It starts to darken past the wrist and forward past the lower band and on the bottom about 1/2 way around.
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Sounds like the wood itself. I would not mess with it any further; originality is key.
Sounds Like sap wood/heart wood. A clue that would rule that out & favor being sun bleached is the hand guard. Is it two tone or all one color?
I took some photos of both Remington 03A3s today. I have had one of them since 1980 when I bought it while on leave from the Army at a combination auto parts and gun shop in Washington PA. It is the one with the Boyt 1943 dated sling which it came with. The other is the one I picked up this weekend.
https://www.milsurps.com/images/impo...3pair001-1.jpg
https://www.milsurps.com/images/impo...3pair002-1.jpg
https://www.milsurps.com/images/impo...3pair003-1.jpg
You sir, have both a good eye and good luck. Two real beauties! Your earlier purchase has a Smith Corona safety housing.