Looks Like a Sedgley sporter and a nice condition one at that. Don't hold back posting info and questions on classic rifles on this forum,,there's alot of that here! Michael Petrov will surely be along to better fill you in on the history and info on these rifles. I can only relate that Sedgley's 03 sporters were usually made up from low# 03 Springfield actions and parts the company bought from the US Gov't (as scrap). Usually re-heatreated in his shop, reproofed to something like 70 or 80K psi. Not unusual for the make/model and ser# to be ground off and the top receiver ring matted. Sedgley added his own assembly #'s to the guns and perhaps a Sedgley ser#, but Mr Petrov can better comment on that. The standard rear site was the Lyman 48 (a pricey item these days in itself). The barrels were Winchester made as were the butt plates I think. They made a deluxe version also with better figure wood and I think you could get it with a cheek piece. I'm not sure if these were 1920's or '30s era or both perhaps. I have one that I shoot often with cast bullet loads and it is a very accurate rifle. You will undoubtedly hear all the warnings of getting to close to a low# 03 and actually fireing it. The decision is obviously up to you. Very nice rifle,,congrats!
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Here's a recent thread on this forum on some other '03 sporters that may interest you..
http://doublegunshop.com/forums/ubbthreads.php?ubb=showflat&Number=32939&page=7#Post32939