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.