Capella -- The Beacon Chain

Introduction
Custom types
Constants
- Domain types
Preset
Configuration
Containers
- New containers
- Extended Containers
Helpers
- Beacon state mutators
  - withdraw_balance
- Predicates
Beacon chain state transition function
- Epoch processing
  - Full withdrawals
  - Partial withdrawals
- Block processing
Testing

Introduction

Capella is a consensus-layer upgrade containing a number of features related to validator withdrawals. Including:

Automatic withdrawals of withdrawable validators.
Partial withdrawals sweep for validators with 0x01 withdrawal credentials and balances in excess of MAX_EFFECTIVE_BALANCE.
Operation to change from BLS_WITHDRAWAL_PREFIX to ETH1_ADDRESS_WITHDRAWAL_PREFIX versioned withdrawal credentials to enable withdrawals for a validator.

Custom types

We define the following Python custom types for type hinting and readability:

Name	SSZ equivalent	Description
`WithdrawalIndex`	`uint64`	an index of a `Withdrawal`

Constants

Domain types

Name	Value
`DOMAIN_BLS_TO_EXECUTION_CHANGE`	`DomainType('0x0A000000')`

Preset

Misc

Name	Value
`MAX_PARTIAL_WITHDRAWALS_PER_EPOCH`	`uint64(2**8)` (= 256)

State list lengths

Name	Value	Unit
`WITHDRAWAL_QUEUE_LIMIT`	`uint64(2**40)` (= 1,099,511,627,776)	withdrawals enqueued in state

Max operations per block

Name	Value
`MAX_BLS_TO_EXECUTION_CHANGES`	`2**4` (= 16)

Execution

Name	Value	Description
`MAX_WITHDRAWALS_PER_PAYLOAD`	`uint64(2**4)` (= 16)	Maximum amount of withdrawals allowed in each payload

Configuration

Containers

New containers

`Withdrawal`

class Withdrawal(Container):
    index: WithdrawalIndex
    validator_index: ValidatorIndex
    address: ExecutionAddress
    amount: Gwei

`BLSToExecutionChange`

class BLSToExecutionChange(Container):
    validator_index: ValidatorIndex
    from_bls_pubkey: BLSPubkey
    to_execution_address: ExecutionAddress

`SignedBLSToExecutionChange`

class SignedBLSToExecutionChange(Container):
    message: BLSToExecutionChange
    signature: BLSSignature

Extended Containers

`ExecutionPayload`

class ExecutionPayload(Container):
    # Execution block header fields
    parent_hash: Hash32
    fee_recipient: ExecutionAddress  # 'beneficiary' in the yellow paper
    state_root: Bytes32
    receipts_root: Bytes32
    logs_bloom: ByteVector[BYTES_PER_LOGS_BLOOM]
    prev_randao: Bytes32  # 'difficulty' in the yellow paper
    block_number: uint64  # 'number' in the yellow paper
    gas_limit: uint64
    gas_used: uint64
    timestamp: uint64
    extra_data: ByteList[MAX_EXTRA_DATA_BYTES]
    base_fee_per_gas: uint256
    # Extra payload fields
    block_hash: Hash32  # Hash of execution block
    transactions: List[Transaction, MAX_TRANSACTIONS_PER_PAYLOAD]
    withdrawals: List[Withdrawal, MAX_WITHDRAWALS_PER_PAYLOAD]  # [New in Capella]

`ExecutionPayloadHeader`

class ExecutionPayloadHeader(Container):
    # Execution block header fields
    parent_hash: Hash32
    fee_recipient: ExecutionAddress
    state_root: Bytes32
    receipts_root: Bytes32
    logs_bloom: ByteVector[BYTES_PER_LOGS_BLOOM]
    prev_randao: Bytes32
    block_number: uint64
    gas_limit: uint64
    gas_used: uint64
    timestamp: uint64
    extra_data: ByteList[MAX_EXTRA_DATA_BYTES]
    base_fee_per_gas: uint256
    # Extra payload fields
    block_hash: Hash32  # Hash of execution block
    transactions_root: Root
    withdrawals_root: Root  # [New in Capella]

`BeaconBlockBody`

class BeaconBlockBody(Container):
    randao_reveal: BLSSignature
    eth1_data: Eth1Data  # Eth1 data vote
    graffiti: Bytes32  # Arbitrary data
    # Operations
    proposer_slashings: List[ProposerSlashing, MAX_PROPOSER_SLASHINGS]
    attester_slashings: List[AttesterSlashing, MAX_ATTESTER_SLASHINGS]
    attestations: List[Attestation, MAX_ATTESTATIONS]
    deposits: List[Deposit, MAX_DEPOSITS]
    voluntary_exits: List[SignedVoluntaryExit, MAX_VOLUNTARY_EXITS]
    sync_aggregate: SyncAggregate
    # Execution
    execution_payload: ExecutionPayload
    # Capella operations
    bls_to_execution_changes: List[SignedBLSToExecutionChange, MAX_BLS_TO_EXECUTION_CHANGES]  # [New in Capella]

`BeaconState`

class BeaconState(Container):
    # Versioning
    genesis_time: uint64
    genesis_validators_root: Root
    slot: Slot
    fork: Fork
    # History
    latest_block_header: BeaconBlockHeader
    block_roots: Vector[Root, SLOTS_PER_HISTORICAL_ROOT]
    state_roots: Vector[Root, SLOTS_PER_HISTORICAL_ROOT]
    historical_roots: List[Root, HISTORICAL_ROOTS_LIMIT]
    # Eth1
    eth1_data: Eth1Data
    eth1_data_votes: List[Eth1Data, EPOCHS_PER_ETH1_VOTING_PERIOD * SLOTS_PER_EPOCH]
    eth1_deposit_index: uint64
    # Registry
    validators: List[Validator, VALIDATOR_REGISTRY_LIMIT]
    balances: List[Gwei, VALIDATOR_REGISTRY_LIMIT]
    # Randomness
    randao_mixes: Vector[Bytes32, EPOCHS_PER_HISTORICAL_VECTOR]
    # Slashings
    slashings: Vector[Gwei, EPOCHS_PER_SLASHINGS_VECTOR]  # Per-epoch sums of slashed effective balances
    # Participation
    previous_epoch_participation: List[ParticipationFlags, VALIDATOR_REGISTRY_LIMIT]
    current_epoch_participation: List[ParticipationFlags, VALIDATOR_REGISTRY_LIMIT]
    # Finality
    justification_bits: Bitvector[JUSTIFICATION_BITS_LENGTH]  # Bit set for every recent justified epoch
    previous_justified_checkpoint: Checkpoint
    current_justified_checkpoint: Checkpoint
    finalized_checkpoint: Checkpoint
    # Inactivity
    inactivity_scores: List[uint64, VALIDATOR_REGISTRY_LIMIT]
    # Sync
    current_sync_committee: SyncCommittee
    next_sync_committee: SyncCommittee
    # Execution
    latest_execution_payload_header: ExecutionPayloadHeader
    # Withdrawals
    withdrawal_queue: List[Withdrawal, WITHDRAWAL_QUEUE_LIMIT]  # [New in Capella]
    next_withdrawal_index: WithdrawalIndex  # [New in Capella]
    next_partial_withdrawal_validator_index: ValidatorIndex  # [New in Capella]

Helpers

Beacon state mutators

`withdraw_balance`

def withdraw_balance(state: BeaconState, validator_index: ValidatorIndex, amount: Gwei) -> None:
    # Decrease the validator's balance
    decrease_balance(state, validator_index, amount)
    # Create a corresponding withdrawal receipt
    withdrawal = Withdrawal(
        index=state.next_withdrawal_index,
        validator_index=validator_index,
        address=ExecutionAddress(state.validators[validator_index].withdrawal_credentials[12:]),
        amount=amount,
    )
    state.next_withdrawal_index = WithdrawalIndex(state.next_withdrawal_index + 1)
    state.withdrawal_queue.append(withdrawal)

Predicates

`has_eth1_withdrawal_credential`

def has_eth1_withdrawal_credential(validator: Validator) -> bool:
    """
    Check if ``validator`` has an 0x01 prefixed "eth1" withdrawal credential.
    """
    return validator.withdrawal_credentials[:1] == ETH1_ADDRESS_WITHDRAWAL_PREFIX

`is_fully_withdrawable_validator`

def is_fully_withdrawable_validator(validator: Validator, balance: Gwei, epoch: Epoch) -> bool:
    """
    Check if ``validator`` is fully withdrawable.
    """
    return (
        has_eth1_withdrawal_credential(validator)
        and validator.withdrawable_epoch <= epoch
        and balance > 0
    )

`is_partially_withdrawable_validator`

def is_partially_withdrawable_validator(validator: Validator, balance: Gwei) -> bool:
    """
    Check if ``validator`` is partially withdrawable.
    """
    has_max_effective_balance = validator.effective_balance == MAX_EFFECTIVE_BALANCE
    has_excess_balance = balance > MAX_EFFECTIVE_BALANCE
    return has_eth1_withdrawal_credential(validator) and has_max_effective_balance and has_excess_balance

Beacon chain state transition function

Epoch processing

def process_epoch(state: BeaconState) -> None:
    process_justification_and_finalization(state)
    process_inactivity_updates(state)
    process_rewards_and_penalties(state)
    process_registry_updates(state)
    process_slashings(state)
    process_eth1_data_reset(state)
    process_effective_balance_updates(state)
    process_slashings_reset(state)
    process_randao_mixes_reset(state)
    process_historical_roots_update(state)
    process_participation_flag_updates(state)
    process_sync_committee_updates(state)
    process_full_withdrawals(state)  # [New in Capella]
    process_partial_withdrawals(state)  # [New in Capella]

Full withdrawals

Note: The function process_full_withdrawals is new.

def process_full_withdrawals(state: BeaconState) -> None:
    current_epoch = get_current_epoch(state)
    for index in range(len(state.validators)):
        balance = state.balances[index]
        validator = state.validators[index]
        if is_fully_withdrawable_validator(validator, balance, current_epoch):
            withdraw_balance(state, ValidatorIndex(index), balance)

Partial withdrawals

Note: The function process_partial_withdrawals is new.

def process_partial_withdrawals(state: BeaconState) -> None:
    partial_withdrawals_count = 0
    # Begin where we left off last time
    validator_index = state.next_partial_withdrawal_validator_index
    for _ in range(len(state.validators)):
        balance = state.balances[validator_index]
        validator = state.validators[validator_index]
        if is_partially_withdrawable_validator(validator, balance):
            withdraw_balance(state, validator_index, balance - MAX_EFFECTIVE_BALANCE)
            partial_withdrawals_count += 1

        # Iterate to next validator to check for partial withdrawal
        validator_index = ValidatorIndex((validator_index + 1) % len(state.validators))
        # Exit if performed maximum allowable withdrawals
        if partial_withdrawals_count == MAX_PARTIAL_WITHDRAWALS_PER_EPOCH:
            break

    state.next_partial_withdrawal_validator_index = validator_index

Block processing

def process_block(state: BeaconState, block: BeaconBlock) -> None:
    process_block_header(state, block)
    if is_execution_enabled(state, block.body):
        process_withdrawals(state, block.body.execution_payload)  # [New in Capella]
        process_execution_payload(state, block.body.execution_payload, EXECUTION_ENGINE)  # [Modified in Capella]
    process_randao(state, block.body)
    process_eth1_data(state, block.body)
    process_operations(state, block.body)
    process_sync_aggregate(state, block.body.sync_aggregate)

New `process_withdrawals`

def process_withdrawals(state: BeaconState, payload: ExecutionPayload) -> None:
    num_withdrawals = min(MAX_WITHDRAWALS_PER_PAYLOAD, len(state.withdrawal_queue))
    dequeued_withdrawals = state.withdrawal_queue[:num_withdrawals]

    assert len(dequeued_withdrawals) == len(payload.withdrawals)
    for dequeued_withdrawal, withdrawal in zip(dequeued_withdrawals, payload.withdrawals):
        assert dequeued_withdrawal == withdrawal

    # Remove dequeued withdrawals from state
    state.withdrawal_queue = state.withdrawal_queue[num_withdrawals:]

Modified `process_execution_payload`

Note: The function process_execution_payload is modified to use the new ExecutionPayloadHeader type.

def process_execution_payload(state: BeaconState, payload: ExecutionPayload, execution_engine: ExecutionEngine) -> None:
    # Verify consistency of the parent hash with respect to the previous execution payload header
    if is_merge_transition_complete(state):
        assert payload.parent_hash == state.latest_execution_payload_header.block_hash
    # Verify prev_randao
    assert payload.prev_randao == get_randao_mix(state, get_current_epoch(state))
    # Verify timestamp
    assert payload.timestamp == compute_timestamp_at_slot(state, state.slot)
    # Verify the execution payload is valid
    assert execution_engine.notify_new_payload(payload)
    # Cache execution payload header
    state.latest_execution_payload_header = ExecutionPayloadHeader(
        parent_hash=payload.parent_hash,
        fee_recipient=payload.fee_recipient,
        state_root=payload.state_root,
        receipts_root=payload.receipts_root,
        logs_bloom=payload.logs_bloom,
        prev_randao=payload.prev_randao,
        block_number=payload.block_number,
        gas_limit=payload.gas_limit,
        gas_used=payload.gas_used,
        timestamp=payload.timestamp,
        extra_data=payload.extra_data,
        base_fee_per_gas=payload.base_fee_per_gas,
        block_hash=payload.block_hash,
        transactions_root=hash_tree_root(payload.transactions),
        withdrawals_root=hash_tree_root(payload.withdrawals),  # [New in Capella]
    )

Modified `process_operations`

Note: The function process_operations is modified to process BLSToExecutionChange operations included in the block.

def process_operations(state: BeaconState, body: BeaconBlockBody) -> None:
    # Verify that outstanding deposits are processed up to the maximum number of deposits
    assert len(body.deposits) == min(MAX_DEPOSITS, state.eth1_data.deposit_count - state.eth1_deposit_index)

    def for_ops(operations: Sequence[Any], fn: Callable[[BeaconState, Any], None]) -> None:
        for operation in operations:
            fn(state, operation)

    for_ops(body.proposer_slashings, process_proposer_slashing)
    for_ops(body.attester_slashings, process_attester_slashing)
    for_ops(body.attestations, process_attestation)
    for_ops(body.deposits, process_deposit)
    for_ops(body.voluntary_exits, process_voluntary_exit)
    for_ops(body.bls_to_execution_changes, process_bls_to_execution_change)  # [New in Capella]

New `process_bls_to_execution_change`

def process_bls_to_execution_change(state: BeaconState,
                                    signed_address_change: SignedBLSToExecutionChange) -> None:
    address_change = signed_address_change.message

    assert address_change.validator_index < len(state.validators)

    validator = state.validators[address_change.validator_index]

    assert validator.withdrawal_credentials[:1] == BLS_WITHDRAWAL_PREFIX
    assert validator.withdrawal_credentials[1:] == hash(address_change.from_bls_pubkey)[1:]

    domain = get_domain(state, DOMAIN_BLS_TO_EXECUTION_CHANGE)
    signing_root = compute_signing_root(address_change, domain)
    assert bls.Verify(address_change.from_bls_pubkey, signing_root, signed_address_change.signature)

    validator.withdrawal_credentials = (
        ETH1_ADDRESS_WITHDRAWAL_PREFIX
        + b'\x00' * 11
        + address_change.to_execution_address
    )

Testing

Note: The function initialize_beacon_state_from_eth1 is modified for pure Capella testing only. Modifications include:

Use CAPELLA_FORK_VERSION as the previous and current fork version.
Utilize the Capella BeaconBlockBody when constructing the initial latest_block_header.

def initialize_beacon_state_from_eth1(eth1_block_hash: Hash32,
                                      eth1_timestamp: uint64,
                                      deposits: Sequence[Deposit],
                                      execution_payload_header: ExecutionPayloadHeader=ExecutionPayloadHeader()
                                      ) -> BeaconState:
    fork = Fork(
        previous_version=CAPELLA_FORK_VERSION,  # [Modified in Capella] for testing only
        current_version=CAPELLA_FORK_VERSION,  # [Modified in Capella]
        epoch=GENESIS_EPOCH,
    )
    state = BeaconState(
        genesis_time=eth1_timestamp + GENESIS_DELAY,
        fork=fork,
        eth1_data=Eth1Data(block_hash=eth1_block_hash, deposit_count=uint64(len(deposits))),
        latest_block_header=BeaconBlockHeader(body_root=hash_tree_root(BeaconBlockBody())),
        randao_mixes=[eth1_block_hash] * EPOCHS_PER_HISTORICAL_VECTOR,  # Seed RANDAO with Eth1 entropy
    )

    # Process deposits
    leaves = list(map(lambda deposit: deposit.data, deposits))
    for index, deposit in enumerate(deposits):
        deposit_data_list = List[DepositData, 2**DEPOSIT_CONTRACT_TREE_DEPTH](*leaves[:index + 1])
        state.eth1_data.deposit_root = hash_tree_root(deposit_data_list)
        process_deposit(state, deposit)

    # Process activations
    for index, validator in enumerate(state.validators):
        balance = state.balances[index]
        validator.effective_balance = min(balance - balance % EFFECTIVE_BALANCE_INCREMENT, MAX_EFFECTIVE_BALANCE)
        if validator.effective_balance == MAX_EFFECTIVE_BALANCE:
            validator.activation_eligibility_epoch = GENESIS_EPOCH
            validator.activation_epoch = GENESIS_EPOCH

    # Set genesis validators root for domain separation and chain versioning
    state.genesis_validators_root = hash_tree_root(state.validators)

    # Fill in sync committees
    # Note: A duplicate committee is assigned for the current and next committee at genesis
    state.current_sync_committee = get_next_sync_committee(state)
    state.next_sync_committee = get_next_sync_committee(state)

    # Initialize the execution payload header
    state.latest_execution_payload_header = execution_payload_header

    return state

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