I agree it being a WW2 Remington production 03A3.
You can just barely see the REM,,on the top of the recv'r ring in the last pic before the scope block covers it.
The stamped trigger guard, magazine, follower and floorplate unit was standard on the A3.
The rear of the recv'r cut-off boss is machined like an 03-A3.
No matter,,the Remington 03-A3 was made from Chrome-Moly alloy. Plenty strong and no worrys about the Low#/heat treat thing.
Aftermarket trigger w/ side safety for scope use. As others have stated that can be a plus for just being there to a valuable add-on. Some aftermarket triggers are very pricey. Some are not.
Check it's operation and any alterations done with it;s installation. Sloppy grinding and alteration of the sear surface in the bolt, ect are sure signs of trouble and a less than safe rifle.
Test for 'push off' and wether the rifle obviously fires with the safe on. But also if the rifle fires after pulling the trigger with the safety engaged and it appears 'safe',,then mearly flipping the safety to the off (fire) position,,the rifles fires w/o touching the trigger.
Orig bbl? may have the US proof up at the front yet or part of it left there after refinishing. Probably a 44 date.
Check headspace if you can,,not always possible I know. Surplus 03As's are pretty secure in that area. A custom bbl'd gun is where you can get some pretty wild specs and dimensions to chambers/throats, ect.
Pretty nice looking rifle. Nice crisp lines to the metal work,,no sloppy rounded over corners.
Pull the bbl's action if you can and check the bedding for cracks, ect. Glass bedding is OK, You want it secure in the wood and not moving around allowing cracks to happen. The recoil lug and the bottom of the rear tang are the primary contact points
Since these were orig Parkerized, I'd have to assume someone who built it took a lot of time to polish the action and parts correctly to remove the sandblaster Park finish keeping everything clean and sharp. Then reblued the metal, Labor intensive for sure. No buffer work showing.
Low scope bolt handle, again nice sharp metal work and lines..
No way you could build that particular rifle even at min wage and sell it for $350. You'd still be loosing money.