> Bitcoin literally stops existing if you stop believing in it.
That is the case for countless things. Is a corporation a real thing or a belief? Where is the physical entity Facebook or the physical entity Apple? Is it the people working for them? Their logo? Their contracts? It's all that and a collective belief in an abstract entity. That's true for fiat or states too, even if that belief can be enforced through e.g. army, that doesn't change the fact that's is a collective belief in something that has no material reality.
But fiat has taxes, and state-backed violence and jails.
If your state demands your taxes be paid in FIAT, no matter what you wan't, you'll be paying in FIAT (or fined, or in jail, or depending on the circunstances maybe dead).
Say someone wealthy wants to escape the taxman and spends all their fiat buying things that "have value as long as people believe it has value", like land, stocks, jewelry, art works, antique cars.
When the taxman comes knocking on their door, do you think this person will escape by saying "sorry, I don't have fiat available to pay for the taxes, come back next year!"? No, the taxman will respond by either seizing their assets or forcing the person to liquidate into fiat.
What makes Bitcoin (or crypto) different in that regard?
What's with the capitals? The "fiat" in "fiat money" is neither an acronym nor an Italian automobile manufacturer. (The Italian automobile manufacturer, OTOH, is an acronym, just like "OTOH". One stands for "on the other hand"; the other for "Fabricca Italiana de Automobili, Torino".)
that's a stretch of what fiat means. Fiat backing is not just the belief in the backer's ability to back it. Fiat specifically requires government/authority.
bitcoin acts more like a commodity than fiat. Bitcoin is backed by the laws of mathematics, rather than laws of nature (which is the case for gold).
Fiat does not require a government or authority. Fiat money simply means it's not commodity money. Commodity money means the money is backed by a commodity, i.e. the issuer promises to redeem the notes for a certain quantity of a commodity.
Your claim that bitcoin is not fiat because it's backed by the laws of mathematics makes as much sense as claiming that the dollar is not fiat because it's backed by the printing press. This is not what 'backed' means in the context of money.
That is the case for countless things. Is a corporation a real thing or a belief? Where is the physical entity Facebook or the physical entity Apple? Is it the people working for them? Their logo? Their contracts? It's all that and a collective belief in an abstract entity. That's true for fiat or states too, even if that belief can be enforced through e.g. army, that doesn't change the fact that's is a collective belief in something that has no material reality.