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 I love the idea of having paper money that is somehow Bitcoin Satoshis for those out of cell service locations  
 well, if you have the wallet and you can unlock it and you have the key you can sign a TX and pass it to someone who gave you the address to send it to and it acts a lot like a cheque

yeah, it's a cheque! an e-cheque

it can bounce, as in, they can spend it before you broadcast it, but it's totally analogous to a cheque 
 is this possible with lightning transactions too? 

is this somethign that can be printed out as a QR code?

I'm just imagining myself reading in bitcoin checks into an ATM or scanning them with my phone. 
 you can always make an invoice and copy it and give it to someone in physical form, on a usb stick or printed as a QR code

but that's an invoice, the signed payment is a payment (payment request, actual payment)

lightning payments in this payer-initiated format are called "keysend" or "AMP" and have to be submitted to the payer's lightning node to work, meaning access to the LN RPC, which is not the usual situation for a lightning node (usually access to that RPC is private to the person using it, for security reasons). 
 Keysend is neat. how do you feel about the bolt12? 
 well, it's something that would also enable a kind of offline cheque payment mechanism too, that's its whole purpose 
 bolt 12 is like a comitment to pay that can be redeemed by the receiver

it's a very cool thing, that has only got contingent risk upon the closure of the channels the bolt 12 offer contains