Stock marking on a M1

[RCS]

I think you are looking at the P proof stamp ? There were different kinds/types used on M1 stocks. The original proof P stamp would be in a circle, the plain P stamp would be from rebuild and the P in a square would be post WW2 rebuild. Some stocks have the original P in a circle and another P proof - which would indicate another barrel being installed. The stocks in these photos are from WW2