
That is the only one that the gun, rather than the barrels, is known to have survived once.

BTW, the pressures described in the book don't match the official numbers.

Best regards,
WC-