A key is an account
In this plan your account is not on a server; it is your Lana key on your phone (the same key you sign in with). An account in EUR, GBP or USD is only the sum of signed records that name that key. A server can show you a balance — it will not hold it, and it will not be able to pay in your name.
Notes, not a ledger
Every payment is a note the giver signs: to whom, how much, in which currency, and which of my notes came before. Each member's notes form a chain — one per currency. Two notes pointing at the same previous note are a fork — a double spend that everyone can see. Gravity — the morning tide into the Common Good — is not anyone's note; it is a rule anyone can recompute from the notes, and the sum of all accounts still stays zero: gravity lowers the member's account and raises the Common Good's by the same amount.
Relays keep the notes
Lana already has relays that hold the ecosystem's records. Notes are one more kind of record on the same relays. Every member carries their own notes; the relays carry everyone's. If the app disappeared tomorrow, the books could be rebuilt from the relays on any other computer in minutes — nothing is lost.
Who holds your money — in public
Money you pay in is not a number in a database. It is a certificate signed by a money holder (custodian): "I hold 1 000 EUR for this key." The part of your wave that you paid in with money is the sum of such certificates, and everyone can see which custodian stands behind it. Custodians are listed in a public registry, publish reserve attestations (money held ≥ certificates issued, with the evidence linked; signed by the custodian itself or by an auditor it names — until an auditor signs, it is the custodian's own word), and a wave can move from one custodian to another. A computer cannot prove that a custodian has the money — that is why everything about them is public and checkable, so trust rests on evidence, not on a name.
Circle nodes countersign; circles federate
A circle — a community — runs a node, the scribe. It cannot forge a note (it has no keys), but it checks that the giver can still give that much and that the receiver is a member of a circle, and countersigns; the receiver trusts the countersignature. Circles recognise each other through a short federation list; a payment across circles is one note with two countersignatures. The address carries the circle code, like an IBAN carries the bank, so nothing has to be looked up globally.