Oh and about proving with documentation..
I have only had to produce my naturalization document 2 times in 40+ years...once to get an American passport and a 2nd time during 2012 when I applied for old age SS...
I had to prove I was an American citizen to collect SS for which I had paid taxes for DECADES...
an illegal alien can get SS without having to even prove his own name...
I’m sure I’ll have to produce mah Birf Certificate along with my well-worn SS card to get my SS in 20 years.