Photobucket has screwed itself up royal and I cannot access my library and post 03 serial numbers. You can find examples of stamping styles on the web. The stamping on your receiver looks very sloppy and looks very suspect to me. You have hidden the rest of your rifle, but it does look like a later bolt handle.
It would be very unusual to find a 1913 barrel on a late model receiver. Barrels wear out before receivers.
As to the safety of your rifle heck that is impossible to determine. There are "good" low number receivers and "bad" low number receivers. The Army could not sort them out and decided to destroy all low number receivers due to the number of problems they were having.
The most dangerous condition is a case head rupture where gas spills back into the receiver. Even in "good" receivers, low number receivers are made from plain carbon steels and these receivers tend to fail in a brittle fashion. That is they frag. All 03's have the same bad gas handling characteristics and gas, wood fragments, and brass particles go straight back into the shooter.
I would keep loads light, remember most of the rounds made were closer to 40K psia than 50 Kpsia, use only the best brass, and always wear shooting glasses. One poor fellow who had a National Ordnance M1903A3 give way wrote that he still had brass particles in his eyes and it burnt to look at the sun.
That said, you rifle's receiver was one of the last produced, if authentic, and the parts bins may have been getting low at that time. Who's to say that a '13 barrel wasn't down there on the bottom. Remember, US Marines went ashore on Guadalcanal carrying both low numbered and high numbered "03 Springfields. They did their own rebuild on rifles, some in Philly, some at Springfield, and it could have been one of theirs.
I consider it a criminal decision to retain rifles with a known defect, a defect, while rare, when the rifle broke it injured Soldiers and had the potential to kill the shooter or a stander by.
Safety standards of the day were different. People were cheap and things were expensive. A Soldiers health and life were worth less than a $40.00 rifle.
But times change.
I do not consider my eyes, my health to be worth $40.00 or less, or even $650.00.