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This is for load balancing between several public nodes by including route hints for all the nodes in the invoice. How would that give you deniability that you recieved a payment?
Use your imagination! It requires a custom implementation AFAIK... Ask your AI agent to build it for you!
You can use this exact approach to "load balance" between several (or just one) "private" nodes (which don't actually exist). Just generate a fake channel ID, fake node pubkey, etc. for your invoice and run an HTLC interceptor on the "load-balancing" node that intercepts and claims the payment using the pre-image you created for your special bolt11 invoice.
This "phantom invoice" shows your "actual" node as a route-hint -- not the destination.
So you can plausibly claim that your node did not receive the payment, you just routed it to the private node in the invoice using your private channel (which does not have to be backed by a real UTXO onchain).
Most wallets don't actually verify that the private channel in a route hint is real.
You can encode a bolt11 invoice (supported everywhere) in such a way that it gives you deniability that you received the payment.
https://lightningdevkit.org/blog/introducing-phantom-node-payments/