You seem to be making up your own definition of the Layers 😜 But even within your definition, Cashu tokens are a "coupon" or "currency" - because they are a bearer asset, pre-funded by bitcoin (via minting)... which is redeemable on demand by melting back to bitcoin. In the generally understood definition of Bitcoin layers, Cashu is a Layer 2, because it is a protocol built on top of L1 core to improve scalability, transaction speed, and functionality without altering the L1 code. The fact it integrates with Lightning doesn't change that, the same way that Liquid integration with Lightning doesn't make it L3 either. A Cashu mint COULD conceivably mint and melt directly to the L1 chain. It doesn't currently for speed of settlement, but it could. NUT-04/05 are flexible in that regard. L3 doesn't really exist for Bitcoin - it is the "application layer" - for DApps like you'd find in ETH or SOL.

I am not sure where you are pulling the layer definitions from but these are monetary terms not digital asset specific ones. Money scales in layers Layer 1: The bearer asset with the express purpose of storing value. Layer 2: The coupon/ currency that is redeemable for the bearer asset on demand from the coupon issuer. (In the case of Lightning the issuer is either the party or counter-party) Layer 3: The credit token. This historically is where loans and financial stress is added to the lower layers upon calls to redeem. Because the credit tokens by definition create more tokens than assets outstanding. These are based on reputation and trust to create more value than held in the credited currency. I know that cashu can be minted to layer 1 but it is less secure than lightning so, It is not used that way. Issuing cashu tokens on lighting is creating credit tokens redeemable for lightning/liquid which is then redeemable for bitcoin. There is nothing stopping a mint from issuing more credit that lightning held and redemption is based soley on the reputation and trust in the mint. Cashu is credit.