eth2.0-specs/specs/altair/beacon-chain.md

Ethereum 2.0 Altair

Table of contents

• Introduction
• Custom types
• Constants
  • Participation flag indices
  • Participation flag fractions
  • Misc
• Configuration
  • Updated penalty values
  • Misc
  • Time parameters
  • Domain types
• Containers
  • Modified containers
    • BeaconBlockBody
    • BeaconState
  • New containers
    • SyncCommittee
• Helper functions
  • Predicates
    • eth2_fast_aggregate_verify
  • Misc
    • get_flag_indices_and_numerators
    • add_flag
    • has_flag
  • Beacon state accessors
    • get_sync_committee_indices
    • get_sync_committee
    • get_base_reward
    • get_unslashed_participating_indices
    • get_flag_deltas
    • New get_inactivity_penalty_deltas
  • Beacon state mutators
    • New slash_validator
  • Block processing
    • Modified process_attestation
    • Modified process_deposit
    • Sync committee processing
  • Epoch processing
    • Justification and finalization
    • Leak scores
    • Rewards and penalties
    • Slashings
    • Participation flags updates
    • Sync committee updates

Introduction

Altair is a patch implementing the first hard fork to the beacon chain. It has four main features:

• Light client support via sync committees
• Incentive accounting reforms, reducing spec complexity and [TODO] reducing the cost of processing chains that have very little or zero participation for a long span of epochs
• Update penalty configuration values, moving them toward their planned maximally punitive configuration
• Fork choice rule changes to address weaknesses recently discovered in the existing fork choice

Custom types

Name	SSZ equivalent	Description
ParticipationFlags	uint8	A succinct representation of 8 boolean participation flags

Constants

Participation flag indices

Name	Value
TIMELY_HEAD_FLAG_INDEX	0
TIMELY_SOURCE_FLAG_INDEX	1
TIMELY_TARGET_FLAG_INDEX	2

Participation flag fractions

Name	Value
TIMELY_HEAD_FLAG_NUMERATOR	12
TIMELY_SOURCE_FLAG_NUMERATOR	12
TIMELY_TARGET_FLAG_NUMERATOR	32
FLAG_DENOMINATOR	64

Note: The participatition flag fractions add up to 7/8. The remaining 1/8 is for proposer incentives and other future micro-incentives.

Misc

Name	Value
G2_POINT_AT_INFINITY	BLSSignature(b'\xc0' + b'\x00' * 95)

Configuration

Updated penalty values

This patch updates a few configuration values to move penalty constants toward their final, maxmium security values.

Note: The spec does not override previous configuration values but instead creates new values and replaces usage throughout.

Name	Value
ALTAIR_INACTIVITY_PENALTY_QUOTIENT	uint64(3 * 2**24) (= 50,331,648)
ALTAIR_MIN_SLASHING_PENALTY_QUOTIENT	uint64(2**6) (=64)
ALTAIR_PROPORTIONAL_SLASHING_MULTIPLIER	uint64(2)

Misc

Name	Value
SYNC_COMMITTEE_SIZE	uint64(2**10) (= 1,024)
SYNC_SUBCOMMITTEE_SIZE	uint64(2**6) (= 64)
LEAK_SCORE_BIAS	4

Time parameters

Name	Value	Unit	Duration
EPOCHS_PER_SYNC_COMMITTEE_PERIOD	Epoch(2**8) (= 256)	epochs	~27 hours

Domain types

Name	Value
DOMAIN_SYNC_COMMITTEE	DomainType('0x07000000')

Containers

Modified containers

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 committee aggregate signature
    sync_committee_bits: Bitvector[SYNC_COMMITTEE_SIZE]  # [New in Altair]
    sync_committee_signature: BLSSignature  # [New in Altair]

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]  # [New in Altair]
    current_epoch_participation: List[ParticipationFlags, VALIDATOR_REGISTRY_LIMIT]  # [New in Altair]
    # 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
    # Light client sync committees
    current_sync_committee: SyncCommittee  # [New in Altair]
    next_sync_committee: SyncCommittee  # [New in Altair]
    # Leak
    leak_scores: List[uint64, VALIDATOR_REGISTRY_LIMIT]  # [New in Altair]

New containers

SyncCommittee

class SyncCommittee(Container):
    pubkeys: Vector[BLSPubkey, SYNC_COMMITTEE_SIZE]
    pubkey_aggregates: Vector[BLSPubkey, SYNC_COMMITTEE_SIZE // SYNC_SUBCOMMITTEE_SIZE]

Helper functions

Predicates

eth2_fast_aggregate_verify

def eth2_fast_aggregate_verify(pubkeys: Sequence[BLSPubkey], message: Bytes32, signature: BLSSignature) -> bool:
    """
    Wrapper to ``bls.FastAggregateVerify`` accepting the ``G2_POINT_AT_INFINITY`` signature when ``pubkeys`` is empty.
    """
    if len(pubkeys) == 0 and signature == G2_POINT_AT_INFINITY:
        return True
    return bls.FastAggregateVerify(pubkeys, message, signature)

Misc

get_flag_indices_and_numerators

def get_flag_indices_and_numerators() -> Sequence[Tuple[int, int]]:
    return (
        (TIMELY_HEAD_FLAG_INDEX, TIMELY_HEAD_FLAG_NUMERATOR),
        (TIMELY_SOURCE_FLAG_INDEX, TIMELY_SOURCE_FLAG_NUMERATOR),
        (TIMELY_TARGET_FLAG_INDEX, TIMELY_TARGET_FLAG_NUMERATOR),
    )

add_flag

def add_flag(flags: ParticipationFlags, flag_index: int) -> ParticipationFlags:
    flag = ParticipationFlags(2**flag_index)
    return flags | flag

has_flag

def has_flag(flags: ParticipationFlags, flag_index: int) -> bool:
    flag = ParticipationFlags(2**flag_index)
    return flags & flag == flag

Beacon state accessors

get_sync_committee_indices

def get_sync_committee_indices(state: BeaconState, epoch: Epoch) -> Sequence[ValidatorIndex]:
    """
    Return the sequence of sync committee indices (which may include duplicate indices) for a given state and epoch.
    """
    MAX_RANDOM_BYTE = 2**8 - 1
    base_epoch = Epoch((max(epoch // EPOCHS_PER_SYNC_COMMITTEE_PERIOD, 1) - 1) * EPOCHS_PER_SYNC_COMMITTEE_PERIOD)
    active_validator_indices = get_active_validator_indices(state, base_epoch)
    active_validator_count = uint64(len(active_validator_indices))
    seed = get_seed(state, base_epoch, DOMAIN_SYNC_COMMITTEE)
    i = 0
    sync_committee_indices: List[ValidatorIndex] = []
    while len(sync_committee_indices) < SYNC_COMMITTEE_SIZE:
        shuffled_index = compute_shuffled_index(uint64(i % active_validator_count), active_validator_count, seed)
        candidate_index = active_validator_indices[shuffled_index]
        random_byte = hash(seed + uint_to_bytes(uint64(i // 32)))[i % 32]
        effective_balance = state.validators[candidate_index].effective_balance
        if effective_balance * MAX_RANDOM_BYTE >= MAX_EFFECTIVE_BALANCE * random_byte:  # Sample with replacement
            sync_committee_indices.append(candidate_index)
        i += 1
    return sync_committee_indices

get_sync_committee

def get_sync_committee(state: BeaconState, epoch: Epoch) -> SyncCommittee:
    """
    Return the sync committee for a given state and epoch.
    """
    indices = get_sync_committee_indices(state, epoch)
    pubkeys = [state.validators[index].pubkey for index in indices]
    subcommitees = [pubkeys[i:i + SYNC_SUBCOMMITTEE_SIZE] for i in range(0, len(pubkeys), SYNC_SUBCOMMITTEE_SIZE)]
    pubkey_aggregates = [bls.AggregatePKs(subcommitee) for subcommitee in subcommitees]
    return SyncCommittee(pubkeys=pubkeys, pubkey_aggregates=pubkey_aggregates)

get_base_reward

Note: The function get_base_reward is modified with the removal of BASE_REWARDS_PER_EPOCH.

def get_base_reward(state: BeaconState, index: ValidatorIndex) -> Gwei:
    total_balance = get_total_active_balance(state)
    effective_balance = state.validators[index].effective_balance
    return Gwei(effective_balance * BASE_REWARD_FACTOR // integer_squareroot(total_balance))

get_unslashed_participating_indices

def get_unslashed_participating_indices(state: BeaconState, flag_index: int, epoch: Epoch) -> Set[ValidatorIndex]:
    """
    Retrieve the active and unslashed validator indices for the given epoch and flag index.
    """
    assert epoch in (get_previous_epoch(state), get_current_epoch(state))
    if epoch == get_current_epoch(state):
        epoch_participation = state.current_epoch_participation
    else:
        epoch_participation = state.previous_epoch_participation
    active_validator_indices = get_active_validator_indices(state, epoch)
    participating_indices = [i for i in active_validator_indices if has_flag(epoch_participation[i], flag_index)]
    return set(filter(lambda index: not state.validators[index].slashed, participating_indices))

get_flag_deltas

def get_flag_deltas(state: BeaconState,
                    flag_index: int,
                    numerator: uint64) -> Tuple[Sequence[Gwei], Sequence[Gwei]]:
    """
    Compute the rewards and penalties associated with a particular duty, by scanning through the participation
    flags to determine who participated and who did not and assigning them the appropriate rewards and penalties.
    """
    rewards = [Gwei(0)] * len(state.validators)
    penalties = [Gwei(0)] * len(state.validators)

    unslashed_participating_indices = get_unslashed_participating_indices(state, flag_index, get_previous_epoch(state))
    increment = EFFECTIVE_BALANCE_INCREMENT  # Factored out from balances to avoid uint64 overflow
    unslashed_participating_increments = get_total_balance(state, unslashed_participating_indices) // increment
    active_increments = get_total_active_balance(state) // increment
    for index in get_eligible_validator_indices(state):
        base_reward = get_base_reward(state, index)
        if index in unslashed_participating_indices:
            if is_in_inactivity_leak(state):
                # Optimal participation is fully rewarded to cancel the inactivity penalty
                rewards[index] = base_reward * numerator // FLAG_DENOMINATOR
            else:
                rewards[index] = (
                    (base_reward * numerator * unslashed_participating_increments)
                    // (active_increments * FLAG_DENOMINATOR)
                )
        else:
            penalties[index] = base_reward * numerator // FLAG_DENOMINATOR
    return rewards, penalties

New get_inactivity_penalty_deltas

Note: The function get_inactivity_penalty_deltas is modified in the selection of matching target indices and the removal of BASE_REWARDS_PER_EPOCH.

def get_inactivity_penalty_deltas(state: BeaconState) -> Tuple[Sequence[Gwei], Sequence[Gwei]]:
    """
    Compute the penalties associated with the inactivity leak, by scanning through the participation
    flags to determine who participated and who did not, applying the leak penalty globally and applying
    compensatory rewards to participants.
    """
    rewards = [Gwei(0) for _ in range(len(state.validators))]
    penalties = [Gwei(0) for _ in range(len(state.validators))]

    if not is_in_inactivity_leak(state):
        return rewards, penalties

    reward_numerator_sum = sum(numerator for (_, numerator) in get_flag_indices_and_numerators())
    matching_target_attesting_indices = get_unslashed_participating_indices(
        state, TIMELY_TARGET_FLAG_INDEX, get_previous_epoch(state)
    )
    for index in get_eligible_validator_indices(state):
        # If validator is performing optimally this cancels all attestation rewards for a neutral balance
        penalties[index] += Gwei(get_base_reward(state, index) * reward_numerator_sum // FLAG_DENOMINATOR)
        if index not in matching_target_attesting_indices and state.leak_scores[index] >= LEAK_SCORE_BIAS:
            effective_balance = state.validators[index].effective_balance
            leak_penalty = Gwei(
                effective_balance * state.leak_scores[index] // LEAK_SCORE_BIAS // ALTAIR_INACTIVITY_PENALTY_QUOTIENT
            )
            penalties[index] += leak_penalty

    return rewards, penalties

Beacon state mutators

New slash_validator

Note: The function slash_validator is modified with the substitution of MIN_SLASHING_PENALTY_QUOTIENT with ALTAIR_MIN_SLASHING_PENALTY_QUOTIENT.

def slash_validator(state: BeaconState,
                    slashed_index: ValidatorIndex,
                    whistleblower_index: ValidatorIndex=None) -> None:
    """
    Slash the validator with index ``slashed_index``.
    """
    epoch = get_current_epoch(state)
    initiate_validator_exit(state, slashed_index)
    validator = state.validators[slashed_index]
    validator.slashed = True
    validator.withdrawable_epoch = max(validator.withdrawable_epoch, Epoch(epoch + EPOCHS_PER_SLASHINGS_VECTOR))
    state.slashings[epoch % EPOCHS_PER_SLASHINGS_VECTOR] += validator.effective_balance
    decrease_balance(state, slashed_index, validator.effective_balance // ALTAIR_MIN_SLASHING_PENALTY_QUOTIENT)

    # Apply proposer and whistleblower rewards
    proposer_index = get_beacon_proposer_index(state)
    if whistleblower_index is None:
        whistleblower_index = proposer_index
    whistleblower_reward = Gwei(validator.effective_balance // WHISTLEBLOWER_REWARD_QUOTIENT)
    proposer_reward = Gwei(whistleblower_reward // PROPOSER_REWARD_QUOTIENT)
    increase_balance(state, proposer_index, proposer_reward)
    increase_balance(state, whistleblower_index, Gwei(whistleblower_reward - proposer_reward))

Block processing

def process_block(state: BeaconState, block: BeaconBlock) -> None:
    process_block_header(state, block)
    process_randao(state, block.body)
    process_eth1_data(state, block.body)
    process_operations(state, block.body)  # [Modified in Altair]
    process_sync_committee(state, block.body)  # [New in Altair]

Modified process_attestation

Note: The function process_attestation is modified to do incentive accounting with epoch participation flags.

def process_attestation(state: BeaconState, attestation: Attestation) -> None:
    data = attestation.data
    assert data.target.epoch in (get_previous_epoch(state), get_current_epoch(state))
    assert data.target.epoch == compute_epoch_at_slot(data.slot)
    assert data.slot + MIN_ATTESTATION_INCLUSION_DELAY <= state.slot <= data.slot + SLOTS_PER_EPOCH
    assert data.index < get_committee_count_per_slot(state, data.target.epoch)

    committee = get_beacon_committee(state, data.slot, data.index)
    assert len(attestation.aggregation_bits) == len(committee)

    if data.target.epoch == get_current_epoch(state):
        epoch_participation = state.current_epoch_participation
        justified_checkpoint = state.current_justified_checkpoint
    else:
        epoch_participation = state.previous_epoch_participation
        justified_checkpoint = state.previous_justified_checkpoint

    # Matching roots
    is_matching_head = data.beacon_block_root == get_block_root_at_slot(state, data.slot)
    is_matching_source = data.source == justified_checkpoint
    is_matching_target = data.target.root == get_block_root(state, data.target.epoch)
    assert is_matching_source

    # Verify signature
    assert is_valid_indexed_attestation(state, get_indexed_attestation(state, attestation))

    # Participation flag indices
    participation_flag_indices = []
    if is_matching_head and is_matching_target and state.slot <= data.slot + MIN_ATTESTATION_INCLUSION_DELAY:
        participation_flag_indices.append(TIMELY_HEAD_FLAG_INDEX)
    if is_matching_source and state.slot <= data.slot + integer_squareroot(SLOTS_PER_EPOCH):
        participation_flag_indices.append(TIMELY_SOURCE_FLAG_INDEX)
    if is_matching_target and state.slot <= data.slot + SLOTS_PER_EPOCH:
        participation_flag_indices.append(TIMELY_TARGET_FLAG_INDEX)

    # Update epoch participation flags
    proposer_reward_numerator = 0
    for index in get_attesting_indices(state, data, attestation.aggregation_bits):
        for flag_index, flag_numerator in get_flag_indices_and_numerators():
            if flag_index in participation_flag_indices and not has_flag(epoch_participation[index], flag_index):
                epoch_participation[index] = add_flag(epoch_participation[index], flag_index)
                proposer_reward_numerator += get_base_reward(state, index) * flag_numerator

    # Reward proposer
    proposer_reward = Gwei(proposer_reward_numerator // (FLAG_DENOMINATOR * PROPOSER_REWARD_QUOTIENT))
    increase_balance(state, get_beacon_proposer_index(state), proposer_reward)

Modified process_deposit

Note: The function process_deposit is modified to initialize leak_scores, previous_epoch_participation, current_epoch_participation.

def process_deposit(state: BeaconState, deposit: Deposit) -> None:
    # Verify the Merkle branch
    assert is_valid_merkle_branch(
        leaf=hash_tree_root(deposit.data),
        branch=deposit.proof,
        depth=DEPOSIT_CONTRACT_TREE_DEPTH + 1,  # Add 1 for the List length mix-in
        index=state.eth1_deposit_index,
        root=state.eth1_data.deposit_root,
    )

    # Deposits must be processed in order
    state.eth1_deposit_index += 1

    pubkey = deposit.data.pubkey
    amount = deposit.data.amount
    validator_pubkeys = [v.pubkey for v in state.validators]
    if pubkey not in validator_pubkeys:
        # Verify the deposit signature (proof of possession) which is not checked by the deposit contract
        deposit_message = DepositMessage(
            pubkey=deposit.data.pubkey,
            withdrawal_credentials=deposit.data.withdrawal_credentials,
            amount=deposit.data.amount,
        )
        domain = compute_domain(DOMAIN_DEPOSIT)  # Fork-agnostic domain since deposits are valid across forks
        signing_root = compute_signing_root(deposit_message, domain)
        if not bls.Verify(pubkey, signing_root, deposit.data.signature):
            return

        # Add validator and balance entries
        state.validators.append(get_validator_from_deposit(state, deposit))
        state.balances.append(amount)
        state.previous_epoch_participation.append(ParticipationFlags(0b0000_0000))  # [New in Altair]
        state.current_epoch_participation.append(ParticipationFlags(0b0000_0000))  # [New in Altair]
        state.leak_scores.append(0)  # [New in Altair]
    else:
        # Increase balance by deposit amount
        index = ValidatorIndex(validator_pubkeys.index(pubkey))
        increase_balance(state, index, amount)

Sync committee processing

def process_sync_committee(state: BeaconState, body: BeaconBlockBody) -> None:
    # Verify sync committee aggregate signature signing over the previous slot block root
    previous_slot = Slot(max(int(state.slot), 1) - 1)
    committee_indices = get_sync_committee_indices(state, get_current_epoch(state))
    participant_indices = [index for index, bit in zip(committee_indices, body.sync_committee_bits) if bit]
    committee_pubkeys = state.current_sync_committee.pubkeys
    participant_pubkeys = [pubkey for pubkey, bit in zip(committee_pubkeys, body.sync_committee_bits) if bit]
    domain = get_domain(state, DOMAIN_SYNC_COMMITTEE, compute_epoch_at_slot(previous_slot))
    signing_root = compute_signing_root(get_block_root_at_slot(state, previous_slot), domain)
    assert eth2_fast_aggregate_verify(participant_pubkeys, signing_root, body.sync_committee_signature)

    # Reward sync committee participants
    proposer_rewards = Gwei(0)
    active_validator_count = uint64(len(get_active_validator_indices(state, get_current_epoch(state))))
    for participant_index in participant_indices:
        proposer_reward = get_proposer_reward(state, participant_index)
        proposer_rewards += proposer_reward
        base_reward = get_base_reward(state, participant_index)
        max_participant_reward = base_reward - proposer_reward
        reward = Gwei(max_participant_reward * active_validator_count // (len(committee_indices) * SLOTS_PER_EPOCH))
        increase_balance(state, participant_index, reward)

    # Reward beacon proposer
    increase_balance(state, get_beacon_proposer_index(state), proposer_rewards)

Epoch processing

def process_epoch(state: BeaconState) -> None:
    process_justification_and_finalization(state)  # [Modified in Altair]
    process_leak_updates(state)  # [New in Altair]
    process_rewards_and_penalties(state)  # [Modified in Altair]
    process_registry_updates(state)
    process_slashings(state)  # [Modified in Altair]
    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)  # [New in Altair]
    process_sync_committee_updates(state)  # [New in Altair]

Justification and finalization

Note: The function process_justification_and_finalization is modified with matching_target_attestations replaced by matching_target_indices.

def process_justification_and_finalization(state: BeaconState) -> None:
    # Initial FFG checkpoint values have a `0x00` stub for `root`.
    # Skip FFG updates in the first two epochs to avoid corner cases that might result in modifying this stub.
    if get_current_epoch(state) <= GENESIS_EPOCH + 1:
        return
    previous_epoch = get_previous_epoch(state)
    current_epoch = get_current_epoch(state)
    old_previous_justified_checkpoint = state.previous_justified_checkpoint
    old_current_justified_checkpoint = state.current_justified_checkpoint

    # Process justifications
    state.previous_justified_checkpoint = state.current_justified_checkpoint
    state.justification_bits[1:] = state.justification_bits[:JUSTIFICATION_BITS_LENGTH - 1]
    state.justification_bits[0] = 0b0
    matching_target_indices = get_unslashed_participating_indices(state, TIMELY_TARGET_FLAG_INDEX, previous_epoch)
    if get_total_balance(state, matching_target_indices) * 3 >= get_total_active_balance(state) * 2:
        state.current_justified_checkpoint = Checkpoint(epoch=previous_epoch,
                                                        root=get_block_root(state, previous_epoch))
        state.justification_bits[1] = 0b1
    matching_target_indices = get_unslashed_participating_indices(state, TIMELY_TARGET_FLAG_INDEX, current_epoch)
    if get_total_balance(state, matching_target_indices) * 3 >= get_total_active_balance(state) * 2:
        state.current_justified_checkpoint = Checkpoint(epoch=current_epoch,
                                                        root=get_block_root(state, current_epoch))
        state.justification_bits[0] = 0b1

    # Process finalizations
    bits = state.justification_bits
    # The 2nd/3rd/4th most recent epochs are justified, the 2nd using the 4th as source
    if all(bits[1:4]) and old_previous_justified_checkpoint.epoch + 3 == current_epoch:
        state.finalized_checkpoint = old_previous_justified_checkpoint
    # The 2nd/3rd most recent epochs are justified, the 2nd using the 3rd as source
    if all(bits[1:3]) and old_previous_justified_checkpoint.epoch + 2 == current_epoch:
        state.finalized_checkpoint = old_previous_justified_checkpoint
    # The 1st/2nd/3rd most recent epochs are justified, the 1st using the 3rd as source
    if all(bits[0:3]) and old_current_justified_checkpoint.epoch + 2 == current_epoch:
        state.finalized_checkpoint = old_current_justified_checkpoint
    # The 1st/2nd most recent epochs are justified, the 1st using the 2nd as source
    if all(bits[0:2]) and old_current_justified_checkpoint.epoch + 1 == current_epoch:
        state.finalized_checkpoint = old_current_justified_checkpoint

Leak scores

Note: The function process_leak_updates is new.

def process_leak_updates(state: BeaconState) -> None:
    matching_target_attesting_indices = get_unslashed_participating_indices(
        state, TIMELY_TARGET_FLAG_INDEX, get_previous_epoch(state)
    )
    for index in get_eligible_validator_indices(state):
        if index in matching_target_attesting_indices:
            if state.leak_scores[index] > 0:
                state.leak_scores[index] -= 1
        elif is_in_inactivity_leak(state):
            state.leak_scores[index] += LEAK_SCORE_BIAS

Rewards and penalties

Note: The function process_rewards_and_penalties is modified to support the incentive reforms.

def process_rewards_and_penalties(state: BeaconState) -> None:
    # No rewards are applied at the end of `GENESIS_EPOCH` because rewards are for work done in the previous epoch
    if get_current_epoch(state) == GENESIS_EPOCH:
        return
    flag_deltas = [
        get_flag_deltas(state, flag_index, flag_numerator)
        for (flag_index, flag_numerator) in get_flag_indices_and_numerators()
    ]
    deltas = flag_deltas + [get_inactivity_penalty_deltas(state)]
    for (rewards, penalties) in deltas:
        for index in range(len(state.validators)):
            increase_balance(state, ValidatorIndex(index), rewards[index])
            decrease_balance(state, ValidatorIndex(index), penalties[index])

Slashings

Note: The function process_slashings is modified to use ALTAIR_PROPORTIONAL_SLASHING_MULTIPLIER.

def process_slashings(state: BeaconState) -> None:
    epoch = get_current_epoch(state)
    total_balance = get_total_active_balance(state)
    adjusted_total_slashing_balance = min(sum(state.slashings) * ALTAIR_PROPORTIONAL_SLASHING_MULTIPLIER, total_balance)
    for index, validator in enumerate(state.validators):
        if validator.slashed and epoch + EPOCHS_PER_SLASHINGS_VECTOR // 2 == validator.withdrawable_epoch:
            increment = EFFECTIVE_BALANCE_INCREMENT  # Factored out from penalty numerator to avoid uint64 overflow
            penalty_numerator = validator.effective_balance // increment * adjusted_total_slashing_balance
            penalty = penalty_numerator // total_balance * increment
            decrease_balance(state, ValidatorIndex(index), penalty)

Participation flags updates

Note: The function process_participation_flag_updates is new.

def process_participation_flag_updates(state: BeaconState) -> None:
    state.previous_epoch_participation = state.current_epoch_participation
    state.current_epoch_participation = [ParticipationFlags(0b0000_0000) for _ in range(len(state.validators))]

Sync committee updates

Note: The function process_sync_committee_updates is new.

def process_sync_committee_updates(state: BeaconState) -> None:
    next_epoch = get_current_epoch(state) + Epoch(1)
    if next_epoch % EPOCHS_PER_SYNC_COMMITTEE_PERIOD == 0:
        state.current_sync_committee = state.next_sync_committee
        state.next_sync_committee = get_sync_committee(state, next_epoch + EPOCHS_PER_SYNC_COMMITTEE_PERIOD)