.32 Rimfire - Headstamp "P"

This cartridge, which I believe is a .32 short Rimfire for the Smith & Wesson revolver, features the letter “P” on the headstamp, which indicates that it was produced by the Phoenix Metallic Cartridge Company.
Am I right in this identification?
I do not have much data to support, however, I would be grateful if anyone could corroborate this information, correct it, or add more data.
Thanks.

yes

I have to write more because a post has to be over 5 letters long so all this other than the yes is useless electrons being wasted.

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Thanks Pete

Dang, and the were probably good electrons, too!