#bitcoin is "backed" by the pure attributes of money, which people value in and of themselves. It's not "backed" by work: the "proof of work" is simply to prove the miner has done the work to earn/win the block reward. The "difficulty adjustments" are to maintain the block reward frequency based on changing hashrates.

#bitcoin doesn't really need to be "backed" by anything, just like gold didn't need to be "backed" by anything--it simply *is* money.

You might argue that gold had uses before it was used as money, and had properties that made it a good money, but that it was "backed" by those pre-monetary uses.

OK.

In that case, bitcoin is "backed" by math and cryptography--both of which, I'm sure you would admit, have been useful for a very long time.

Does math have "industrial uses"?