A bearer asset is not redeemable for anything. That's the definition of an asset. An asset IS the thing. So, you keep using that term incorrectly.
As far as fractional printing of dollars to gold reserves, yes currency doesn't preclude over-printing. But cashu tokens are not redeemable for the asset like dollars were. They are redeemable for lightning which is THEN redeemable for Bitcoin.
Cashu is more akin to (pre 1971) somone depositing dollars to a bank in exchange for credit to be spent outside of business hours. You can then redeem the credit for dollars, THEN redeem those dollars for gold.
Again, anything above the first layer is not an asset, it is a liability.
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You didn't want to start a "big thing", but keep doubling down. So kudos for that - but your underlying assertion is still wrong. I'll have one last go at explaining, in case it's a semantics issue, but otherwise we're done.
"Bearer" = denotes ownership by possession.
"Asset" - thing of value. Can be cash/cash equivalent or even credit.
Bitcoin private keys are an example of a bearer asset (NYK-NYC). They’re not the Bitcoin itself—they’re the proof of ownership and control over it, held by possession. Not a credit or liability.
Lightning *is* Bitcoin. Not credit. Not "backed" anything. The on-chain Bitcoin is locked in an HTLC in the Lightning channel. Only the accounting is abstracted.
If a mint closed the underlying Lightning channel, they would then unlock and receive the bitcoin on-chain according to the accounting. The abstraction of Lightning is simply a protocol, not a separate asset.
Cashu on Lightning is therefore a 1:1 Bitcoin-backed asset.
So your dollars → credit → gold analogy is just plain wrong.