For the first part, I'll just say that you vastly overestimate our technical abilities if you think we could even specify the problem of arbitration in such a way that a computer could solve it, nevermind actually implement the solver. You've chosen a relatively simple case (proof of property) but arbitration in general is much more complex.

For hyperinflation, I have been born and continue to live in Romania, a country that went exactly through that in the 90s, to the extent that a loaf of bread that was initially maybe 10-20 ROL would cost 10k ROL. I remember as a child not being able to afford popcorn when going to the park with my grandparents, or my grandfather selling his old car and buying the family's first color TV with the money. I remember living as a family of four in a 2 bedroom apartment (my parents had their bedroom, while my brother and I shared the livingroom until we were in our twenties).

But that wasn't the problem of our economy, it was just what kept it (barely) working! If we couldn't go to hyperinflation, we would have simply not payed salaries or other debts.

The problem of the economy was that we had sold most of our communist-era industry for parts in a quest for 'privatization' and a 'free market', and were left not being able to produce locally or export almost anything. Even today, we are a temperate, extremely water-rich plains country that imports a good segment of its food - to the absurd degree that we are importing fruit from Holland and Israel among others.

Of course, poor governance and corruption played a huge role as well. The government promising ever higher pensions and salaries for state employees, the works. But those problems would not have gone away if people were getting bitcoin instead of Lei.

Scarcity is a problem of production, not of money. Money itself is almost immaterial. If we could produce enough food, water, energy, cars, fridges, computers, furniture etc. for every single person on Earth, and all of their children, to have all they need at the same time, we could renounce money entirely, Star Trek style.

You have a terrible understanding of economics (and of the plight of people who lived through hyperinflation, like myself) if you think that people in a country experiencing hyperinflation would fare any better if they could trade in BTC instead of the de-valued fiat. The only ones who would be better off are the rich, whose reserves of cash would not suddenly lose their value. But people who live off wages would see pay cuts and eventually just stop getting payed if the currency were forced to a global standard instead of suffering inflation.

Note: there may be cases where a country, often a dictatorship, simply prints money out of stupidity, and also forces the population not to trade in foreign money. This is not the most common cause of hyperinflation, and it is significantly better fixed by BTC, since that is more or less as easy or hard to outlaw as the ownership of dollars.

Oh, and guess what - the country got richer and better without the currency having to go through deflation! In fact, bread still costs 10-20k ROL, and a PC still costs 40-50 million ROL, we just 're-branded' our currency to RON at a fixed 1:10k RON:ROL exchange rate to make the numbers more manageable. We started having productive industries with products that others wanted to buy, and governance got better (we still have huge problems and some of the poorest regions in the EU, but that is besides the point).