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Phase 0 -- Beacon Chain Fork Choice

Table of contents

Introduction

This document is the beacon chain fork choice spec, part of Phase 0. It assumes the beacon chain state transition function spec.

Fork choice

The head block root associated with a store is defined as get_head(store). At genesis, let store = get_forkchoice_store(genesis_state, genesis_block) and update store by running:

  • on_tick(store, time) whenever time > store.time where time is the current Unix time
  • on_block(store, block) whenever a block block: SignedBeaconBlock is received
  • on_attestation(store, attestation) whenever an attestation attestation is received
  • on_attester_slashing(store, attester_slashing) whenever an attester slashing attester_slashing is received

Any of the above handlers that trigger an unhandled exception (e.g. a failed assert or an out-of-range list access) are considered invalid. Invalid calls to handlers must not modify store.

Notes:

1) Leap seconds: Slots will last SECONDS_PER_SLOT + 1 or SECONDS_PER_SLOT - 1 seconds around leap seconds. This is automatically handled by UNIX time. 2) Honest clocks: Honest nodes are assumed to have clocks synchronized within SECONDS_PER_SLOT seconds of each other. 3) Eth1 data: The large ETH1_FOLLOW_DISTANCE specified in the honest validator document should ensure that state.latest_eth1_data of the canonical beacon chain remains consistent with the canonical Ethereum proof-of-work chain. If not, emergency manual intervention will be required. 4) Manual forks: Manual forks may arbitrarily change the fork choice rule but are expected to be enacted at epoch transitions, with the fork details reflected in state.fork. 5) Implementation: The implementation found in this specification is constructed for ease of understanding rather than for optimization in computation, space, or any other resource. A number of optimized alternatives can be found here.

Constant

Name Value
INTERVALS_PER_SLOT uint64(3)

Configuration

Name Value
PROPOSER_SCORE_BOOST uint64(40)
REORG_HEAD_WEIGHT_THRESHOLD uint64(20)
REORG_PARENT_WEIGHT_THRESHOLD uint64(160)
REORG_MAX_EPOCHS_SINCE_FINALIZATION Epoch(2)
  • The proposer score boost and re-org weight threshold are percentage values that are measured with respect to the weight of a single committee. See calculate_committee_fraction.

Helpers

LatestMessage

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@dataclass(eq=True, frozen=True)
class LatestMessage(object):
    epoch: Epoch
    root: Root

Store

The Store is responsible for tracking information required for the fork choice algorithm. The important fields being tracked are described below:

  • justified_checkpoint: the justified checkpoint used as the starting point for the LMD GHOST fork choice algorithm.
  • finalized_checkpoint: the highest known finalized checkpoint. The fork choice only considers blocks that are not conflicting with this checkpoint.
  • unrealized_justified_checkpoint & unrealized_finalized_checkpoint: these track the highest justified & finalized checkpoints resp., without regard to whether on-chain realization has occurred, i.e. FFG processing of new attestations within the state transition function. This is an important distinction from justified_checkpoint & finalized_checkpoint, because they will only track the checkpoints that are realized on-chain. Note that on-chain processing of FFG information only happens at epoch boundaries.
  • unrealized_justifications: stores a map of block root to the unrealized justified checkpoint observed in that block.
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@dataclass
class Store(object):
    time: uint64
    genesis_time: uint64
    justified_checkpoint: Checkpoint
    finalized_checkpoint: Checkpoint
    unrealized_justified_checkpoint: Checkpoint
    unrealized_finalized_checkpoint: Checkpoint
    proposer_boost_root: Root
    equivocating_indices: Set[ValidatorIndex]
    blocks: Dict[Root, BeaconBlock] = field(default_factory=dict)
    block_states: Dict[Root, BeaconState] = field(default_factory=dict)
    block_timeliness: Dict[Root, boolean] = field(default_factory=dict)
    checkpoint_states: Dict[Checkpoint, BeaconState] = field(default_factory=dict)
    latest_messages: Dict[ValidatorIndex, LatestMessage] = field(default_factory=dict)
    unrealized_justifications: Dict[Root, Checkpoint] = field(default_factory=dict)

is_previous_epoch_justified

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def is_previous_epoch_justified(store: Store) -> bool:
    current_epoch = get_current_store_epoch(store)
    return store.justified_checkpoint.epoch + 1 == current_epoch

get_forkchoice_store

The provided anchor-state will be regarded as a trusted state, to not roll back beyond. This should be the genesis state for a full client.

Note With regards to fork choice, block headers are interchangeable with blocks. The spec is likely to move to headers for reduced overhead in test vectors and better encapsulation. Full implementations store blocks as part of their database and will often use full blocks when dealing with production fork choice.

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def get_forkchoice_store(anchor_state: BeaconState, anchor_block: BeaconBlock) -> Store:
    assert anchor_block.state_root == hash_tree_root(anchor_state)
    anchor_root = hash_tree_root(anchor_block)
    anchor_epoch = get_current_epoch(anchor_state)
    justified_checkpoint = Checkpoint(epoch=anchor_epoch, root=anchor_root)
    finalized_checkpoint = Checkpoint(epoch=anchor_epoch, root=anchor_root)
    proposer_boost_root = Root()
    return Store(
        time=uint64(anchor_state.genesis_time + SECONDS_PER_SLOT * anchor_state.slot),
        genesis_time=anchor_state.genesis_time,
        justified_checkpoint=justified_checkpoint,
        finalized_checkpoint=finalized_checkpoint,
        unrealized_justified_checkpoint=justified_checkpoint,
        unrealized_finalized_checkpoint=finalized_checkpoint,
        proposer_boost_root=proposer_boost_root,
        equivocating_indices=set(),
        blocks={anchor_root: copy(anchor_block)},
        block_states={anchor_root: copy(anchor_state)},
        checkpoint_states={justified_checkpoint: copy(anchor_state)},
        unrealized_justifications={anchor_root: justified_checkpoint}
    )

get_slots_since_genesis

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def get_slots_since_genesis(store: Store) -> int:
    return (store.time - store.genesis_time) // SECONDS_PER_SLOT

get_current_slot

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def get_current_slot(store: Store) -> Slot:
    return Slot(GENESIS_SLOT + get_slots_since_genesis(store))

get_current_store_epoch

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def get_current_store_epoch(store: Store) -> Epoch:
    return compute_epoch_at_slot(get_current_slot(store))

compute_slots_since_epoch_start

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def compute_slots_since_epoch_start(slot: Slot) -> int:
    return slot - compute_start_slot_at_epoch(compute_epoch_at_slot(slot))

get_ancestor

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def get_ancestor(store: Store, root: Root, slot: Slot) -> Root:
    block = store.blocks[root]
    if block.slot > slot:
        return get_ancestor(store, block.parent_root, slot)
    return root

calculate_committee_fraction

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def calculate_committee_fraction(state: BeaconState, committee_percent: uint64) -> Gwei:
    committee_weight = get_total_active_balance(state) // SLOTS_PER_EPOCH
    return Gwei((committee_weight * committee_percent) // 100)

get_checkpoint_block

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def get_checkpoint_block(store: Store, root: Root, epoch: Epoch) -> Root:
    """
    Compute the checkpoint block for epoch ``epoch`` in the chain of block ``root``
    """
    epoch_first_slot = compute_start_slot_at_epoch(epoch)
    return get_ancestor(store, root, epoch_first_slot)

get_proposer_score

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def get_proposer_score(store: Store) -> Gwei:
    justified_checkpoint_state = store.checkpoint_states[store.justified_checkpoint]
    committee_weight = get_total_active_balance(justified_checkpoint_state) // SLOTS_PER_EPOCH
    return (committee_weight * PROPOSER_SCORE_BOOST) // 100

get_weight

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def get_weight(store: Store, root: Root) -> Gwei:
    state = store.checkpoint_states[store.justified_checkpoint]
    unslashed_and_active_indices = [
        i for i in get_active_validator_indices(state, get_current_epoch(state))
        if not state.validators[i].slashed
    ]
    attestation_score = Gwei(sum(
        state.validators[i].effective_balance for i in unslashed_and_active_indices
        if (i in store.latest_messages
            and i not in store.equivocating_indices
            and get_ancestor(store, store.latest_messages[i].root, store.blocks[root].slot) == root)
    ))
    if store.proposer_boost_root == Root():
        # Return only attestation score if ``proposer_boost_root`` is not set
        return attestation_score

    # Calculate proposer score if ``proposer_boost_root`` is set
    proposer_score = Gwei(0)
    # Boost is applied if ``root`` is an ancestor of ``proposer_boost_root``
    if get_ancestor(store, store.proposer_boost_root, store.blocks[root].slot) == root:
        proposer_score = get_proposer_score(store)
    return attestation_score + proposer_score

get_voting_source

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def get_voting_source(store: Store, block_root: Root) -> Checkpoint:
    """
    Compute the voting source checkpoint in event that block with root ``block_root`` is the head block
    """
    block = store.blocks[block_root]
    current_epoch = get_current_store_epoch(store)
    block_epoch = compute_epoch_at_slot(block.slot)
    if current_epoch > block_epoch:
        # The block is from a prior epoch, the voting source will be pulled-up
        return store.unrealized_justifications[block_root]
    else:
        # The block is not from a prior epoch, therefore the voting source is not pulled up
        head_state = store.block_states[block_root]
        return head_state.current_justified_checkpoint

filter_block_tree

Note: External calls to filter_block_tree (i.e., any calls that are not made by the recursive logic in this function) MUST set block_root to store.justified_checkpoint.

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def filter_block_tree(store: Store, block_root: Root, blocks: Dict[Root, BeaconBlock]) -> bool:
    block = store.blocks[block_root]
    children = [
        root for root in store.blocks.keys()
        if store.blocks[root].parent_root == block_root
    ]

    # If any children branches contain expected finalized/justified checkpoints,
    # add to filtered block-tree and signal viability to parent.
    if any(children):
        filter_block_tree_result = [filter_block_tree(store, child, blocks) for child in children]
        if any(filter_block_tree_result):
            blocks[block_root] = block
            return True
        return False

    current_epoch = get_current_store_epoch(store)
    voting_source = get_voting_source(store, block_root)

    # The voting source should be either at the same height as the store's justified checkpoint or
    # not more than two epochs ago
    correct_justified = (
        store.justified_checkpoint.epoch == GENESIS_EPOCH
        or voting_source.epoch == store.justified_checkpoint.epoch
        or voting_source.epoch + 2 >= current_epoch
    )

    finalized_checkpoint_block = get_checkpoint_block(
        store,
        block_root,
        store.finalized_checkpoint.epoch,
    )

    correct_finalized = (
        store.finalized_checkpoint.epoch == GENESIS_EPOCH
        or store.finalized_checkpoint.root == finalized_checkpoint_block
    )

    # If expected finalized/justified, add to viable block-tree and signal viability to parent.
    if correct_justified and correct_finalized:
        blocks[block_root] = block
        return True

    # Otherwise, branch not viable
    return False

get_filtered_block_tree

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def get_filtered_block_tree(store: Store) -> Dict[Root, BeaconBlock]:
    """
    Retrieve a filtered block tree from ``store``, only returning branches
    whose leaf state's justified/finalized info agrees with that in ``store``.
    """
    base = store.justified_checkpoint.root
    blocks: Dict[Root, BeaconBlock] = {}
    filter_block_tree(store, base, blocks)
    return blocks

get_head

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def get_head(store: Store) -> Root:
    # Get filtered block tree that only includes viable branches
    blocks = get_filtered_block_tree(store)
    # Execute the LMD-GHOST fork choice
    head = store.justified_checkpoint.root
    while True:
        children = [
            root for root in blocks.keys()
            if blocks[root].parent_root == head
        ]
        if len(children) == 0:
            return head
        # Sort by latest attesting balance with ties broken lexicographically
        # Ties broken by favoring block with lexicographically higher root
        head = max(children, key=lambda root: (get_weight(store, root), root))

update_checkpoints

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def update_checkpoints(store: Store, justified_checkpoint: Checkpoint, finalized_checkpoint: Checkpoint) -> None:
    """
    Update checkpoints in store if necessary
    """
    # Update justified checkpoint
    if justified_checkpoint.epoch > store.justified_checkpoint.epoch:
        store.justified_checkpoint = justified_checkpoint

    # Update finalized checkpoint
    if finalized_checkpoint.epoch > store.finalized_checkpoint.epoch:
        store.finalized_checkpoint = finalized_checkpoint

update_unrealized_checkpoints

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def update_unrealized_checkpoints(store: Store, unrealized_justified_checkpoint: Checkpoint,
                                  unrealized_finalized_checkpoint: Checkpoint) -> None:
    """
    Update unrealized checkpoints in store if necessary
    """
    # Update unrealized justified checkpoint
    if unrealized_justified_checkpoint.epoch > store.unrealized_justified_checkpoint.epoch:
        store.unrealized_justified_checkpoint = unrealized_justified_checkpoint

    # Update unrealized finalized checkpoint
    if unrealized_finalized_checkpoint.epoch > store.unrealized_finalized_checkpoint.epoch:
        store.unrealized_finalized_checkpoint = unrealized_finalized_checkpoint

Proposer head and reorg helpers

Implementing these helpers is optional.

is_head_late
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def is_head_late(store: Store, head_root: Root) -> bool:
    return not store.block_timeliness[head_root]
is_shuffling_stable
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def is_shuffling_stable(slot: Slot) -> bool:
    return slot % SLOTS_PER_EPOCH != 0
is_ffg_competitive
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def is_ffg_competitive(store: Store, head_root: Root, parent_root: Root) -> bool:
    return (store.unrealized_justifications[head_root] == store.unrealized_justifications[parent_root])
is_finalization_ok
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def is_finalization_ok(store: Store, slot: Slot) -> bool:
    epochs_since_finalization = compute_epoch_at_slot(slot) - store.finalized_checkpoint.epoch
    return epochs_since_finalization <= REORG_MAX_EPOCHS_SINCE_FINALIZATION
is_proposing_on_time
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def is_proposing_on_time(store: Store) -> bool:
    # Use half `SECONDS_PER_SLOT // INTERVALS_PER_SLOT` as the proposer reorg deadline
    time_into_slot = (store.time - store.genesis_time) % SECONDS_PER_SLOT
    proposer_reorg_cutoff = SECONDS_PER_SLOT // INTERVALS_PER_SLOT // 2
    return time_into_slot <= proposer_reorg_cutoff
is_head_weak
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def is_head_weak(store: Store, head_root: Root) -> bool:
    justified_state = store.checkpoint_states[store.justified_checkpoint]
    reorg_threshold = calculate_committee_fraction(justified_state, REORG_HEAD_WEIGHT_THRESHOLD)
    head_weight = get_weight(store, head_root)
    return head_weight < reorg_threshold
is_parent_strong
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def is_parent_strong(store: Store, parent_root: Root) -> bool:
    justified_state = store.checkpoint_states[store.justified_checkpoint]
    parent_threshold = calculate_committee_fraction(justified_state, REORG_PARENT_WEIGHT_THRESHOLD)
    parent_weight = get_weight(store, parent_root)
    return parent_weight > parent_threshold
get_proposer_head
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def get_proposer_head(store: Store, head_root: Root, slot: Slot) -> Root:
    head_block = store.blocks[head_root]
    parent_root = head_block.parent_root
    parent_block = store.blocks[parent_root]

    # Only re-org the head block if it arrived later than the attestation deadline.
    head_late = is_head_late(store, head_root)

    # Do not re-org on an epoch boundary where the proposer shuffling could change.
    shuffling_stable = is_shuffling_stable(slot)

    # Ensure that the FFG information of the new head will be competitive with the current head.
    ffg_competitive = is_ffg_competitive(store, head_root, parent_root)

    # Do not re-org if the chain is not finalizing with acceptable frequency.
    finalization_ok = is_finalization_ok(store, slot)

    # Only re-org if we are proposing on-time.
    proposing_on_time = is_proposing_on_time(store)

    # Only re-org a single slot at most.
    parent_slot_ok = parent_block.slot + 1 == head_block.slot
    current_time_ok = head_block.slot + 1 == slot
    single_slot_reorg = parent_slot_ok and current_time_ok

    # Check that the head has few enough votes to be overpowered by our proposer boost.
    assert store.proposer_boost_root != head_root  # ensure boost has worn off
    head_weak = is_head_weak(store, head_root)

    # Check that the missing votes are assigned to the parent and not being hoarded.
    parent_strong = is_parent_strong(store, parent_root)

    if all([head_late, shuffling_stable, ffg_competitive, finalization_ok,
            proposing_on_time, single_slot_reorg, head_weak, parent_strong]):
        # We can re-org the current head by building upon its parent block.
        return parent_root
    else:
        return head_root

Note: The ordering of conditions is a suggestion only. Implementations are free to optimize by re-ordering the conditions from least to most expensive and by returning early if any of the early conditions are False.

Pull-up tip helpers

compute_pulled_up_tip
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def compute_pulled_up_tip(store: Store, block_root: Root) -> None:
    state = store.block_states[block_root].copy()
    # Pull up the post-state of the block to the next epoch boundary
    process_justification_and_finalization(state)

    store.unrealized_justifications[block_root] = state.current_justified_checkpoint
    update_unrealized_checkpoints(store, state.current_justified_checkpoint, state.finalized_checkpoint)

    # If the block is from a prior epoch, apply the realized values
    block_epoch = compute_epoch_at_slot(store.blocks[block_root].slot)
    current_epoch = get_current_store_epoch(store)
    if block_epoch < current_epoch:
        update_checkpoints(store, state.current_justified_checkpoint, state.finalized_checkpoint)

on_tick helpers

on_tick_per_slot
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def on_tick_per_slot(store: Store, time: uint64) -> None:
    previous_slot = get_current_slot(store)

    # Update store time
    store.time = time

    current_slot = get_current_slot(store)

    # If this is a new slot, reset store.proposer_boost_root
    if current_slot > previous_slot:
        store.proposer_boost_root = Root()

    # If a new epoch, pull-up justification and finalization from previous epoch
    if current_slot > previous_slot and compute_slots_since_epoch_start(current_slot) == 0:
        update_checkpoints(store, store.unrealized_justified_checkpoint, store.unrealized_finalized_checkpoint)

on_attestation helpers

validate_target_epoch_against_current_time
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def validate_target_epoch_against_current_time(store: Store, attestation: Attestation) -> None:
    target = attestation.data.target

    # Attestations must be from the current or previous epoch
    current_epoch = get_current_store_epoch(store)
    # Use GENESIS_EPOCH for previous when genesis to avoid underflow
    previous_epoch = current_epoch - 1 if current_epoch > GENESIS_EPOCH else GENESIS_EPOCH
    # If attestation target is from a future epoch, delay consideration until the epoch arrives
    assert target.epoch in [current_epoch, previous_epoch]
validate_on_attestation
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def validate_on_attestation(store: Store, attestation: Attestation, is_from_block: bool) -> None:
    target = attestation.data.target

    # If the given attestation is not from a beacon block message, we have to check the target epoch scope.
    if not is_from_block:
        validate_target_epoch_against_current_time(store, attestation)

    # Check that the epoch number and slot number are matching
    assert target.epoch == compute_epoch_at_slot(attestation.data.slot)

    # Attestation target must be for a known block. If target block is unknown, delay consideration until block is found
    assert target.root in store.blocks

    # Attestations must be for a known block. If block is unknown, delay consideration until the block is found
    assert attestation.data.beacon_block_root in store.blocks
    # Attestations must not be for blocks in the future. If not, the attestation should not be considered
    assert store.blocks[attestation.data.beacon_block_root].slot <= attestation.data.slot

    # LMD vote must be consistent with FFG vote target
    assert target.root == get_checkpoint_block(store, attestation.data.beacon_block_root, target.epoch)

    # Attestations can only affect the fork choice of subsequent slots.
    # Delay consideration in the fork choice until their slot is in the past.
    assert get_current_slot(store) >= attestation.data.slot + 1
store_target_checkpoint_state
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def store_target_checkpoint_state(store: Store, target: Checkpoint) -> None:
    # Store target checkpoint state if not yet seen
    if target not in store.checkpoint_states:
        base_state = copy(store.block_states[target.root])
        if base_state.slot < compute_start_slot_at_epoch(target.epoch):
            process_slots(base_state, compute_start_slot_at_epoch(target.epoch))
        store.checkpoint_states[target] = base_state
update_latest_messages
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def update_latest_messages(store: Store, attesting_indices: Sequence[ValidatorIndex], attestation: Attestation) -> None:
    target = attestation.data.target
    beacon_block_root = attestation.data.beacon_block_root
    non_equivocating_attesting_indices = [i for i in attesting_indices if i not in store.equivocating_indices]
    for i in non_equivocating_attesting_indices:
        if i not in store.latest_messages or target.epoch > store.latest_messages[i].epoch:
            store.latest_messages[i] = LatestMessage(epoch=target.epoch, root=beacon_block_root)

Handlers

on_tick

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def on_tick(store: Store, time: uint64) -> None:
    # If the ``store.time`` falls behind, while loop catches up slot by slot
    # to ensure that every previous slot is processed with ``on_tick_per_slot``
    tick_slot = (time - store.genesis_time) // SECONDS_PER_SLOT
    while get_current_slot(store) < tick_slot:
        previous_time = store.genesis_time + (get_current_slot(store) + 1) * SECONDS_PER_SLOT
        on_tick_per_slot(store, previous_time)
    on_tick_per_slot(store, time)

on_block

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def on_block(store: Store, signed_block: SignedBeaconBlock) -> None:
    block = signed_block.message
    # Parent block must be known
    assert block.parent_root in store.block_states
    # Make a copy of the state to avoid mutability issues
    pre_state = copy(store.block_states[block.parent_root])
    # Blocks cannot be in the future. If they are, their consideration must be delayed until they are in the past.
    assert get_current_slot(store) >= block.slot

    # Check that block is later than the finalized epoch slot (optimization to reduce calls to get_ancestor)
    finalized_slot = compute_start_slot_at_epoch(store.finalized_checkpoint.epoch)
    assert block.slot > finalized_slot
    # Check block is a descendant of the finalized block at the checkpoint finalized slot
    finalized_checkpoint_block = get_checkpoint_block(
        store,
        block.parent_root,
        store.finalized_checkpoint.epoch,
    )
    assert store.finalized_checkpoint.root == finalized_checkpoint_block

    # Check the block is valid and compute the post-state
    state = pre_state.copy()
    block_root = hash_tree_root(block)
    state_transition(state, signed_block, True)
    # Add new block to the store
    store.blocks[block_root] = block
    # Add new state for this block to the store
    store.block_states[block_root] = state

    # Add block timeliness to the store
    time_into_slot = (store.time - store.genesis_time) % SECONDS_PER_SLOT
    is_before_attesting_interval = time_into_slot < SECONDS_PER_SLOT // INTERVALS_PER_SLOT
    is_timely = get_current_slot(store) == block.slot and is_before_attesting_interval
    store.block_timeliness[hash_tree_root(block)] = is_timely

    # Add proposer score boost if the block is timely and not conflicting with an existing block
    is_first_block = store.proposer_boost_root == Root()
    if is_timely and is_first_block:
        store.proposer_boost_root = hash_tree_root(block)

    # Update checkpoints in store if necessary
    update_checkpoints(store, state.current_justified_checkpoint, state.finalized_checkpoint)

    # Eagerly compute unrealized justification and finality
    compute_pulled_up_tip(store, block_root)

on_attestation

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def on_attestation(store: Store, attestation: Attestation, is_from_block: bool=False) -> None:
    """
    Run ``on_attestation`` upon receiving a new ``attestation`` from either within a block or directly on the wire.

    An ``attestation`` that is asserted as invalid may be valid at a later time,
    consider scheduling it for later processing in such case.
    """
    validate_on_attestation(store, attestation, is_from_block)

    store_target_checkpoint_state(store, attestation.data.target)

    # Get state at the `target` to fully validate attestation
    target_state = store.checkpoint_states[attestation.data.target]
    indexed_attestation = get_indexed_attestation(target_state, attestation)
    assert is_valid_indexed_attestation(target_state, indexed_attestation)

    # Update latest messages for attesting indices
    update_latest_messages(store, indexed_attestation.attesting_indices, attestation)

on_attester_slashing

Note: on_attester_slashing should be called while syncing and a client MUST maintain the equivocation set of AttesterSlashings from at least the latest finalized checkpoint.

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def on_attester_slashing(store: Store, attester_slashing: AttesterSlashing) -> None:
    """
    Run ``on_attester_slashing`` immediately upon receiving a new ``AttesterSlashing``
    from either within a block or directly on the wire.
    """
    attestation_1 = attester_slashing.attestation_1
    attestation_2 = attester_slashing.attestation_2
    assert is_slashable_attestation_data(attestation_1.data, attestation_2.data)
    state = store.block_states[store.justified_checkpoint.root]
    assert is_valid_indexed_attestation(state, attestation_1)
    assert is_valid_indexed_attestation(state, attestation_2)

    indices = set(attestation_1.attesting_indices).intersection(attestation_2.attesting_indices)
    for index in indices:
        store.equivocating_indices.add(index)