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

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Ethereum 2.0 Sharding -- Beacon Chain changes

Notice: This document is a work-in-progress for researchers and implementers.

Table of contents

Introduction

This document describes the extensions made to the Phase 0 design of The Beacon Chain to support data sharding, based on the ideas here and more broadly here, using KZG10 commitments to commit to data to remove any need for fraud proofs (and hence, safety-critical synchrony assumptions) in the design.

Custom types

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

Name SSZ equivalent Description
Shard uint64 A shard number
BLSCommitment Bytes48 A G1 curve point
BLSPoint uint256 A number x in the range 0 <= x < MODULUS

Constants

The following values are (non-configurable) constants used throughout the specification.

Name Value Notes
PRIMITIVE_ROOT_OF_UNITY 5 Primitive root of unity of the BLS12_381 (inner) modulus
DATA_AVAILABILITY_INVERSE_CODING_RATE 2**1 (= 2) Factor by which samples are extended for data availability encoding
POINTS_PER_SAMPLE uint64(2**3) (= 8) 31 * 8 = 248 bytes
MODULUS 0x73eda753299d7d483339d80809a1d80553bda402fffe5bfeffffffff00000001 (curve order of BLS12_381)

Configuration

Misc

Name Value Notes
MAX_SHARDS uint64(2**10) (= 1,024) Theoretical max shard count (used to determine data structure sizes)
INITIAL_ACTIVE_SHARDS uint64(2**6) (= 64) Initial shard count
GASPRICE_ADJUSTMENT_COEFFICIENT uint64(2**3) (= 8) Gasprice may decrease/increase by at most exp(1 / this value) per epoch
MAX_SHARD_HEADERS_PER_SHARD 4
MAX_SHARD_PROPOSER_SLASHINGS 2**4 (= 16) Maximum amount of shard proposer slashing operations per block

Shard block configs

Name Value Notes
MAX_SAMPLES_PER_BLOCK uint64(2**11) (= 2,048) 248 * 2,048 = 507,904 bytes
TARGET_SAMPLES_PER_BLOCK uint64(2**10) (= 1,024) 248 * 1,024 = 253,952 bytes

Precomputed size verification points

Name Value
G1_SETUP Type List[G1]. The G1-side trusted setup [G, G*s, G*s**2....]; note that the first point is the generator.
G2_SETUP Type List[G2]. The G2-side trusted setup [G, G*s, G*s**2....]
ROOT_OF_UNITY pow(PRIMITIVE_ROOT_OF_UNITY, (MODULUS - 1) // int(MAX_SAMPLES_PER_BLOCK * POINTS_PER_SAMPLE), MODULUS)

Gwei values

Name Value Unit Description
MAX_GASPRICE Gwei(2**33) (= 8,589,934,592) Gwei Max gasprice charged for a TARGET-sized shard block
MIN_GASPRICE Gwei(2**3) (= 8) Gwei Min gasprice charged for a TARGET-sized shard block

Time parameters

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

Domain types

Name Value
DOMAIN_SHARD_PROPOSER DomainType('0x80000000')
DOMAIN_SHARD_COMMITTEE DomainType('0x81000000')

Updated containers

The following containers have updated definitions to support Sharding.

AttestationData

class AttestationData(Container):
    slot: Slot
    index: CommitteeIndex
    # LMD GHOST vote
    beacon_block_root: Root
    # FFG vote
    source: Checkpoint
    target: Checkpoint
    # Shard header root
    shard_header_root: Root  # [New in Sharding]

BeaconBlockBody

class BeaconBlockBody(merge.BeaconBlockBody):  # [extends The Merge block body]
    shard_proposer_slashings: List[ShardProposerSlashing, MAX_SHARD_PROPOSER_SLASHINGS]
    shard_headers: List[SignedShardBlobHeader, MAX_SHARDS * MAX_SHARD_HEADERS_PER_SHARD]

BeaconState

class BeaconState(merge.BeaconState):  # [extends The Merge block body]
    # [Updated fields]
    previous_epoch_attestations: List[PendingAttestation, MAX_ATTESTATIONS * SLOTS_PER_EPOCH]
    current_epoch_attestations: List[PendingAttestation, MAX_ATTESTATIONS * SLOTS_PER_EPOCH]
    # [New fields]
    previous_epoch_pending_shard_headers: List[PendingShardHeader, MAX_SHARDS * MAX_SHARD_HEADERS_PER_SHARD * SLOTS_PER_EPOCH]
    current_epoch_pending_shard_headers: List[PendingShardHeader, MAX_SHARDS * MAX_SHARD_HEADERS_PER_SHARD * SLOTS_PER_EPOCH]
    grandparent_epoch_confirmed_commitments: Vector[Vector[DataCommitment, SLOTS_PER_EPOCH], MAX_SHARDS]
    shard_gasprice: uint64
    current_epoch_start_shard: Shard

New containers

The shard data itself is network-layer only, and can be found in the P2P specification. The beacon chain registers just the commitments of the shard data.

DataCommitment

class DataCommitment(Container):
    # KZG10 commitment to the data
    point: BLSCommitment
    # Length of the data in samples
    length: uint64

ShardBlobBodySummary

class ShardBlobBodySummary(Container):
    # The actual data commitment
    commitment: DataCommitment
    # Proof that the degree < commitment.length
    degree_proof: BLSCommitment
    # Hash-tree-root as summary of the data field
    data_root: Root
    # Latest block root of the Beacon Chain, before shard_blob.slot
    beacon_block_root: Root

ShardBlobHeader

class ShardBlobHeader(Container):
    # Slot and shard that this header is intended for
    slot: Slot
    shard: Shard
    body_summary: ShardBlobBodySummary
    # Proposer of the shard-blob
    proposer_index: ValidatorIndex

SignedShardBlobHeader

class SignedShardBlobHeader(Container):
    message: ShardBlobHeader
    signature: BLSSignature

PendingShardHeader

class PendingShardHeader(Container):
    # Slot and shard that this header is intended for
    slot: Slot
    shard: Shard
    # KZG10 commitment to the data
    commitment: DataCommitment
    # hash_tree_root of the ShardHeader (stored so that attestations can be checked against it)
    root: Root
    # Who voted for the header
    votes: Bitlist[MAX_VALIDATORS_PER_COMMITTEE]
    # Has this header been confirmed?
    confirmed: boolean

ShardBlobReference

class ShardBlobReference(Container):
    # Slot and shard that this reference is intended for
    slot: Slot
    shard: Shard
    # Hash-tree-root of commitment data
    body_root: Root
    # Proposer of the shard-blob
    proposer_index: ValidatorIndex

SignedShardBlobReference

class SignedShardBlobReference(Container):
    message: ShardBlobReference
    signature: BLSSignature

ShardProposerSlashing

class ShardProposerSlashing(Container):
    signed_reference_1: SignedShardBlobReference
    signed_reference_2: SignedShardBlobReference

Helper functions

Misc

next_power_of_two

def next_power_of_two(x):
    return 2 ** ((x - 1).bit_length())

compute_previous_slot

def compute_previous_slot(slot: Slot) -> Slot:
    if slot > 0:
        return Slot(slot - 1)
    else:
        return Slot(0)

compute_updated_gasprice

def compute_updated_gasprice(prev_gasprice: Gwei, shard_block_length: uint64, adjustment_quotient: uint64) -> Gwei:
    if shard_block_length > TARGET_SAMPLES_PER_BLOCK:
        delta = max(1, prev_gasprice * (shard_block_length - TARGET_SAMPLES_PER_BLOCK)
                       // TARGET_SAMPLES_PER_BLOCK // adjustment_quotient)
        return min(prev_gasprice + delta, MAX_GASPRICE)
    else:
        delta = max(1, prev_gasprice * (TARGET_SAMPLES_PER_BLOCK - shard_block_length)
                       // TARGET_SAMPLES_PER_BLOCK // adjustment_quotient)
        return max(prev_gasprice, MIN_GASPRICE + delta) - delta

compute_committee_source_epoch

def compute_committee_source_epoch(epoch: Epoch, period: uint64) -> Epoch:
    """
    Return the source epoch for computing the committee.
    """
    source_epoch = Epoch(epoch - epoch % period)
    if source_epoch >= period:
        source_epoch -= period  # `period` epochs lookahead
    return source_epoch

Beacon state accessors

Updated get_committee_count_per_slot

def get_committee_count_per_slot(state: BeaconState, epoch: Epoch) -> uint64:
    """
    Return the number of committees in each slot for the given ``epoch``.
    """
    return max(uint64(1), min(
        get_active_shard_count(state, epoch),
        uint64(len(get_active_validator_indices(state, epoch))) // SLOTS_PER_EPOCH // TARGET_COMMITTEE_SIZE,
    ))

get_active_shard_count

def get_active_shard_count(state: BeaconState, epoch: Epoch) -> uint64:
    """
    Return the number of active shards.
    Note that this puts an upper bound on the number of committees per slot.
    """
    return INITIAL_ACTIVE_SHARDS

get_shard_committee

def get_shard_committee(beacon_state: BeaconState, epoch: Epoch, shard: Shard) -> Sequence[ValidatorIndex]:
    """
    Return the shard committee of the given ``epoch`` of the given ``shard``.
    """
    source_epoch = compute_committee_source_epoch(epoch, SHARD_COMMITTEE_PERIOD)
    active_validator_indices = get_active_validator_indices(beacon_state, source_epoch)
    seed = get_seed(beacon_state, source_epoch, DOMAIN_SHARD_COMMITTEE)
    return compute_committee(
        indices=active_validator_indices,
        seed=seed,
        index=shard,
        count=get_active_shard_count(beacon_state, epoch),
    )

compute_proposer_index

Updated version to get a proposer index that will only allow proposers with a certain minimum balance, ensuring that the balance is always sufficient to cover gas costs.

def compute_proposer_index(beacon_state: BeaconState,
                           indices: Sequence[ValidatorIndex],
                           seed: Bytes32,
                           min_effective_balance: GWei = GWei(0)) -> ValidatorIndex:
    """
    Return from ``indices`` a random index sampled by effective balance.
    """
    assert len(indices) > 0
    MAX_RANDOM_BYTE = 2**8 - 1
    i = uint64(0)
    total = uint64(len(indices))
    while True:
        candidate_index = indices[compute_shuffled_index(i % total, total, seed)]
        random_byte = hash(seed + uint_to_bytes(uint64(i // 32)))[i % 32]
        effective_balance = beacon_state.validators[candidate_index].effective_balance
        if effective_balance <= min_effective_balance:
            continue
        if effective_balance * MAX_RANDOM_BYTE >= MAX_EFFECTIVE_BALANCE * random_byte:
            return candidate_index
        i += 1

get_shard_proposer_index

def get_shard_proposer_index(beacon_state: BeaconState, slot: Slot, shard: Shard) -> ValidatorIndex:
    """
    Return the proposer's index of shard block at ``slot``.
    """
    epoch = compute_epoch_at_slot(slot)
    committee = get_shard_committee(beacon_state, epoch, shard)
    seed = hash(get_seed(beacon_state, epoch, DOMAIN_BEACON_PROPOSER) + uint_to_bytes(slot))

    # Proposer must have sufficient balance to pay for worst case fee burn
    EFFECTIVE_BALANCE_MAX_DOWNWARD_DEVIATION = (
        (EFFECTIVE_BALANCE_INCREMENT - EFFECTIVE_BALANCE_INCREMENT)
        * HYSTERESIS_DOWNWARD_MULTIPLIER // HYSTERESIS_QUOTIENT
    )
    min_effective_balance = (
        beacon_state.shard_gasprice * MAX_SAMPLES_PER_BLOCK // TARGET_SAMPLES_PER_BLOCK
        + EFFECTIVE_BALANCE_MAX_DOWNWARD_DEVIATION
    )
    return compute_proposer_index(beacon_state, committee, seed, min_effective_balance)

get_start_shard

def get_start_shard(state: BeaconState, slot: Slot) -> Shard:
    """
    Return the start shard at ``slot``.
    """
    current_epoch_start_slot = compute_start_slot_at_epoch(get_current_epoch(state))
    shard = state.current_epoch_start_shard
    if slot > current_epoch_start_slot:
        # Current epoch or the next epoch lookahead
        for _slot in range(current_epoch_start_slot, slot):
            committee_count = get_committee_count_per_slot(state, compute_epoch_at_slot(Slot(_slot)))
            active_shard_count = get_active_shard_count(state, compute_epoch_at_slot(Slot(_slot)))
            shard = (shard + committee_count) % active_shard_count
    elif slot < current_epoch_start_slot:
        # Previous epoch
        for _slot in list(range(slot, current_epoch_start_slot))[::-1]:
            committee_count = get_committee_count_per_slot(state, compute_epoch_at_slot(Slot(_slot)))
            active_shard_count = get_active_shard_count(state, compute_epoch_at_slot(Slot(_slot)))
            # Ensure positive
            shard = (shard + active_shard_count - committee_count) % active_shard_count
    return Shard(shard)

compute_shard_from_committee_index

def compute_shard_from_committee_index(state: BeaconState, slot: Slot, index: CommitteeIndex) -> Shard:
    active_shards = get_active_shard_count(state, compute_epoch_at_slot(slot))
    return Shard((index + get_start_shard(state, slot)) % active_shards)

compute_committee_index_from_shard

def compute_committee_index_from_shard(state: BeaconState, slot: Slot, shard: Shard) -> CommitteeIndex:
    active_shards = get_active_shard_count(state, compute_epoch_at_slot(slot))
    return CommitteeIndex((active_shards + shard - get_start_shard(state, slot)) % active_shards)

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 Sharding]
    process_execution_payload(state, block.body)  # [New in Merge]

Operations

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)
    # New shard proposer slashing processing
    for_ops(body.shard_proposer_slashings, process_shard_proposer_slashing)
    # Limit is dynamic based on active shard count
    assert len(body.shard_headers) <= MAX_SHARD_HEADERS_PER_SHARD * get_active_shard_count(state, get_current_epoch(state))
    for_ops(body.shard_headers, process_shard_header)
    # New attestation processing
    for_ops(body.attestations, process_attestation)
    for_ops(body.deposits, process_deposit)
    for_ops(body.voluntary_exits, process_voluntary_exit)

New Attestation processing

Updated process_attestation

def process_attestation(state: BeaconState, attestation: Attestation) -> None:
    phase0.process_attestation(state, attestation)
    update_pending_votes(state, attestation)

update_pending_votes

def update_pending_votes(state: BeaconState, attestation: Attestation) -> None:
    # Find and update the PendingShardHeader object, invalid block if pending header not in state
    if compute_epoch_at_slot(attestation.data.slot) == get_current_epoch(state):
        pending_headers = state.current_epoch_pending_shard_headers
    else:
        pending_headers = state.previous_epoch_pending_shard_headers
    pending_header = None
    for header in pending_headers:
        if header.root == attestation.data.shard_header_root:
            pending_header = header
    assert pending_header is not None
    assert pending_header.slot == attestation.data.slot
    assert pending_header.shard == compute_shard_from_committee_index(
        state,
        attestation.data.slot,
        attestation.data.index,
    )
    for i in range(len(pending_header.votes)):
        pending_header.votes[i] = pending_header.votes[i] or attestation.aggregation_bits[i]

    # Check if the PendingShardHeader is eligible for expedited confirmation
    # Requirement 1: nothing else confirmed
    all_candidates = [
        c for c in pending_headers if
        (c.slot, c.shard) == (pending_header.slot, pending_header.shard)
    ]
    if True in [c.confirmed for c in all_candidates]:
        return

    # Requirement 2: >= 2/3 of balance attesting
    participants = get_attesting_indices(state, attestation.data, pending_header.votes)
    participants_balance = get_total_balance(state, participants)
    full_committee = get_beacon_committee(state, attestation.data.slot, attestation.data.index)
    full_committee_balance = get_total_balance(state, full_committee)
    if participants_balance * 3 >= full_committee_balance * 2:
        pending_header.confirmed = True

process_shard_header

def process_shard_header(state: BeaconState,
                         signed_header: SignedShardBlobHeader) -> None:
    header = signed_header.message
    # Verify the header is not 0, and not from the future.
    assert Slot(0) < header.slot <= state.slot
    header_epoch = compute_epoch_at_slot(header.slot)
    # Verify that the header is within the processing time window
    assert header_epoch in [get_previous_epoch(state), get_current_epoch(state)]
    # Verify that the shard is active
    assert header.shard < get_active_shard_count(state, header_epoch)
    # Verify that the block root matches,
    # to ensure the header will only be included in this specific Beacon Chain sub-tree.
    assert header.body_summary.beacon_block_root == get_block_root_at_slot(state, header.slot - 1)
    # Verify proposer
    assert header.proposer_index == get_shard_proposer_index(state, header.slot, header.shard)
    # Verify signature
    signing_root = compute_signing_root(header, get_domain(state, DOMAIN_SHARD_HEADER))
    assert bls.Verify(state.validators[header.proposer_index].pubkey, signing_root, signed_header.signature)

    # Verify the length by verifying the degree.
    body_summary = header.body_summary
    if body_summary.commitment.length == 0:
        assert body_summary.degree_proof == G1_SETUP[0]
    assert (
        bls.Pairing(body_summary.degree_proof, G2_SETUP[0])
        == bls.Pairing(body_summary.commitment.point, G2_SETUP[-body_summary.commitment.length])
    )

    # Get the correct pending header list
    if header_epoch == get_current_epoch(state):
        pending_headers = state.current_epoch_pending_shard_headers
    else:
        pending_headers = state.previous_epoch_pending_shard_headers

    header_root = hash_tree_root(header)
    # Check that this header is not yet in the pending list
    assert header_root not in [pending_header.root for pending_header in pending_headers]

    # Include it in the pending list
    index = compute_committee_index_from_shard(state, header.slot, header.shard)
    committee_length = len(get_beacon_committee(state, header.slot, index))
    pending_headers.append(PendingShardHeader(
        slot=header.slot,
        shard=header.shard,
        commitment=body_summary.commitment,
        root=header_root,
        votes=Bitlist[MAX_VALIDATORS_PER_COMMITTEE]([0] * committee_length),
        confirmed=False,
    ))

The degree proof works as follows. For a block B with length l (so l values in [0...l - 1], seen as a polynomial B(X) which takes these values), the length proof is the commitment to the polynomial B(X) * X**(MAX_DEGREE + 1 - l), where MAX_DEGREE is the maximum power of s available in the setup, which is MAX_DEGREE = len(G2_SETUP) - 1. The goal is to ensure that a proof can only be constructed if deg(B) < l (there are not hidden higher-order terms in the polynomial, which would thwart reconstruction).

Shard Proposer slashings
def process_shard_proposer_slashing(state: BeaconState, proposer_slashing: ShardProposerSlashing) -> None:
    reference_1 = proposer_slashing.signed_reference_1.message
    reference_2 = proposer_slashing.signed_reference_2.message

    # Verify header slots match
    assert reference_1.slot == reference_2.slot
    # Verify header shards match
    assert reference_1.shard == reference_2.shard
    # Verify header proposer indices match
    assert reference_1.proposer_index == reference_2.proposer_index
    # Verify the headers are different (i.e. different body)
    assert reference_1 != reference_2
    # Verify the proposer is slashable
    proposer = state.validators[reference_1.proposer_index]
    assert is_slashable_validator(proposer, get_current_epoch(state))
    # Verify signatures
    for signed_header in (proposer_slashing.signed_reference_1, proposer_slashing.signed_reference_2):
        domain = get_domain(state, DOMAIN_SHARD_PROPOSER, compute_epoch_at_slot(signed_header.message.slot))
        signing_root = compute_signing_root(signed_header.message, domain)
        assert bls.Verify(proposer.pubkey, signing_root, signed_header.signature)

    slash_validator(state, reference_1.proposer_index)

Epoch transition

This epoch transition overrides the Merge epoch transition:

def process_epoch(state: BeaconState) -> None:
    process_justification_and_finalization(state)
    process_rewards_and_penalties(state)
    process_registry_updates(state)

    process_slashings(state)

    # Sharding
    process_pending_headers(state)
    process_confirmed_header_fees(state)
    reset_pending_headers(state)

    # Final updates
    # Phase 0
    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_record_updates(state)

    process_shard_epoch_increment(state)

Pending headers

def process_pending_headers(state: BeaconState) -> None:
    # Pending header processing applies to the previous epoch.
    # Skip if `GENESIS_EPOCH` because no prior epoch to process.
    if get_current_epoch(state) == GENESIS_EPOCH:
        return

    previous_epoch = get_previous_epoch(state)
    previous_epoch_start_slot = compute_start_slot_at_epoch(previous_epoch)
    for slot in range(previous_epoch_start_slot, previous_epoch_start_slot + SLOTS_PER_EPOCH):
        for shard in range(get_active_shard_count(state, previous_epoch)):
            # Pending headers for this (slot, shard) combo
            candidates = [
                c for c in state.previous_epoch_pending_shard_headers
                if (c.slot, c.shard) == (slot, shard)
            ]
            # If any candidates already confirmed, skip
            if True in [c.confirmed for c in candidates]:
                continue

            # The entire committee (and its balance)
            full_committee = get_beacon_committee(state, slot, shard)
            # The set of voters who voted for each header (and their total balances)
            voting_sets = [
                [v for i, v in enumerate(full_committee) if c.votes[i]]
                for c in candidates
            ]
            voting_balances = [
                get_total_balance(state, voters)
                for voters in voting_sets
            ]
            # Get the index with the most total balance voting for them.
            # NOTE: if two choices get exactly the same voting balance,
            # the candidate earlier in the list wins
            if max(voting_balances) > 0:
                winning_index = voting_balances.index(max(voting_balances))
            else:
                # If no votes, zero wins
                winning_index = [c.root for c in candidates].index(Root())
            candidates[winning_index].confirmed = True
    for slot_index in range(SLOTS_PER_EPOCH):
        for shard in range(SHARD_COUNT):
            state.grandparent_epoch_confirmed_commitments[shard][slot_index] = DataCommitment()
    confirmed_headers = [candidate for candidate in state.previous_epoch_pending_shard_headers if candidate.confirmed]
    for header in confirmed_headers:
        state.grandparent_epoch_confirmed_commitments[header.shard][header.slot % SLOTS_PER_EPOCH] = header.commitment

def charge_confirmed_header_fees(state: BeaconState) -> None:
    new_gasprice = state.shard_gasprice
    adjustment_quotient = (
        get_active_shard_count(state, get_current_epoch(state))
        * SLOTS_PER_EPOCH * GASPRICE_ADJUSTMENT_COEFFICIENT
    )
    previous_epoch_start_slot = compute_start_slot_at_epoch(get_previous_epoch(state))
    for slot in range(previous_epoch_start_slot, previous_epoch_start_slot + SLOTS_PER_EPOCH):
        for shard in range(SHARD_COUNT):
            confirmed_candidates = [
                c for c in state.previous_epoch_pending_shard_headers
                if (c.slot, c.shard, c.confirmed) == (slot, shard, True)
            ]
            if not any(confirmed_candidates):
                continue
            candidate = confirmed_candidates[0]

            # Charge EIP 1559 fee
            proposer = get_shard_proposer_index(state, slot, shard)
            fee = (
                (state.shard_gasprice * candidate.commitment.length)
                // TARGET_SAMPLES_PER_BLOCK
            )
            decrease_balance(state, proposer, fee)

            # Track updated gas price
            new_gasprice = compute_updated_gasprice(
                new_gasprice,
                candidate.commitment.length,
                adjustment_quotient,
            )
    state.shard_gasprice = new_gasprice

def reset_pending_headers(state: BeaconState) -> None:
    state.previous_epoch_pending_shard_headers = state.current_epoch_pending_shard_headers
    state.current_epoch_pending_shard_headers = []
    # Add dummy "empty" PendingShardHeader (default vote for if no shard header available)
    next_epoch = get_current_epoch(state) + 1
    next_epoch_start_slot = compute_start_slot_at_epoch(next_epoch)
    for slot in range(next_epoch_start_slot, next_epoch_start_slot + SLOTS_PER_EPOCH):
        for index in range(get_committee_count_per_slot(state, next_epoch)):
            shard = compute_shard_from_committee_index(state, slot, index)
            committee_length = len(get_beacon_committee(state, slot, shard))
            state.current_epoch_pending_shard_headers.append(PendingShardHeader(
                slot=slot,
                shard=shard,
                commitment=DataCommitment(),
                root=Root(),
                votes=Bitlist[MAX_VALIDATORS_PER_COMMITTEE]([0] * committee_length),
                confirmed=False,
            ))

Shard epoch increment

def process_shard_epoch_increment(state: BeaconState) -> None:
    # Update current_epoch_start_shard
    state.current_epoch_start_shard = get_start_shard(state, Slot(state.slot + 1))