They'll take your coins and compensate you in paper.
I will let you in on a little goldbug secret. To answer your question nostr:npub1qny3tkh0acurzla8x3zy4nhrjz5zd8l9sy9jys09umwng00manysew95gx and nostr:npub1guh5grefa7vkay4ps6udxg8lrqxg2kgr3qh9n4gduxut64nfxq0q9y6hjy
1 oz US American Gold Eagle is issued as $50 USD. TSA says you have to declare anything more than $10,000. $10,000/$50 =200 US American Gold Eagles. Which the street value would be approximately $840,000. So in theory, you can carry up to 200 US Gold Eagles before having to declare. Same thing for other sovereign mints.
Discussion
I am not sure what you just said.