Welcome to the forum.
You have a "Model of 1953 .32 RP", 4 screw, built on the New I Frame. It became the Model 31 in 1958, and the Model 31-1 in 1961 when it was changed to being built on the 1/8" longer J Frame.
Your # 635xxx was likely shipped in the first half of 1956 because it still has the older style pre 1953 hammer spur shape and 2nd style flat latch cyl release. S&W didn't build or ship in serial # order, therefore we have to resort to its features for its age.