The 'R' could be a 'P'
What is seen there as the slanted leg that is the difference in the two letters could be nothing more than the movement of the pen (pencil) dragging a bit from the completion of a P and moving over to begin writing the G.
The 'G' initial is very distinctive. The long horizontal & verticle bar parts of the letter are there,,though very faint where they meet.
If the next letter is a 'G' ('G'oldsxxxx),,that letter doesn't look at all like previous 'G'. It almost looks like a 'C' with a sort of stumble to the writing at the bottom of the curl.
That same stumble could as easily account for a poorly written 'G' I suppose. But it's just some things I saw.
Not easy writing on a piece of tape while it's on the side of a stock either lying in your lap, on a bench or holding it in your other hand.
Maybe the 6044 is the last 4 of the ser# of the bbl'd action that came out of it. Separated for whatever reason (repair),,just never made it back.
Most gunsmiths accumulations end up with stocks w/o the metal and actions w/o the wood. Perhaps it is one and the info is a customers name.