Unrealized capital gains would be calculated at the end of a tax period, quarterly in many cases. Some market value would be assigned - left for you to do the calculations - don’t get it wrong, as you are the one ultimately responsible for the accuracy of your tax return and the one penalized if you do get it wrong. Severe penalties will be applied if intentional, and you’re guilty until you prove you’re innocent at the end of a long and expensive court proceeding. So, most plead guilty in return for a lesser penalty. Keep good records, be able to account for basis, etc.
What if the market is closed on the day a tax period ends? What if experts cannot agree on today’s value of my art? What if I store my valuables overseas? What happens if I sell my valuables to a friend at a very good deal while I buy his for a very good price? How is the government to know of my valuables and where they are stored? This is just off the top of my head without even putting any effort into enforcement issues.