Yes, but the merchant has to have a way to check for double-spending, or otherwise verify that the signed txn they have been given represents money that can be "taken to the bank".

Checking the signature on some blob that says "this be money" is not enough.

True. But if the system is implemented by a country this could be implemented using the law system and insurances.

For example, when each transaction is done, both parties might keep a cryptographic proof which they are required to submit once they are online again.

Failing to submit could result in a small fine (to encourage submission) and double spending which can then be detected could result in a large fine (or even a prison sentence), for example.

There is, perhaps, a privacy issue, just like with blockchain. But it's not more of an issue than online transactions.

You don't need a blockchain for that, see how old credit cards worked without network access.

I didn't say you need a blockchain. I just said a cryptographic protocol (mostly offline and unrelated to blockchain) would help to automatically and quickly detect and proof fraud.

The offline credit card system does not proof fraud but just has insurance.

I figure you can ‘solve’ it socially and legally by treating double spend while offline the same as writing a bad check. Recipients of offline transactions knowing the risk would limit it to small amounts and or emergencies.

Card networks have supported this mode of operation for a long time.

card networks can do a lot of things, doesn't mean issuers and merchants are using it.

What cryptocurrencies work offline without Internet access to the ledger?

All of them? As long as eventually the connection is restored and the transaction can propagate over the network.

The point of the ledger is to prevent double-spending.

Offline payment specifically allows double-spending. If you have offline payment, you don't need a ledger at all; you can just use PGP.

Those transactions simply won't be accepted. Sucks for the seller, but how to deal with that mess is an issue that has to be solved on an upper layer by ToS or laws.

Also, "all of them"-- as in, when you pay multiple parties offline with the same exact crypto-dollar, all of them will get paid.

Even better, when you're back online the network will run a sanity check to protect against the evils of inflation.

(Note: inflation-check fees will vary between 0 and 100% per payee.)

Doesn't Solana require the hash of a recent (~ 1 minute) block before signing?

They do, but the payee accepts risk.