Routed Payments
Let's introduce Charlie, who trusts Bob up to 50,000:
<charlie>: TRUST <bob> 50000
and Derek, who trusts Charlie up to 70,000 satoshis:
<derek>: TRUST <charlie> 70000
Now the Cassis server is aware of all these trust relationships, making it possible for it to compute a route between Alice and Derek, through which a payment of up to 50,000 satoshis can be routed.
Suppose Derek has an online store that sells hats and he wants to accept payments using Cassis, so Derek can either create a new keypair for his store and trust his own personal key with it -- or, for simplicity, he can just use his personal keypair for the store.
Now when Alice visits Derek's Hat Shop webpage and clicks to buy a hat she will be presented with an invoice for 24,277 satoshis, which she fulfills:
<alice>: TRANSFER <derek> 24277
Since there is a route available the payment gets computed instantly and now the balances read like
<alice> owes <bob>: 27940
<bob> owes <charlie>: 24277
<charlie> owes <derek>: 24277
What do we do with all these debts now?