Account Tree

How Arweave stores the account tree in memory: the relationship between the account tree, the patricia tree, the diff DAG, the sink, diffs, and the reconstruction of the previous, following, and uncle representations.

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Cast of characters

Concepts

Concept	What it is
account tree	a block's full state, the mapping address → {balance, last_tx, denomination, mining_permission}. One per block
patricia tree	the radix-trie structure that implements one account tree with shared-prefix paths and content-hashed nodes; its root hash is the block's wallet_list
sink	the current account tree, the one representation stored as a full tree, resting at the chain tip. Every other, older, tree exists only as a diff against it. It moves forward as new blocks extend the tip via set_current, and backward to hash a block on a competing fork, serve a historical get_chunk, or reach the fork point during a reorg. See Layer 4
diff	the edge between two consecutive blocks, a map {address → new value | remove} of the accounts that changed from one to the next, older to newer
diff DAG	the whole graph of block states wired together by diff edges. It spans the blocks the node still keeps, a recent window up to the current tip, pruned and not reaching back to genesis, plus any forks it stores. One node is kept as a full tree, the sink; every other exists only as the diffs along the path to it, so all are reachable from that one copy
parent, child	adjacent blocks: a child block extends its parent
sibling	two blocks with the same parent, a fork
ancestor, descendant	a block reachable by following parents is an ancestor, one reachable by following children is a descendant
uncle	a sibling of an ancestor, a block on a competing fork. For example B1' is B2's uncle: the sibling of B2's parent B1

Modules

Module	Role
ar_account_tree	gen_server manager of the account tree, the single serialized point of access. Owns the ETS table that holds the sink and owns the diff DAG, and drives every operation on them: moving the sink, applying and reversing diffs, and persisting
ar_patricia_tree_core	the shared patricia tree algorithm — insert, get, delete, hash, iterate — parameterized by a storage backend. The two variants below supply storage and delegate here
ar_patricia_tree_ets	the ETS storage backend that backs the sink: a single mutable ETS table holding one full tree, mutated in place to represent whichever block's tree the sink currently points at
ar_patricia_tree	the immutable, map-based storage backend, used where a standalone tree is needed: genesis, peer download, JSON serialization, disk reads
ar_diff_dag	the diff DAG: stores the diffs as edge labels and the sink pointer

To address a potential naming confusion, ar_wallet manages cryptographic wallets. It generates keypairs, translates public keys to wallet addresses, and verifies signatures, and is not directly related to account management. The connection is that wallet addresses are keys in the account tree, produced from public keys via the ar_wallet:to_address functions. For example, ar_wallet:to_address(TX#tx.owner) returns the address the transaction takes funds from. A transaction can send AR to any 32-byte target, which ends up as a key in the account tree but may not have an actual cryptographic wallet behind it. The protocol also used to allow shorter target values, so the account tree has an entry for the <<>> empty-binary key. B#block.wallet_list is the legacy field name for the account-tree root hash.

Why a patricia trie?

The account tree is re-hashed every block, yet a block changes only a handful of accounts out of potentially millions. Therefore, we need a structure that scales well with the growing number of total entries while the number of updated entries remains below a fixed upper bound. Currently the maximum number of updates possible per block is 2002 - 1000 tx source addresses + 1000 tx target address + 1 reward address + possibly 1 banned address.

The core strength of the patricia tree is that it does not require rebalancing:

• Depth is capped by the key length. Addresses are 32 bytes and the trie branches one byte at a time, so any root-to-leaf path crosses at most 32 branch nodes. Traversing the path from root to leaf takes O(32).

• Width is capped by 256 so hashing intermediate nodes is O(256).

• In practice the tree is far shallower. Addresses are hashes of public keys, so they are distributed nearly uniformly. The expected depth is ≈ log256(n), about 3 bytes deep for millions of accounts.

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Example

Consider the following chain state:

• B0, B1, B1', B2 are blocks. The chain forks after B0: B1 and B1' are siblings, and B2 extends B1, the tip.

• a, b, c are accounts. Each is a 4-tuple {balance, last_tx, denomination, mining_permission}, but the diagram shows only the balance for readability, so a:5 means account a has balance 5.

        B0  {a:10, b:20}
       /  \
     B1'   B1   {a:5,  b:25}
   {a:7,    \
    b:20,    B2  {a:8, b:22}   ◄── tip
    c:3}

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"Account tree" is the concept; "patricia tree" is the structure

B0's account tree is logically just a map from each account's address to its value:

a → {balance:10, …}
b → {balance:20, …}

It is stored as a patricia radix trie keyed by that address, a ≤ 32-byte hash. Accounts whose addresses share leading bytes share the beginning of the path from the root to the leaf. To compute the root hash, we hash each node's contents, and the hashes combine recursively to produce the root, the block's wallet_list:

                (root) #h0
                   │
        a, b share a leading prefix
                   │
                (inner) #h1
               /          \
           leaf a        leaf b
          {balance,…} #ha    {balance,…} #hb

   root hash #h0  ==  B0's wallet_list

The whole trie lives in one mutable ETS table, ar_patricia_tree_ets, or one immutable map, ar_patricia_tree, both driven by the shared algorithm in ar_patricia_tree_core.

Node structure and how each kind is hashed

Every node is a tuple carrying its parent, its set of children, its cached hash, the path prefix, and an optional value. This is how compute_hash treats each of the three different inputs:

• Leaf: a value and no children. The value is the account itself, stored as a tuple, {balance, last_tx} for accounts not updated since the re-denomination upgrade, and {balance, last_tx, denomination, mining_permission} for the rest.

• Internal node: children hashes and no value of its own. Its hash combines its children's hashes. A node with a single child is compressed, taking that child's hash unchanged so the intermediate step adds no hashing.

• Internal node that also holds a value: both children and a value. This arises when one stored key is a proper prefix of another, so the shorter key's node sits on the path to the longer one. Two 32-byte addresses can never nest this way, but the protocol historically allowed targets shorter than 32 bytes, and such a short key can be a proper prefix of a full address. It is hashed by first hashing the node's own value as if it were a leaf, then combining that leaf hash together with the child hashes into the node hash, so the value participates as one more entry alongside the children.

The hashing is defined by ar_block:wallet_list_hash_fun, and the combining step goes through ar_deep_hash, which takes a list and folds it into one hash. An internal node's hash is ar_deep_hash of the list of its children's hashes in key order, with the node's own value hash prepended when it has one. A legacy {balance, last_tx} leaf is hashed by passing the list [address, balance, last_tx] to ar_deep_hash. The current four-field leaf is the exception: its fields are length-prefixed and concatenated into a single preimage hashed with SHA-384 directly, not through ar_deep_hash.

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The diff DAG: one full tree (the "sink") + diffs on the edges

   ar_diff_dag  (lives in the gen_server State)
   ┌──────────────────────────────────────────────────┐
   │                                                    │
   │      B0 ───diff{a,b}─── B1                         │
   │      │                   │                         │
   │  diff{a,c}           diff{a,b}                     │
   │      │                   │                         │
   │     B1'                  B2  ◄═══ SINK             │
   │   (virtual)          (fully stored: the ONE        │
   │                       real ETS trie)               │
   └──────────────────────────────────────────────────┘

• Each DAG node is a block's account-tree representation, identified by its root hash, B#block.wallet_list.

• Only the sink, B2, is a real, full patricia trie in the ETS table. Every other node is virtual, existing only as a diff relative to a neighbour.

• An edge diff is small: diff(B0→B1) = {a: 10→5, b: 20→25}, just two accounts.

So instead of 4 tries, the node stores 1 trie for B2 plus 3 little diffs.

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Reconstructing another representation: walk edges, apply and reverse diffs

The sink can be moved to any DAG node by walking the path and mutating the one trie. Reading B0 while the sink is at B2, reverse each diff as you climb:

 sink = B2:  {a:8,  b:22}
   reverse diff(B1→B2) {a:5→8,  b:25→22}  ──►  {a:5,  b:25}   (== B1)
   reverse diff(B0→B1) {a:10→5, b:20→25}  ──►  {a:10, b:20}   (== B0)
 sink now holds B0 in full  ✓

Reaching the uncle B1', reverse to the common ancestor B0, then apply down the other branch:

 B2  ──reverse──►  B1  ──reverse──►  B0  ──apply diff(B0→B1')──►  B1'
                                          {a:10→7, c:∅→3}
 result: {a:7, b:20, c:3}   (== B1')  ✓

Why moving the sink stays cheap: cached intermediate hashes

Each trie node caches its own hash alongside its contents. Applying or reversing a diff as the sink walks an edge goes through insert and delete, which mark only the touched root-to-leaf paths no_hash and leave every other node's cached hash intact. The next compute_hash recomputes a node only when its hash is no_hash; a node that still carries a hash is returned as is, and its whole subtree is skipped.

So re-hashing after the sink moves one edge costs work proportional to the accounts on that edge's diff, not to the size of the tree. It is the same locality that makes a single block cheap to hash, now applied per hop. Walking several edges to reach a distant representation re-hashes only the union of the paths those diffs touched, never the untouched subtrees between them.

The snapshot mechanism used for non-tip work leans on the same caching. While a snapshot is active, every write records the pre-snapshot value of the one node it overwrites, so an excursion accumulates entries only for the nodes it actually touches, the paths along the diffs it walked. snapshot_restore then rewrites just those nodes back to their recorded values and leaves the rest of the tree alone; it does not rebuild the tree. Because each recorded value is the node's exact prior bytes, its cached hash comes back with it, so the tip is restored clean with nothing left to re-hash.

Trade-off: memory footprint against recomputation on fork switches

Cached hashes live only in the sink, and only one representation is the sink at a time. Every hashing of a non-tip representation, such as validating a block on a competing fork with apply_block or add_wallets, runs inside a snapshot: it moves the sink there, hashes, then rolls the sink back to the tip and discards the hashes it just computed. A read-only excursion like get_wallet_list_chunk takes the same round trip but only reads a range, so it moves the sink without hashing at all. Either way the work for a fork is never retained: reaching that fork again re-applies every diff along the path from the tip, re-hashes the paths each block on the way touches when a root hash is needed, and none of that work is reused on the next request, which repeats all of it.

This is a deliberate choice of a smaller memory footprint over less computation. The node keeps exactly one full tree resident and pays to recompute any other representation on demand, however many times it is asked for. The opposite choice would cache the hashes, or whole materialized trees, for several representations, so repeated fork switches reuse earlier work and skip the re-hash, at the cost of holding more than one tree's worth of nodes in memory. Arweave currently favours the smaller footprint, on the expectation that a given fork is rarely hashed often enough for the recomputation to outweigh the memory a cache would cost.