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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
<!-- TOC -->
<!-- START doctoc generated TOC please keep comment here to allow auto update -->
<!-- DON'T EDIT THIS SECTION, INSTEAD RE-RUN doctoc TO UPDATE -->
- [Introduction](#introduction)
- [Custom types](#custom-types)
- [Constants](#constants)
- [Misc](#misc)
- [Domain types](#domain-types)
- [Shard Header Status](#shard-header-status)
- [Preset](#preset)
- [Misc](#misc-1)
- [Shard block samples](#shard-block-samples)
- [Precomputed size verification points](#precomputed-size-verification-points)
- [Gwei values](#gwei-values)
- [Configuration](#configuration)
- [Updated containers](#updated-containers)
- [`AttestationData`](#attestationdata)
- [`BeaconBlockBody`](#beaconblockbody)
- [`BeaconState`](#beaconstate)
- [New containers](#new-containers)
- [`DataCommitment`](#datacommitment)
- [`ShardBlobBodySummary`](#shardblobbodysummary)
- [`ShardBlobHeader`](#shardblobheader)
- [`SignedShardBlobHeader`](#signedshardblobheader)
- [`PendingShardHeader`](#pendingshardheader)
- [`ShardBlobReference`](#shardblobreference)
- [`SignedShardBlobReference`](#signedshardblobreference)
- [`ShardProposerSlashing`](#shardproposerslashing)
- [`ShardCommitteeWork`](#shardcommitteework)
- [Helper functions](#helper-functions)
- [Misc](#misc-2)
- [`next_power_of_two`](#next_power_of_two)
- [`compute_previous_slot`](#compute_previous_slot)
- [`compute_updated_gasprice`](#compute_updated_gasprice)
- [`compute_committee_source_epoch`](#compute_committee_source_epoch)
- [Beacon state accessors](#beacon-state-accessors)
- [Updated `get_committee_count_per_slot`](#updated-get_committee_count_per_slot)
- [`get_active_shard_count`](#get_active_shard_count)
- [`get_shard_committee`](#get_shard_committee)
- [`compute_proposer_index`](#compute_proposer_index)
- [`get_shard_proposer_index`](#get_shard_proposer_index)
- [`get_start_shard`](#get_start_shard)
- [`compute_shard_from_committee_index`](#compute_shard_from_committee_index)
- [`compute_committee_index_from_shard`](#compute_committee_index_from_shard)
- [Block processing](#block-processing)
- [Operations](#operations)
- [New Attestation processing](#new-attestation-processing)
- [Updated `process_attestation`](#updated-process_attestation)
- [`update_pending_votes`](#update_pending_votes)
- [`process_shard_header`](#process_shard_header)
- [Shard Proposer slashings](#shard-proposer-slashings)
- [Epoch transition](#epoch-transition)
- [Pending headers](#pending-headers)
- [Shard epoch increment](#shard-epoch-increment)
<!-- END doctoc generated TOC please keep comment here to allow auto update -->
<!-- /TOC -->
## 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](https://hackmd.io/G-Iy5jqyT7CXWEz8Ssos8g) and more broadly [here](https://arxiv.org/abs/1809.09044),
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.
### Misc
| 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) |
### Domain types
| Name | Value |
| - | - |
| `DOMAIN_SHARD_PROPOSER` | `DomainType('0x80000000')` |
| `DOMAIN_SHARD_COMMITTEE` | `DomainType('0x81000000')` |
### Shard Header Status
| Name | Value | Notes |
| - | - | - |
| `UNCONFIRMED_SHARD_DATA` | `0` | Unconfirmed, nullified after confirmation time elapses |
| `CONFIRMED_SHARD_DATA` | `1` | Confirmed, reduced to just the commitment |
| `PENDING_SHARD_DATA` | `2` | Pending, a list of competing headers |
## Preset
### Misc
| Name | Value | Notes |
| - | - | - |
| `MAX_SHARDS` | `uint64(2**10)` (= 1,024) | Theoretical max shard count (used to determine data structure sizes) |
| `GASPRICE_ADJUSTMENT_COEFFICIENT` | `uint64(2**3)` (= 8) | Gasprice may decrease/increase by at most exp(1 / this value) *per epoch* |
| `MAX_SHARD_PROPOSER_SLASHINGS` | `2**4` (= 16) | Maximum amount of shard proposer slashing operations per block |
| `MAX_SHARD_HEADERS_PER_SHARD` | `4` | |
| `SHARD_STATE_MEMORY_SLOTS` | `uint64(2**8)` (=256) | Number of slots for which shard commitments and confirmation status is directly available in the state |
### Shard block samples
| 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 |
## Configuration
| Name | Value | Notes |
| - | - | - |
| `INITIAL_ACTIVE_SHARDS` | `uint64(2**6)` (= 64) | Initial shard count |
## Updated containers
The following containers have updated definitions to support Sharding.
### `AttestationData`
```python
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`
```python
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`
```python
class BeaconState(merge.BeaconState): # [extends The Merge state]
# [Updated fields] (Warning: this changes with Altair, Sharding will rebase to use participation-flags)
previous_epoch_attestations: List[PendingAttestation, MAX_ATTESTATIONS * SLOTS_PER_EPOCH]
current_epoch_attestations: List[PendingAttestation, MAX_ATTESTATIONS * SLOTS_PER_EPOCH]
# [New fields]
# A ring buffer of the latest slots, with information per active shard.
shard_buffer: Vector[List[ShardCommitteeWork, MAX_SHARDS], SHARD_STATE_MEMORY_SLOTS]
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](./p2p-interface.md).
The beacon chain registers just the commitments of the shard data.
### `DataCommitment`
```python
class DataCommitment(Container):
# KZG10 commitment to the data
point: BLSCommitment
# Length of the data in samples
length: uint64
```
### `ShardBlobBodySummary`
```python
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`
```python
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`
```python
class SignedShardBlobHeader(Container):
message: ShardBlobHeader
signature: BLSSignature
```
### `PendingShardHeader`
```python
class PendingShardHeader(Container):
# 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]
# Sum of effective balances of votes
weight: Gwei
```
### `ShardBlobReference`
```python
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`
```python
class SignedShardBlobReference(Container):
message: ShardBlobReference
signature: BLSSignature
```
### `ShardProposerSlashing`
```python
class ShardProposerSlashing(Container):
signed_reference_1: SignedShardBlobReference
signed_reference_2: SignedShardBlobReference
```
### `ShardCommitteeWork`
```python
class ShardWork(Container):
# Upon confirmation the data is reduced to just the header.
status: Union[ # See Shard Header Status enum
None, # UNCONFIRMED_SHARD_DATA
DataCommitment, # CONFIRMED_SHARD_DATA
List[PendingShardHeader, MAX_SHARD_HEADERS_PER_SHARD] # PENDING_SHARD_DATA
]
```
## Helper functions
### Misc
#### `next_power_of_two`
```python
def next_power_of_two(x: int) -> int:
return 2 ** ((x - 1).bit_length())
```
#### `compute_previous_slot`
```python
def compute_previous_slot(slot: Slot) -> Slot:
if slot > 0:
return Slot(slot - 1)
else:
return Slot(0)
```
#### `compute_updated_gasprice`
```python
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`
```python
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`
```python
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`
```python
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`
```python
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.
```python
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`
```python
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_SHARD_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`
```python
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`
```python
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))
assert index < active_shards
return Shard((index + get_start_shard(state, slot)) % active_shards)
```
#### `compute_committee_index_from_shard`
```python
def compute_committee_index_from_shard(state: BeaconState, slot: Slot, shard: Shard) -> CommitteeIndex:
epoch = compute_epoch_at_slot(slot)
active_shards = get_active_shard_count(state, epoch)
index = CommitteeIndex((active_shards + shard - get_start_shard(state, slot)) % active_shards)
assert index >= get_committee_count_per_slot(state, epoch)
return index
```
### Block processing
```python
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]
# Pre-merge, skip execution payload processing
if is_execution_enabled(state, block):
process_execution_payload(state, block.body.execution_payload, EXECUTION_ENGINE) # [New in Merge]
```
#### Operations
```python
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`
```python
def process_attestation(state: BeaconState, attestation: Attestation) -> None:
phase0.process_attestation(state, attestation)
update_pending_votes(state, attestation)
```
#### `update_pending_votes`
```python
def update_pending_votes(state: BeaconState, attestation: Attestation) -> None:
attestation_shard = compute_shard_from_committee_index(
state,
attestation.data.slot,
attestation.data.index,
)
buffer_index = attestation.data.slot % SHARD_STATE_MEMORY_SLOTS
committee_work = state.shard_buffer[buffer_index][attestation_shard]
# Skip attestation vote accounting if the header is already confirmed
if committee_work.status.selector == CONFIRMED_SHARD_DATA:
return
# Note that shard-slot combinations without an assigned committee do not have a pending state
assert shard_info.status.selector == PENDING_SHARD_DATA
current_headers: Sequence[PendingShardHeader] = committee_work.status.value
# Find the corresponding header, abort if it cannot be found
header_index = [header.root for header in current_headers].index(attestation.data.shard_header_root)
# Update votes bitfield in the state
pending_header: PendingShardHeader = state.shard_buffer[buffer_index][attestation_shard][header_index]
full_committee = get_beacon_committee(state, attestation.data.slot, attestation.data.index)
participants_balance = Gwei(0)
for i, bit in enumerate(attestation.aggregation_bits):
weight = state.validators[full_committee[i]].effective_balance
if bit:
if not pending_header.votes[i]:
pending_header.weight += weight
pending_header.votes[i] = True
participants_balance += weight
# Check if the PendingShardHeader is eligible for expedited confirmation, requiring 2/3 of balance attesting
full_committee_balance = get_total_balance(state, set(full_committee))
if participants_balance * 3 >= full_committee_balance * 2:
if pending_header.commitment == DataCommitment():
# The committee voted to not confirm anything
state.shard_buffer[buffer_index][attestation_shard].change(
selector=UNCONFIRMED_SHARD_DATA,
value=None,
)
else:
state.shard_buffer[buffer_index][attestation_shard].change(
selector=CONFIRMED_SHARD_DATA,
value=pending_header.commitment,
)
```
#### `process_shard_header`
```python
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)
# Check that this data is still pending
committee_work = state.shard_buffer[header.slot % SHARD_STATE_MEMORY_SLOTS][header.slot]
assert committee_work.status.selector == PENDING_SHARD_DATA
# Check that this header is not yet in the pending list
current_headers: Sequence[PendingShardHeader] = committee_work.status.value
assert header_root not in [pending_header.root for pending_header in current_headers]
# 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_PROPOSER))
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])
)
# Initialize the pending header
index = compute_committee_index_from_shard(state, header.slot, header.shard)
committee_length = len(get_beacon_committee(state, header.slot, index))
initial_votes = Bitlist[MAX_VALIDATORS_PER_COMMITTEE]([0] * committee_length)
pending_header = PendingShardHeader(
commitment=body_summary.commitment,
root=header_root,
votes=initial_votes,
weight=0,
)
# Include it in the pending list
state.shard_buffer[header.slot % SHARD_STATE_MEMORY_SLOTS][header.slot].append(pending_header)
```
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
```python
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:
```python
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)
charge_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
```python
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)
# Mark stale headers as unconfirmed
for slot in range(previous_epoch_start_slot, previous_epoch_start_slot + SLOTS_PER_EPOCH):
buffer_index = slot % SHARD_STATE_MEMORY_SLOTS
for shard_index in range(len(state.shard_buffer[buffer_index])):
committee_work = state.shard_buffer[buffer_index][shard_index]
if committee_work.selector == PENDING_SHARD_DATA:
winning_header = max(committee_work.value, key=lambda header: header.weight)
if winning_header.commitment == DataCommitment():
committee_work.change(selector=UNCONFIRMED_SHARD_DATA, value=None)
else:
committee_work.change(selector=CONFIRMED_SHARD_DATA, value=winning_header.commitment)
```
```python
def charge_confirmed_header_fees(state: BeaconState) -> None:
new_gasprice = state.shard_gasprice
previous_epoch = get_previous_epoch(state)
previous_epoch_start_slot = compute_start_slot_at_epoch(previous_epoch)
adjustment_quotient = (
get_active_shard_count(state, previous_epoch)
* SLOTS_PER_EPOCH * GASPRICE_ADJUSTMENT_COEFFICIENT
)
# Iterate through confirmed shard-headers
for slot in range(previous_epoch_start_slot, previous_epoch_start_slot + SLOTS_PER_EPOCH):
buffer_index = slot % SHARD_STATE_MEMORY_SLOTS
for shard_index in range(len(state.shard_buffer[buffer_index])):
committee_work = state.shard_buffer[buffer_index][shard_index]
if committee_work.status.selector == CONFIRMED_SHARD_DATA:
# Charge EIP 1559 fee
proposer = get_shard_proposer_index(state, slot, Shard(shard_index))
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
```
```python
def reset_pending_headers(state: BeaconState) -> None:
# Add dummy "empty" PendingShardHeader (default vote if no shard header is available)
next_epoch = get_current_epoch(state) + 1
next_epoch_start_slot = compute_start_slot_at_epoch(next_epoch)
committees_per_slot = get_committee_count_per_slot(state, next_epoch)
active_shards = get_active_shard_count(state, next_epoch)
for slot in range(next_epoch_start_slot, next_epoch_start_slot + SLOTS_PER_EPOCH):
buffer_index = slot % SHARD_STATE_MEMORY_SLOTS
# Reset the shard work tracking
state.shard_buffer[buffer_index] = [ShardCommitteeWork() for _ in range(active_shards)]
start_shard = get_start_shard(state, slot)
for shard_index in range(state.shard_buffer[buffer_index]):
if start_shard <= shard_index < start_shard + committees_per_slot:
# a committee is available, initialize a pending shard-header list
committee_index = CommitteeIndex(shard_index - start_shard)
committee_length = len(get_beacon_committee(state, slot, committee_index))
state.shard_buffer[buffer_index][shard_index].change(
selector=PENDING_SHARD_DATA,
value=List[PendingShardHeader, MAX_SHARD_HEADERS_PER_SHARD](
PendingShardHeader(
commitment=DataCommitment(),
root=Root(),
votes=Bitlist[MAX_VALIDATORS_PER_COMMITTEE]([0] * committee_length),
weight=0,
)
)
)
# the shard is inactive for this slot otherwise, no committee available, default to UNCONFIRMED_SHARD_DATA.
```
#### Shard epoch increment
```python
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))
```
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