Can someone help me understand how the difficulty number relates to the block hash?

Hey guys I'm trying to get a better understanding of how the difficulty number itself relates to the block hash.

I'm under the impression that as difficulty rises the block hash must be a smaller number than a certain threshold. Is this right?

So if I look at the dashboard at

Clark Moody

Under difficulty the number is 20x1012. So does this mean the hash has to be any number below this number? That as difficulty goes up the number space for a valid hash goes down? Am I anywhere close? Help!

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