[gorgoiler]

I was indeed assuming that if you declared a value of $X but then sold N years later for $Y, then you pay N*(Y-X) in taxes.

You are right to imply that it seems unfair if you discover in year 49 of your happy 50 year tenure that your Queens bungalow was built on top of a seam of pure gold nuggets all along.

[apparent]

Wouldn't you pay taxes every year, so N would never be ≥ 1?

[gorgoiler]

I was thinking about the situation where someone cheats and declares their property to be half as valuable as it actually sold for. They would then owe back taxes for all of those years when they declared it as $X when it ended up having a market value of $2X.

But as you rightly pointed out, property values go up and down, so the vendor would say that extra $X was only in the past year, not the previous 10 years or however long they had been self declaring at a low value.