feat(docs): Notes page (#11746)

Closes AztecProtocol/dev-rel#455

---------

Co-authored-by: josh crites <jc@joshcrites.com>
Co-authored-by: josh crites <critesjosh@gmail.com>

docs/docs/aztec/concepts/storage/notes.md

@@ -0,0 +1,29 @@
+---
+title: Notes (UTXOs)
+sidebar_position: 5
+tags: [notes, storage]
+---
+
+import Image from "@theme/IdealImage";
+
+The [state model page](./state_model.md) explains that there is a difference between public and private state. Private state uses UTXOs (unspent transaction ouputs), also known as notes. This page introduces the concept of UTXOs and how notes are abstracted on Aztec.
+
+## What are notes?
+
+In an account-based model such as Ethereum, each account is typically associated with a specific location in the data tree. In a UTXO model, each note specifies its owner and there is no relationship between an account and data's location in the data tree. Notes are encrypted pieces of data that can only be decrypted by their owner.
+
+Rather than storing entire notes in a data tree, note commitments (hashes of the notes) are stored in a merkle tree, aptly named the note hash tree. Users will prove that they have the note pre-image information when they update private state in a contract.
+
+When a note is updated, Aztec nullifies the original commitment in the note hash tree by creating a nullifier from the note data, and may create a new note with the updated information, encrypted to a new owner if necessary. This helps to decouple actions of creating, updating and deleting private state.
+
+<Image img={require("/img/public-and-private-state-diagram.png")} />
+
+Notes are comparable to cash, with some slight differences. When you want to spend $3.50 USD in real life, you give your $5 note to a cashier who will keep $3.50 and give you separate notes that add up to $1.50. Using private notes on Aztec, when you want to spend a $5 note, you nullify it and create a $1.5 note with yourself as the owner and a $3.5 note with the recipient as the owner. Only you and the recipient are aware of $3.5 transaction, they are not aware that you "split" the $5 note.
+
+## Abstracting notes from from apps & users
+
+When using the Aztec protocol, users may not be aware of the specific notes that they own. Their experience should be similar to Ethereum, and should instead see the amount of their assets inside their account.
+
+This is accomplished through the smart contract library, Aztec.nr, which abstracts notes by allowing developers to specify custom note types and also helps users discover all of the notes that have been encrypted to their account and posted to the chain. This means they can specify how notes are interacted with, nullified, transferred, and displayed.
+
+To understand note abstraction in Aztec.nr, you can read the [Build section](../../../developers/guides/smart_contracts/writing_contracts/notes/index.md).

docs/docs/aztec/concepts/storage/state_model.md

@@ -14,24 +14,13 @@ Internal to the Aztec network, public state is stored and updated by the sequenc
 
 ## Private State
 
-Private state must be treated differently from public state and this must be expressed in the semantics of Aztec.nr.
-
-Private state is encrypted and therefore is "owned" by a user or a set of users (via shared secrets) that are able to decrypt the state.
+Private state must be treated differently from public state. Private state is encrypted and therefore is "owned" by a user or a set of users (via shared secrets) that are able to decrypt the state.
 
 Private state is represented in an append-only database since updating a record would leak information about the transaction graph.
 
 The act of "deleting" a private state variable can be represented by adding an associated nullifier to a nullifier set. The nullifier is generated such that, without knowing the decryption key of the owner, an observer cannot link a state record with a nullifier.
 
-Modification of state variables can be emulated by nullifying the state record and creating a new record to represent the variable. Private state has an intrinsic UTXO structure and this must be represented in the language semantics of manipulating private state.
-
-### Abstracting UTXO's from App's / Users
-
-The goal of the Aztec.nr smart contract library is to abstract the UTXO model away from an app user / developer, contract developers are the only actor who should have to think about UTXO's.
-
-This is achieved with two main features:
-
-1. Users sign over transactions, not over specific UTXO's
-2. Aztec.nr contracts support developer defined `unconstrained` getter functions to help dApp's make sense of UTXO's. e.g `getBalance()`. These functions can be called outside of a transaction context to read private state.
+Modification of state variables can be emulated by nullifying the state record and creating a new record to represent the variable. Private state has an intrinsic UTXO structure.
 
 ## Further reading
 

docs/docs/developers/guides/smart_contracts/writing_contracts/notes/index.md

@@ -4,4 +4,6 @@ sidebar_position: 3
 tags: [contracts, notes]
 ---
 
-Notes are the fundamental data structure in Aztec when working with private state. In this section there are guides about how to work with `AddressNote`, `ValueNote`, and custom notes in Aztec.nr. You can learn more about notes in the [concepts section](../../../../../aztec/concepts/storage/state_model.md).
+Notes are the fundamental data structure in Aztec when working with private state. Using Aztec.nr, developers can define note types which allow flexibility in how notes are stored and nullified.
+
+In this section there are guides about how to work with `AddressNote`, `ValueNote`, and custom notes in Aztec.nr. You can learn more about notes in the [concepts section](../../../../../aztec/concepts/storage/notes.md).