The same way they get records on my personal consulting business – they tell me I have to provide them for tax purposes.
If you have more than $1 billion in unrealized gains, you (ie your accountants) should know that. They provide current market values and cost basis. I’d say you pay tax on the portion of your unrealized gains that exceeds $1 billion.
“Whipsawing” is a concern if “market value” means closing price on 12/31. I’d smooth things out by allowing the taxpayer to use the lowest daily closing price in the last three calendar years when calculating unrealized gains.
(And, highest daily closing price when calculating unrealized losses. So, some years there is neither a taxable unrealized gain nor a taxable unrealized loss.)
Yes, that would defer the tax collection a few years, but now it can go multiple decades.
Yes, tax collections would go up somewhat when the economy is booming and down somewhat when it is tanking. That’s a good side effect of taxing unrealized gains.