Bitcoin-backed national currency

[vfCM]

If Bitcoin is truly a new global store of value, it will play a role similar to that played by gold. And in the past, many currencies were backed by gold reserves along with convertibility to gold.

We might imagine contexts where a nation might issue a currency backed by Bitcoin in a similar manner, with reserves of Bitcoin and convertibility into Bitcoin on demand.

For example, a country with a hyperinflated currency might introduce a new, Bitcoin-backed currency to stabilize values, but minimally changing the mode of interaction with the currency. It could still be withdrawn as coins and paper notes, it could still be stored as numbers in a bank database, checks could still be written perhaps and debit cards used drawing on an account with the new currency, just as with the old.

But the value of the new currency would be due to its relation to Bitcoin. It's no longer a fiat currency, but a "Bitcoin standard" currency. (I know that term has been used in a different sense elsewhere, thus the quotes.)

Assuming that such a thing might be desirable, how might it be done?

What would be the best implementation of a "Bitcoin standard", with a currency backed by Bitcoin reserves and convertible into Bitcoin?

My thoughts so far:
Each unit of currency would correspond to a UUID and signature, readable over QR code, NFC, or whatever. (NFC-enabled coins and paper are already available.)

The UUID would be signed using a government public/private key pair, making counterfeiting difficult. Maybe even the key pair associated with the address holding the relevant Bitcoin reserves.

The government would publish one-to-one mappings of UUIDs to coins in the government's proven Bitcoin reserves.

To allow reclamation of reserves assigned to lost or destroyed currency, an expiration date will be enforced, such that currency is no longer legal tender after $N years. (100?)

The key problem is the possibility of double-minting, creating more than one piece of currency with the same UUID, thus leaving currency not fully backed by Bitcoin.

Even though Bitcoin itself solves the double-spending problem, it seems that a Bitcoin-backed currency can still "double mint".

At least, I haven't thought of a way around it yet.

One approach would be to try to incentivize good behavior by the mint through a public clearing-house of salted, hashed UUIDs. By observing institutions' reports of holdings, duplicates could be detected.

Thoughts appreciated.

[Solosanz]

We already have this, they're Wrapped Bitcoin and Bitcoin BEP2, both tokens are the new currency that claimed to peg with Bitcoin price. Do I trust it? nope, do you trust it?

I don't feel secure when I hold a centralized currency because sooner or later it will become worthless because it's controlled by a single entity and there's a chance to gets hacked.