chore(doc): some work on documenting everything better

README.md

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+Mugraph (pronounced *"mew-graph"*) is a Layer 2 Network for the Cardano blockchain for untraceable payments with instant finality.
+
+By **untraceable**, we mean that, inside a given group $A$ of users:
+
+- All transactions between users inside $A$ are untraceable, meaning senders and receivers are not bound in any way.
+- All transactions to users outside $A$ come from a single, shared identity for all group participants.
+
+This shared identity comes from **Delegators**, behaving similarly to Payment Networks in the traditional banking system, like Paypal, Venmo or CashApp, but with some crucial distinctions:
+
+- Delegates hold funds in a fully auditable Smart Contract Vault, held in the Layer 1.
+- Delegates can not spend user funds without their authorization.
+- Delegates are **blind**, meaning they don't know who is transacting.
+- Delegates provide **group anonimity** for their users, signing transactions on behalf of them.
+
+An user can, and usually will, hold balance in multiple Delegates at once, and they do not need to have balance in a Delegate to receive payments there.
+
+Essentially, a Delegate has four main roles:
+
+1. **Handle Payments:** invoices are settled by payments, which can be settled by either a Layer 1 transaction or an internal transaction inside the Delegate itself.
+1. **Handle Commits:** users can commit the state of the Vault on the blockchain to mint funds inside the delegate.
+1. **Sign External Transactions:** delegates can sign external transactions on behalf of users, in order to route payments between them and the outside world.
+
+## Glossary
+
+| Symbol | Description |
+|--------|-------------|
+| $G$    | A generator point in the Ristreto25519 curve. |
+| $n$    | A Note, blindly signed by the Delegate and ready to be used. |
+| $n'$    | A Note with a blinded nullifier to be sent to the Delegate for signing. |
+
+## Types
+
+### Notes
+
+TODO.
+
+### Blinded Notes
+
+TODO.
+
+## Operations
+
+### $F$: Fission
+
+Splits a note into two blinded notes. It is defined as:
+
+$F(n, i) \mapsto \{ n'_o, n'_c \}$
+
+Where:
+
+- $n$ is the input note to be slit in two
+- $i$ is the output amount requested by the operation
+- $n'_o$ is a blinded note for the amount $i$
+- $n'_c$ is another blinded note for the amount $n_i - i$, where $n_i$ is the note amount.
+
+### $F'$: Fusion
+
+Joins two notes with the same asset id and server keys into a single one. It is defined as:
+
+$F'(n_0, n_1) \mapsto n'$
+
+Where:
+
+- $n_0$ and $n_1$ are the input notes to be fused
+- $n'$ is a blinded node for the amount $n_0i + n_1i$
 
 Mugraph (pronounced *"mew-graph"*) is a Layer 2 Network for the Cardano blockchain for untraceable payments with instant finality. It is very simplified in both operations and architecture, meant to be easy to integrate anywhere.