[Docs]: Update State section

docs/architecture/notes.md

@@ -104,7 +104,7 @@ Upon successful verification of the transaction:
 1. The Miden operator records the note’s nullifier as “consumed” in the nullifier database.
 2. The note’s one-time claim is thus extinguished, preventing reuse.
 
-#### Note recipient - restricting consumption
+#### Note recipient restricting consumption
 
 Consumption of a note can be restricted to certain accounts or entities. For instance, the P2ID and P2IDR note scripts target a specific account ID. Alternatively, Miden defines a `RECIPIENT` (represented as a `Word`) computed as:
 
@@ -118,7 +118,7 @@ The [transaction prologue](transactions/kernel.md) requires all necessary data t
 
 For a practical example, refer to the [SWAP note script](https://github.com/0xPolygonMiden/miden-base/blob/main/miden-lib/asm/note_scripts/SWAP.masm), where the `RECIPIENT` ensures that only a defined target can consume the swapped asset.
 
-#### Note nullifier - ensuring private consumption
+#### Note nullifier ensuring private consumption
 
 The note nullifier, computed as:
 

docs/architecture/state.md

@@ -1,91 +1,111 @@
-Miden rollup state describes the current condition of all accounts and notes; i.e. what is currently the case.
+# State
 
-As the state model uses concurrent off-chain state, Polygon Miden aims for private, and parallel transaction execution and state bloat minimization.
+## What is the purpose of state?
 
-Miden's goals include:
+Miden enables secure, private, and scalable transaction execution. By employing a concurrent state model with local execution and proving, Miden achieves three primary objectives: preserving privacy, supporting parallel transactions, and minimizing on-chain data storage (state bloat).
 
-* Notes and nullifiers to ensure privacy of note consumption.
-* Flexible data storage for users who can store their data off-chain or with the network.
-* Parallel transactions executed concurrently by distinct actors.
-* Concurrent state model that allows block production without knowing the full state.
+Miden’s state model focuses on:
 
-Privacy is enforced by a UTXO-like state model consisting of notes and nullifiers combined with off-chain execution using zero-knowledge proofs.
+- **Privacy:**  
+  By using notes and nullifiers, Miden ensures that value transfers remain confidential. Zero-knowledge proofs allow users to prove correctness without revealing sensitive information.
 
-State bloat describes the ever growing state stored in blockchain nodes. Polygon Miden addresses this challenge via its state model that enables concurrent off-chain execution and off-chain storage. Simply put, users can store their own data locally which reduces the burden on the network while integrity is ensured using zero-knowledge.
+- **Flexible data storage:**  
+  Users can store data privately on their own devices or within the network. This approach reduces reliance on the network for data availability, helps maintain user sovereignty, and minimizes unnecessary on-chain storage.
 
-## State components
+- **Concurrency:**  
+  Multiple transactions can be processed concurrently by distinct actors which improves throughput and efficiency.
 
-Miden nodes maintain three databases to describe state:
+Miden’s state model supports a private, secure, and high-throughput environment while also addressing the challenges of state bloat commonly associated with continuously growing blockchain states.
 
-1. A database of accounts.
-2. A database of notes.
-3. A database of nullifiers for already consumed notes.
+## What is state?
 
-![Architecture core concepts](../img/architecture/state/state.png)
+The state of the Miden rollup describes the current condition of all accounts and notes in the protocol; i.e., the current reality.
+
+## State model components
 
-These databases are represented by authenticated data structures that enable easy proof of items added to or removed from a database. This ensures that the commitment to the database remains very small.
+The Miden node maintains three databases to describe state:
 
-Polygon Miden has two databases to capture the note states. The note database is append-only and stores all notes permanently. The nullifier database stores nullifiers that indicate that a note has been previously consumed. Separating note storage into these two databases gives Polygon Miden client-side proving and advanced privacy.
+1. Accounts
+2. Notes
+3. Nullifiers
+
+![Architecture core concepts](../img/architecture/state/state.png)
 
 ### Account database
 
-The latest account states - and data for on-chain accounts - are recorded in a sparse Merkle tree which maps account IDs to account hashes, and account data if needed.
+The accounts database stores the latest account states for public accounts or state commitments for private accounts.
 
 ![Architecture core concepts](../img/architecture/state/account-db.png)
 
 As described in the [accounts section](accounts.md), there are two types of accounts:
 
-* Public accounts where all account data is stored on-chain.
-* Private accounts where only the hashes of accounts are stored on-chain.
+- **Public accounts:** where all account data is stored on-chain.
+- **Private accounts:** where only the hash of the account is stored on-chain.
 
-Private accounts significantly reduce the storage overhead for nodes. A private account contributes only $40$ bytes to the global state ($8$ bytes account ID + $32$ bytes account hash). Or, said another way, 1 billion private accounts takes up only $40$ GB of state.
+Private accounts significantly reduce storage overhead. A private account contributes only $40$ bytes to the global state ($8$ bytes for the account ID + $32$ bytes for the account hash). For example, 1 billion private accounts take up only $40$ GB of state.
+
+The storage contribution of a public account depends on the amount of data it stores.
 
 > **Warning**
->  Losing the state of a private account means loss of funds in a similar manner as a loss of a private key - as the user won't be able to execute transactions. This problem can be mitigated by storing encrypted account state in the cloud or backing it up somewhere else. Unlike storing private keys in the cloud, this does not compromise privacy or account security.
->
->  In the future we hope to enable encrypted accounts where the account data is stored on-chain but in an encrypted format. This is especially interesting for shared accounts like advanced multi-sig wallets.
+> - In Miden, when the user is the custodian of their account state (in the case of a private account), losing this state amounts to losing their funds, similar to losing a private key.
 
 ### Note database
 
-Notes are recorded in an append-only accumulator, a [Merkle Mountain Range](https://github.com/opentimestamps/opentimestamps-server/blob/master/doc/merkle-mountain-range.md). Each leaf is a block header which contains the commitment to all notes created in that block. The commitment is a Sparse Merkle Tree of all the notes in a block. The size of the Merkle Mountain Range grows logarithmically with the number of items in it.
+As described in the [notes section](notes.md), there are two types of notes:
+
+- **Public notes:** where the entire note content is stored on-chain.
+- **Private notes:** where only the note’s hash is stored on-chain.
+
+Private notes greatly reduce storage requirements and thus result in lower fees. They add only $64$ bytes to the state ($32$ bytes when produced and $32$ bytes when consumed).
+
+At high throughput (e.g., 1K TPS), the note database could grow by about 1TB/year. However, only unconsumed public notes and enough information to construct membership proofs must be stored explicitly. Private notes, as well as consumed public notes, can be discarded. This solves the issue of infinitely growing note databases.
 
 ![Architecture core concepts](../img/architecture/state/note-db.png)
 
-As described in [the notes section](notes.md), there are two types of notes:
+### Nullifier database
 
-* Public notes where the entire note content is recorded in the state.
-* Private notes where only a note's hash is recorded in the state.
+Each [note](notes.md) has an associated nullifier which enables the tracking of whether it's associated note has been consumed or not, preventing double-spending.
 
-As with accounts, there is a strong incentive to use private notes as they result in lower fees. This is also beneficial to the network as a private note adds only $64$ bytes to the state ($32$ bytes when it is produced, and $32$ bytes when it is consumed).
+To prove that a note has not been consumed, the operator must provide a Merkle path to the corresponding node and show that the node’s value is `0`. Since nullifiers are $32$ bytes each, the Sparse Merkle Tree height must be sufficient to represent all possible nullifiers. Operators must maintain the entire nullifier set to compute the new tree root after inserting new nullifiers.
 
-Using a Merkle Mountain Range (append-only accumulator) is important for two reasons:
+> **Note**
+> - Nullifiers in Miden break linkability between privately stored notes and their consumption details. To know the [note’s nullifier](notes.md#note-nullifier-ensuring-private-consumption), one must know the note’s data.
 
-1. Membership witnesses (that a note exists in the database) against such an accumulator needs to be updated very infrequently.
-2. Old membership witnesses can be extended to a new accumulator value, but this extension does not need to be done by the original witness holder.
+![Architecture core concepts](../img/architecture/state/nullifier-db.png)
 
-Both of these properties are needed for supporting local transactions using client-side proofs and privacy. In an append-only data structure, witness data does not become stale when the data structure is updated. That means users can generate valid proofs even if they don’t have the latest state of this database; so there is no need to query the operator on a constantly changing state.
+## Additional information
 
-However, the size of the note database does not grow indefinitely. Theoretically, at high tps, it grows very quickly: at $1$K TPS there are about $1$TB/year added to the database. But, only the unconsumed public notes, and enough info to construct membership proofs against them, need to be stored explicitly. Private notes, as well as public notes which have already been consumed, can be safely discarded. Such notes would still remain in the accumulator, but there is no need to store them explicitly as the append-only accumulator can be updated without knowing about all the items stored in it. This reduces actual storage requirements to a fraction of the database's nominal size.
+### Public shared state
 
-### Nullifier database
+In most blockchains, most smart contracts and decentralized applications (e.g., AAVE, Uniswap) need public shared state. Public shared state is also available on Miden and can be represented by the following example:
 
-Nullifiers are stored in a sparse Merkle tree, which maps [note nullifiers](notes.md#note-nullifier-to-ensure-private-consumption) to block numbers at which the nullifiers are inserted into the chain (or to `0` for nullifiers which haven't been recorded yet). Nullifiers provide information on whether a specific note has been consumed. The database allows proving that a given nullifier is not in the database.
+![Public shared state](../img/architecture/state/public-shared-state.png)
 
-![Architecture core concepts](../img/architecture/state/nullifier-db.png)
+In this diagram, multiple participants interact with a common, publicly accessible state. The figure illustrates how notes are created and consumed:
 
-To prove that a note has not been consumed previously, the operator needs to provide a Merkle path to its node, and then show that the value in that node is `0`. In our case nullifiers are $32$ bytes each, and thus, the height of the Sparse Merkle Tree needs to be $256$.
+1. **Independent Transactions Creating Notes (tx1 & tx2):**  
+   Two separate users (Acc1 and Acc2) execute transactions independently:
+   - `tx1` produces **note 1**
+   - `tx2` produces **note 2**
 
-To add new nullifiers to the database, operators need to maintain the entire nullifier set. Otherwise, they would not be able to compute the new root of the tree.
+   These transactions occur in parallel and do not rely on each other, allowing concurrent processing without contention.
 
-> **Note**
-> Nullifiers as constructed in Miden break linkability of privately stored notes and the information about the note's consumption. To know the [note's nullifier](notes.md#note-nullifier-to-ensure-private-consumption) one must know the note's data.
+2. **Sequencing and Consuming Notes (tx3):**  
+   The Miden node executes `tx3` against the shared account, consuming **notes 1 & 2** and producing **notes 3 & 4**. `tx3` is a network transaction executed by the sequencer. It merges independent contributions into a unified state update.
+
+3. **Further Independent Transactions (tx4 & tx5):**  
+   After the shared state is updated:
+   - `tx4` consumes **note 4**
+   - `tx5` consumes **note 5**
+
+   Both users can now interact with notes generated by the public account, continuing the cycle of state evolution.
 
-In the future, when the network experiences a large number of transactions per second (TPS), there will be one tree per epoch (~3 months), and Miden nodes always store trees for at least two epochs. However, the roots of the old trees are still stored. If a user wants to consume a note that is more than $6$ months old, there must be a merkle path provided to the Miden Node for verification.
+### State bloat minimization
 
-## State bloat minimization
+Miden nodes do not need to know the entire state to verify or produce new blocks. Rather than storing the full state data with the nodes, users keep their data locally, and the rollup stores only commitments to that data. While some contracts must remain publicly visible, this approach minimizes state bloat and preserves privacy, since nodes and other users only see hashes of user data.
 
-Operators don’t need to know the entire state to verify or produce a new block. No operator is required to store the entire state.
+This ensures that the account and note databases remain manageable, even under sustained high usage.
 
-At its core, the idea is simple: Instead of storing the full state data with the operators, the users store their data, and the rollup only keeps track of commitments to the data. At least for private accounts, some smart contracts need to be publicly visible. This minimizes state bloat—as the operator doesn’t need to store an ever-growing database, and provides privacy because all other users and the operator only see a hash of other users’ data.
+## Conclusion
 
-That way the account and note databases remain manageable, even at high usage for extended periods of time.
+Miden’s state model lays the foundation for a scalable, privacy-preserving, and user-centric environment. By combining parallelizable execution, flexible data storage, and Zero-knowledge proofs that ensure integrity and confidentiality, Miden addresses many of the challenges of traditional blockchains. As a result, the network can handle high throughput, maintain manageable state sizes, and support a wide range of applications.