> If the value gets low enough the network won't even work and you can't transfer them

If the value goes to zero ($0.000), then yes, the network would probably not work (but just probably, it worked before when it was worth zero, maybe could work again in the future if that happens), but how you reach the conclusion that if it's >0 but very low, it wouldn't work?

As long as there are at least one miner online, there will be transfers happening. And even if you earn zero, some will probably run a miner. BitTorrent kind of proves you can still build useful systems even if the incentive is zero.

I think if the value drops then the security requirements would also drop. And all the existing UTXO's that were already mined when the difficulty was high would also stay secure, so they'd be comparable to Gold bars that could be stored for thousands of years without spending any energy.

> all the existing UTXO's that were already mined when the difficulty was high would also stay secure

Not really, because if there's not exactly one social consensus chain, then you can't prove you're the only owner of anything.

What do you mean by "social consensus chain"?

Any UTXO that you create now, when the mining difficulty is quite high, is going to have a very high security, even if the mining difficulty goes down afterwards.

E.g. right now the social consensus is that the longest chain _minus the top 5_ blocks is the "settled" consensus of committed transactions. If you own the coin in a block 6 deep, then you can prove it.

As the difficulty gets lower, the number of transactions to drop from the top gets higher, and maybe also less certain.

It makes no difference about the mining difficulty in the past. If double-spends are possible _today_ then you can't ever prove you own the coin, regardless of whether you could do it in the past.

But now the question is "is this aesthetic value high enough to sustain the network?". Maybe, maybe not. But it's no longer a mathematical certainty, which is what this paper is about.