1) A record of purchasing a firearm doesn't equate to being a record that shows you own guns, unless the gun in question is an NFA weapon.
2) Whenever we purchase a firearm through an FFL it is recorded in the FFL's Acquisition & Disposition Record, but not all firearm purchases are made from FFL's.
3) Gun parts aren't controlled items under the GCA and subject to the recordkeeping requirements of CFR §478.121. Firearm receivers are.
If you bought a gun from a dealer there is a record of you buying it. That record is proof of ownership unless you provide proof you no longer own it. It’s how that shuts how works in banana republics or communist utopias. I’ve lived the communist part. You own it unless you can prove it otherwise. Even then if they have a hard on for you, you’re SOL.
All guns purchased through a dealer are documented as purchased by you. You sell it to a fried and they sell it again... On paper you’re the only buyer, hence the owner. See how stuff works in banana republics or Communist utopias above.
If we have degenerated enough to start with the confiscation routine and LEO aren’t arresting those issuing such orders (don’t hold your breath on that one) you’re going to be screwed if you can’t account for one of your guns.