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# Phase 0 -- The Beacon Chain
## Table of contents
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- [Introduction](#introduction)
- [Notation](#notation)
- [Custom types](#custom-types)
- [Constants](#constants)
- [Misc](#misc)
- [Withdrawal prefixes](#withdrawal-prefixes)
- [Domain types](#domain-types)
- [Preset](#preset)
- [Misc](#misc-1)
- [Gwei values](#gwei-values)
- [Time parameters](#time-parameters)
- [State list lengths](#state-list-lengths)
- [Rewards and penalties](#rewards-and-penalties)
- [Max operations per block](#max-operations-per-block)
- [Configuration](#configuration)
- [Genesis settings](#genesis-settings)
- [Time parameters](#time-parameters-1)
- [Validator cycle](#validator-cycle)
- [Containers](#containers)
- [Misc dependencies](#misc-dependencies)
- [`Fork`](#fork)
- [`ForkData`](#forkdata)
- [`Checkpoint`](#checkpoint)
- [`Validator`](#validator)
- [`AttestationData`](#attestationdata)
- [`IndexedAttestation`](#indexedattestation)
- [`PendingAttestation`](#pendingattestation)
- [`Eth1Data`](#eth1data)
- [`HistoricalBatch`](#historicalbatch)
- [`DepositMessage`](#depositmessage)
- [`DepositData`](#depositdata)
- [`BeaconBlockHeader`](#beaconblockheader)
- [`SigningData`](#signingdata)
- [Beacon operations](#beacon-operations)
- [`ProposerSlashing`](#proposerslashing)
- [`AttesterSlashing`](#attesterslashing)
- [`Attestation`](#attestation)
- [`Deposit`](#deposit)
- [`VoluntaryExit`](#voluntaryexit)
- [Beacon blocks](#beacon-blocks)
- [`BeaconBlockBody`](#beaconblockbody)
- [`BeaconBlock`](#beaconblock)
- [Beacon state](#beacon-state)
- [`BeaconState`](#beaconstate)
- [Signed envelopes](#signed-envelopes)
- [`SignedVoluntaryExit`](#signedvoluntaryexit)
- [`SignedBeaconBlock`](#signedbeaconblock)
- [`SignedBeaconBlockHeader`](#signedbeaconblockheader)
- [Helper functions](#helper-functions)
- [Math](#math)
- [`integer_squareroot`](#integer_squareroot)
- [`xor`](#xor)
- [`uint_to_bytes`](#uint_to_bytes)
- [`bytes_to_uint64`](#bytes_to_uint64)
- [`saturating_sub`](#saturating_sub)
- [Crypto](#crypto)
- [`hash`](#hash)
- [`hash_tree_root`](#hash_tree_root)
- [BLS signatures](#bls-signatures)
- [Predicates](#predicates)
- [`is_active_validator`](#is_active_validator)
- [`is_eligible_for_activation_queue`](#is_eligible_for_activation_queue)
- [`is_eligible_for_activation`](#is_eligible_for_activation)
- [`is_slashable_validator`](#is_slashable_validator)
- [`is_slashable_attestation_data`](#is_slashable_attestation_data)
- [`is_valid_indexed_attestation`](#is_valid_indexed_attestation)
- [`is_valid_merkle_branch`](#is_valid_merkle_branch)
- [Misc](#misc-2)
- [`compute_shuffled_index`](#compute_shuffled_index)
- [`compute_proposer_index`](#compute_proposer_index)
- [`compute_committee`](#compute_committee)
- [`compute_epoch_at_slot`](#compute_epoch_at_slot)
- [`compute_start_slot_at_epoch`](#compute_start_slot_at_epoch)
- [`compute_activation_exit_epoch`](#compute_activation_exit_epoch)
- [`compute_fork_data_root`](#compute_fork_data_root)
- [`compute_fork_digest`](#compute_fork_digest)
- [`compute_domain`](#compute_domain)
- [`compute_signing_root`](#compute_signing_root)
- [Beacon state accessors](#beacon-state-accessors)
- [`get_current_epoch`](#get_current_epoch)
- [`get_previous_epoch`](#get_previous_epoch)
- [`get_block_root`](#get_block_root)
- [`get_block_root_at_slot`](#get_block_root_at_slot)
- [`get_randao_mix`](#get_randao_mix)
- [`get_active_validator_indices`](#get_active_validator_indices)
- [`get_validator_churn_limit`](#get_validator_churn_limit)
- [`get_seed`](#get_seed)
- [`get_committee_count_per_slot`](#get_committee_count_per_slot)
- [`get_beacon_committee`](#get_beacon_committee)
- [`get_beacon_proposer_index`](#get_beacon_proposer_index)
- [`get_total_balance`](#get_total_balance)
- [`get_total_active_balance`](#get_total_active_balance)
- [`get_domain`](#get_domain)
- [`get_indexed_attestation`](#get_indexed_attestation)
- [`get_attesting_indices`](#get_attesting_indices)
- [Beacon state mutators](#beacon-state-mutators)
- [`increase_balance`](#increase_balance)
- [`decrease_balance`](#decrease_balance)
- [`initiate_validator_exit`](#initiate_validator_exit)
- [`slash_validator`](#slash_validator)
- [Genesis](#genesis)
- [Genesis state](#genesis-state)
- [Genesis block](#genesis-block)
- [Beacon chain state transition function](#beacon-chain-state-transition-function)
- [Epoch processing](#epoch-processing)
- [Helper functions](#helper-functions-1)
- [Justification and finalization](#justification-and-finalization)
- [Rewards and penalties](#rewards-and-penalties-1)
- [Helpers](#helpers)
- [Components of attestation deltas](#components-of-attestation-deltas)
- [`get_attestation_deltas`](#get_attestation_deltas)
- [`process_rewards_and_penalties`](#process_rewards_and_penalties)
- [Registry updates](#registry-updates)
- [Slashings](#slashings)
- [Eth1 data votes updates](#eth1-data-votes-updates)
- [Effective balances updates](#effective-balances-updates)
- [Slashings balances updates](#slashings-balances-updates)
- [Randao mixes updates](#randao-mixes-updates)
- [Historical roots updates](#historical-roots-updates)
- [Participation records rotation](#participation-records-rotation)
- [Block processing](#block-processing)
- [Block header](#block-header)
- [RANDAO](#randao)
- [Eth1 data](#eth1-data)
- [Operations](#operations)
- [Proposer slashings](#proposer-slashings)
- [Attester slashings](#attester-slashings)
- [Attestations](#attestations)
- [Deposits](#deposits)
- [Voluntary exits](#voluntary-exits)
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## Introduction
This document represents the specification for Phase 0 -- The Beacon Chain.
At the core of Ethereum proof-of-stake is a system chain called the "beacon chain". The beacon chain stores and manages the registry of validators. In the initial deployment phases of proof-of-stake, the only mechanism to become a validator is to make a one-way ETH transaction to a deposit contract on the Ethereum proof-of-work chain. Activation as a validator happens when deposit receipts are processed by the beacon chain, the activation balance is reached, and a queuing process is completed. Exit is either voluntary or done forcibly as a penalty for misbehavior.
The primary source of load on the beacon chain is "attestations". Attestations are simultaneously availability votes for a shard block (in a later upgrade) and proof-of-stake votes for a beacon block (Phase 0).
## Notation
Code snippets appearing in `this style` are to be interpreted as Python 3 code.
## Custom types
We define the following Python custom types for type hinting and readability:
| Name | SSZ equivalent | Description |
| - | - | - |
| `Slot` | `uint64` | a slot number |
| `Epoch` | `uint64` | an epoch number |
| `CommitteeIndex` | `uint64` | a committee index at a slot |
| `ValidatorIndex` | `uint64` | a validator registry index |
| `Gwei` | `uint64` | an amount in Gwei |
| `Root` | `Bytes32` | a Merkle root |
| `Hash32` | `Bytes32` | a 256-bit hash |
| `Version` | `Bytes4` | a fork version number |
| `DomainType` | `Bytes4` | a domain type |
| `ForkDigest` | `Bytes4` | a digest of the current fork data |
| `Domain` | `Bytes32` | a signature domain |
| `BLSPubkey` | `Bytes48` | a BLS12-381 public key |
| `BLSSignature` | `Bytes96` | a BLS12-381 signature |
## Constants
The following values are (non-configurable) constants used throughout the specification.
### Misc
| Name | Value |
| - | - |
| `UINT64_MAX` | `uint64(2**64 - 1)` |
| `UINT64_MAX_SQRT` | `uint64(4294967295)` |
| `GENESIS_SLOT` | `Slot(0)` |
| `GENESIS_EPOCH` | `Epoch(0)` |
| `FAR_FUTURE_EPOCH` | `Epoch(2**64 - 1)` |
| `BASE_REWARDS_PER_EPOCH` | `uint64(4)` |
| `DEPOSIT_CONTRACT_TREE_DEPTH` | `uint64(2**5)` (= 32) |
| `JUSTIFICATION_BITS_LENGTH` | `uint64(4)` |
| `ENDIANNESS` | `'little'` |
### Withdrawal prefixes
| Name | Value |
| - | - |
| `BLS_WITHDRAWAL_PREFIX` | `Bytes1('0x00')` |
| `ETH1_ADDRESS_WITHDRAWAL_PREFIX` | `Bytes1('0x01')` |
### Domain types
| Name | Value |
| - | - |
| `DOMAIN_BEACON_PROPOSER` | `DomainType('0x00000000')` |
| `DOMAIN_BEACON_ATTESTER` | `DomainType('0x01000000')` |
| `DOMAIN_RANDAO` | `DomainType('0x02000000')` |
| `DOMAIN_DEPOSIT` | `DomainType('0x03000000')` |
| `DOMAIN_VOLUNTARY_EXIT` | `DomainType('0x04000000')` |
| `DOMAIN_SELECTION_PROOF` | `DomainType('0x05000000')` |
| `DOMAIN_AGGREGATE_AND_PROOF` | `DomainType('0x06000000')` |
| `DOMAIN_APPLICATION_MASK` | `DomainType('0x00000001')` |
*Note*: `DOMAIN_APPLICATION_MASK` reserves the rest of the bitspace in `DomainType` for application usage. This means for some `DomainType` `DOMAIN_SOME_APPLICATION`, `DOMAIN_SOME_APPLICATION & DOMAIN_APPLICATION_MASK` **MUST** be non-zero. This expression for any other `DomainType` in the consensus specs **MUST** be zero.
## Preset
*Note*: The below configuration is bundled as a preset: a bundle of configuration variables which are expected to differ
between different modes of operation, e.g. testing, but not generally between different networks.
Additional preset configurations can be found in the [`configs`](../../configs) directory.
### Misc
| Name | Value |
| - | - |
| `MAX_COMMITTEES_PER_SLOT` | `uint64(2**6)` (= 64) |
| `TARGET_COMMITTEE_SIZE` | `uint64(2**7)` (= 128) |
| `MAX_VALIDATORS_PER_COMMITTEE` | `uint64(2**11)` (= 2,048) |
| `SHUFFLE_ROUND_COUNT` | `uint64(90)` |
| `HYSTERESIS_QUOTIENT` | `uint64(4)` |
| `HYSTERESIS_DOWNWARD_MULTIPLIER` | `uint64(1)` |
| `HYSTERESIS_UPWARD_MULTIPLIER` | `uint64(5)` |
- For the safety of committees, `TARGET_COMMITTEE_SIZE` exceeds [the recommended minimum committee size of 111](http://web.archive.org/web/20190504131341/https://vitalik.ca/files/Ithaca201807_Sharding.pdf); with sufficient active validators (at least `SLOTS_PER_EPOCH * TARGET_COMMITTEE_SIZE`), the shuffling algorithm ensures committee sizes of at least `TARGET_COMMITTEE_SIZE`. (Unbiasable randomness with a Verifiable Delay Function (VDF) will improve committee robustness and lower the safe minimum committee size.)
### Gwei values
| Name | Value |
| - | - |
| `MIN_DEPOSIT_AMOUNT` | `Gwei(2**0 * 10**9)` (= 1,000,000,000) |
| `MAX_EFFECTIVE_BALANCE` | `Gwei(2**5 * 10**9)` (= 32,000,000,000) |
| `EFFECTIVE_BALANCE_INCREMENT` | `Gwei(2**0 * 10**9)` (= 1,000,000,000) |
### Time parameters
| Name | Value | Unit | Duration |
| - | - | :-: | :-: |
| `MIN_ATTESTATION_INCLUSION_DELAY` | `uint64(2**0)` (= 1) | slots | 12 seconds |
| `SLOTS_PER_EPOCH` | `uint64(2**5)` (= 32) | slots | 6.4 minutes |
| `MIN_SEED_LOOKAHEAD` | `uint64(2**0)` (= 1) | epochs | 6.4 minutes |
| `MAX_SEED_LOOKAHEAD` | `uint64(2**2)` (= 4) | epochs | 25.6 minutes |
| `MIN_EPOCHS_TO_INACTIVITY_PENALTY` | `uint64(2**2)` (= 4) | epochs | 25.6 minutes |
| `EPOCHS_PER_ETH1_VOTING_PERIOD` | `uint64(2**6)` (= 64) | epochs | ~6.8 hours |
| `SLOTS_PER_HISTORICAL_ROOT` | `uint64(2**13)` (= 8,192) | slots | ~27 hours |
### State list lengths
| Name | Value | Unit | Duration |
| - | - | :-: | :-: |
| `EPOCHS_PER_HISTORICAL_VECTOR` | `uint64(2**16)` (= 65,536) | epochs | ~0.8 years |
| `EPOCHS_PER_SLASHINGS_VECTOR` | `uint64(2**13)` (= 8,192) | epochs | ~36 days |
| `HISTORICAL_ROOTS_LIMIT` | `uint64(2**24)` (= 16,777,216) | historical roots | ~52,262 years |
| `VALIDATOR_REGISTRY_LIMIT` | `uint64(2**40)` (= 1,099,511,627,776) | validators |
### Rewards and penalties
| Name | Value |
| - | - |
| `BASE_REWARD_FACTOR` | `uint64(2**6)` (= 64) |
| `WHISTLEBLOWER_REWARD_QUOTIENT` | `uint64(2**9)` (= 512) |
| `PROPOSER_REWARD_QUOTIENT` | `uint64(2**3)` (= 8) |
| `INACTIVITY_PENALTY_QUOTIENT` | `uint64(2**26)` (= 67,108,864) |
| `MIN_SLASHING_PENALTY_QUOTIENT` | `uint64(2**7)` (= 128) |
| `PROPORTIONAL_SLASHING_MULTIPLIER` | `uint64(1)` |
- The `INACTIVITY_PENALTY_QUOTIENT` equals `INVERSE_SQRT_E_DROP_TIME**2` where `INVERSE_SQRT_E_DROP_TIME := 2**13` epochs (about 36 days) is the time it takes the inactivity penalty to reduce the balance of non-participating validators to about `1/sqrt(e) ~= 60.6%`. Indeed, the balance retained by offline validators after `n` epochs is about `(1 - 1/INACTIVITY_PENALTY_QUOTIENT)**(n**2/2)`; so after `INVERSE_SQRT_E_DROP_TIME` epochs, it is roughly `(1 - 1/INACTIVITY_PENALTY_QUOTIENT)**(INACTIVITY_PENALTY_QUOTIENT/2) ~= 1/sqrt(e)`. Note this value will be upgraded to `2**24` after Phase 0 mainnet stabilizes to provide a faster recovery in the event of an inactivity leak.
- The `PROPORTIONAL_SLASHING_MULTIPLIER` is set to `1` at initial mainnet launch, resulting in one-third of the minimum accountable safety margin in the event of a finality attack. After Phase 0 mainnet stabilizes, this value will be upgraded to `3` to provide the maximal minimum accountable safety margin.
### Max operations per block
| Name | Value |
| - | - |
| `MAX_PROPOSER_SLASHINGS` | `2**4` (= 16) |
| `MAX_ATTESTER_SLASHINGS` | `2**1` (= 2) |
| `MAX_ATTESTATIONS` | `2**7` (= 128) |
| `MAX_DEPOSITS` | `2**4` (= 16) |
| `MAX_VOLUNTARY_EXITS` | `2**4` (= 16) |
## Configuration
*Note*: The default mainnet configuration values are included here for illustrative purposes.
Defaults for this more dynamic type of configuration are available with the presets in the [`configs`](../../configs) directory.
Testnets and other types of chain instances may use a different configuration.
### Genesis settings
| Name | Value |
| - | - |
| `MIN_GENESIS_ACTIVE_VALIDATOR_COUNT` | `uint64(2**14)` (= 16,384) |
| `MIN_GENESIS_TIME` | `uint64(1606824000)` (Dec 1, 2020, 12pm UTC) |
| `GENESIS_FORK_VERSION` | `Version('0x00000000')` |
| `GENESIS_DELAY` | `uint64(604800)` (7 days) |
### Time parameters
| Name | Value | Unit | Duration |
| - | - | :-: | :-: |
| `SECONDS_PER_SLOT` | `uint64(12)` | seconds | 12 seconds |
| `SECONDS_PER_ETH1_BLOCK` | `uint64(14)` | seconds | 14 seconds |
| `MIN_VALIDATOR_WITHDRAWABILITY_DELAY` | `uint64(2**8)` (= 256) | epochs | ~27 hours |
| `SHARD_COMMITTEE_PERIOD` | `uint64(2**8)` (= 256) | epochs | ~27 hours |
| `ETH1_FOLLOW_DISTANCE` | `uint64(2**11)` (= 2,048) | Eth1 blocks | ~8 hours |
### Validator cycle
| Name | Value |
| - | - |
| `EJECTION_BALANCE` | `Gwei(2**4 * 10**9)` (= 16,000,000,000) |
| `MIN_PER_EPOCH_CHURN_LIMIT` | `uint64(2**2)` (= 4) |
| `CHURN_LIMIT_QUOTIENT` | `uint64(2**16)` (= 65,536) |
## Containers
The following types are [SimpleSerialize (SSZ)](../../ssz/simple-serialize.md) containers.
*Note*: The definitions are ordered topologically to facilitate execution of the spec.
*Note*: Fields missing in container instantiations default to their zero value.
### Misc dependencies
#### `Fork`
```python
class Fork(Container):
previous_version: Version
current_version: Version
epoch: Epoch # Epoch of latest fork
```
#### `ForkData`
```python
class ForkData(Container):
current_version: Version
genesis_validators_root: Root
```
#### `Checkpoint`
```python
class Checkpoint(Container):
epoch: Epoch
root: Root
```
#### `Validator`
```python
class Validator(Container):
pubkey: BLSPubkey
withdrawal_credentials: Bytes32 # Commitment to pubkey for withdrawals
effective_balance: Gwei # Balance at stake
slashed: boolean
# Status epochs
activation_eligibility_epoch: Epoch # When criteria for activation were met
activation_epoch: Epoch
exit_epoch: Epoch
withdrawable_epoch: Epoch # When validator can withdraw funds
```
#### `AttestationData`
```python
class AttestationData(Container):
slot: Slot
index: CommitteeIndex
# LMD GHOST vote
beacon_block_root: Root
# FFG vote
source: Checkpoint
target: Checkpoint
```
#### `IndexedAttestation`
```python
class IndexedAttestation(Container):
attesting_indices: List[ValidatorIndex, MAX_VALIDATORS_PER_COMMITTEE]
data: AttestationData
signature: BLSSignature
```
#### `PendingAttestation`
```python
class PendingAttestation(Container):
aggregation_bits: Bitlist[MAX_VALIDATORS_PER_COMMITTEE]
data: AttestationData
inclusion_delay: Slot
proposer_index: ValidatorIndex
```
#### `Eth1Data`
```python
class Eth1Data(Container):
deposit_root: Root
deposit_count: uint64
block_hash: Hash32
```
#### `HistoricalBatch`
```python
class HistoricalBatch(Container):
block_roots: Vector[Root, SLOTS_PER_HISTORICAL_ROOT]
state_roots: Vector[Root, SLOTS_PER_HISTORICAL_ROOT]
```
#### `DepositMessage`
```python
class DepositMessage(Container):
pubkey: BLSPubkey
withdrawal_credentials: Bytes32
amount: Gwei
```
#### `DepositData`
```python
class DepositData(Container):
pubkey: BLSPubkey
withdrawal_credentials: Bytes32
amount: Gwei
signature: BLSSignature # Signing over DepositMessage
```
#### `BeaconBlockHeader`
```python
class BeaconBlockHeader(Container):
slot: Slot
proposer_index: ValidatorIndex
parent_root: Root
state_root: Root
body_root: Root
```
#### `SigningData`
```python
class SigningData(Container):
object_root: Root
domain: Domain
```
### Beacon operations
#### `ProposerSlashing`
```python
class ProposerSlashing(Container):
signed_header_1: SignedBeaconBlockHeader
signed_header_2: SignedBeaconBlockHeader
```
#### `AttesterSlashing`
```python
class AttesterSlashing(Container):
attestation_1: IndexedAttestation
attestation_2: IndexedAttestation
```
#### `Attestation`
```python
class Attestation(Container):
aggregation_bits: Bitlist[MAX_VALIDATORS_PER_COMMITTEE]
data: AttestationData
signature: BLSSignature
```
#### `Deposit`
```python
class Deposit(Container):
proof: Vector[Bytes32, DEPOSIT_CONTRACT_TREE_DEPTH + 1] # Merkle path to deposit root
data: DepositData
```
#### `VoluntaryExit`
```python
class VoluntaryExit(Container):
epoch: Epoch # Earliest epoch when voluntary exit can be processed
validator_index: ValidatorIndex
```
### Beacon blocks
#### `BeaconBlockBody`
```python
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]
```
#### `BeaconBlock`
```python
class BeaconBlock(Container):
slot: Slot
proposer_index: ValidatorIndex
parent_root: Root
state_root: Root
body: BeaconBlockBody
```
### Beacon state
#### `BeaconState`
```python
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
# Attestations
previous_epoch_attestations: List[PendingAttestation, MAX_ATTESTATIONS * SLOTS_PER_EPOCH]
current_epoch_attestations: List[PendingAttestation, MAX_ATTESTATIONS * SLOTS_PER_EPOCH]
# Finality
justification_bits: Bitvector[JUSTIFICATION_BITS_LENGTH] # Bit set for every recent justified epoch
previous_justified_checkpoint: Checkpoint # Previous epoch snapshot
current_justified_checkpoint: Checkpoint
finalized_checkpoint: Checkpoint
```
### Signed envelopes
#### `SignedVoluntaryExit`
```python
class SignedVoluntaryExit(Container):
message: VoluntaryExit
signature: BLSSignature
```
#### `SignedBeaconBlock`
```python
class SignedBeaconBlock(Container):
message: BeaconBlock
signature: BLSSignature
```
#### `SignedBeaconBlockHeader`
```python
class SignedBeaconBlockHeader(Container):
message: BeaconBlockHeader
signature: BLSSignature
```
## Helper functions
*Note*: The definitions below are for specification purposes and are not necessarily optimal implementations.
### Math
#### `integer_squareroot`
```python
def integer_squareroot(n: uint64) -> uint64:
"""
Return the largest integer ``x`` such that ``x**2 <= n``.
"""
if n == UINT64_MAX:
return UINT64_MAX_SQRT
x = n
y = (x + 1) // 2
while y < x:
x = y
y = (x + n // x) // 2
return x
```
#### `xor`
```python
def xor(bytes_1: Bytes32, bytes_2: Bytes32) -> Bytes32:
"""
Return the exclusive-or of two 32-byte strings.
"""
return Bytes32(a ^ b for a, b in zip(bytes_1, bytes_2))
```
#### `uint_to_bytes`
`def uint_to_bytes(n: uint) -> bytes` is a function for serializing the `uint` type object to bytes in ``ENDIANNESS``-endian. The expected length of the output is the byte-length of the `uint` type.
#### `bytes_to_uint64`
```python
def bytes_to_uint64(data: bytes) -> uint64:
"""
Return the integer deserialization of ``data`` interpreted as ``ENDIANNESS``-endian.
"""
return uint64(int.from_bytes(data, ENDIANNESS))
```
#### `saturating_sub`
```python
def saturating_sub(a: int, b: int) -> int:
"""
Computes a - b, saturating at numeric bounds.
"""
return a - b if a > b else 0
```
### Crypto
#### `hash`
`def hash(data: bytes) -> Bytes32` is SHA256.
#### `hash_tree_root`
`def hash_tree_root(object: SSZSerializable) -> Root` is a function for hashing objects into a single root by utilizing a hash tree structure, as defined in the [SSZ spec](../../ssz/simple-serialize.md#merkleization).
#### BLS signatures
The [IETF BLS signature draft standard v4](https://tools.ietf.org/html/draft-irtf-cfrg-bls-signature-04) with ciphersuite `BLS_SIG_BLS12381G2_XMD:SHA-256_SSWU_RO_POP_` defines the following functions:
- `def Sign(privkey: int, message: Bytes) -> BLSSignature`
- `def Verify(pubkey: BLSPubkey, message: Bytes, signature: BLSSignature) -> bool`
- `def Aggregate(signatures: Sequence[BLSSignature]) -> BLSSignature`
- `def FastAggregateVerify(pubkeys: Sequence[BLSPubkey], message: Bytes, signature: BLSSignature) -> bool`
- `def AggregateVerify(pubkeys: Sequence[BLSPubkey], messages: Sequence[Bytes], signature: BLSSignature) -> bool`
- `def KeyValidate(pubkey: BLSPubkey) -> bool`
The above functions are accessed through the `bls` module, e.g. `bls.Verify`.
### Predicates
#### `is_active_validator`
```python
def is_active_validator(validator: Validator, epoch: Epoch) -> bool:
"""
Check if ``validator`` is active.
"""
return validator.activation_epoch <= epoch < validator.exit_epoch
```
#### `is_eligible_for_activation_queue`
```python
def is_eligible_for_activation_queue(validator: Validator) -> bool:
"""
Check if ``validator`` is eligible to be placed into the activation queue.
"""
return (
validator.activation_eligibility_epoch == FAR_FUTURE_EPOCH
and validator.effective_balance == MAX_EFFECTIVE_BALANCE
)
```
#### `is_eligible_for_activation`
```python
def is_eligible_for_activation(state: BeaconState, validator: Validator) -> bool:
"""
Check if ``validator`` is eligible for activation.
"""
return (
# Placement in queue is finalized
validator.activation_eligibility_epoch <= state.finalized_checkpoint.epoch
# Has not yet been activated
and validator.activation_epoch == FAR_FUTURE_EPOCH
)
```
#### `is_slashable_validator`
```python
def is_slashable_validator(validator: Validator, epoch: Epoch) -> bool:
"""
Check if ``validator`` is slashable.
"""
return (not validator.slashed) and (validator.activation_epoch <= epoch < validator.withdrawable_epoch)
```
#### `is_slashable_attestation_data`
```python
def is_slashable_attestation_data(data_1: AttestationData, data_2: AttestationData) -> bool:
"""
Check if ``data_1`` and ``data_2`` are slashable according to Casper FFG rules.
"""
return (
# Double vote
(data_1 != data_2 and data_1.target.epoch == data_2.target.epoch) or
# Surround vote
(data_1.source.epoch < data_2.source.epoch and data_2.target.epoch < data_1.target.epoch)
)
```
#### `is_valid_indexed_attestation`
```python
def is_valid_indexed_attestation(state: BeaconState, indexed_attestation: IndexedAttestation) -> bool:
"""
Check if ``indexed_attestation`` is not empty, has sorted and unique indices and has a valid aggregate signature.
"""
# Verify indices are sorted and unique
indices = indexed_attestation.attesting_indices
if len(indices) == 0 or not indices == sorted(set(indices)):
return False
# Verify aggregate signature
pubkeys = [state.validators[i].pubkey for i in indices]
domain = get_domain(state, DOMAIN_BEACON_ATTESTER, indexed_attestation.data.target.epoch)
signing_root = compute_signing_root(indexed_attestation.data, domain)
return bls.FastAggregateVerify(pubkeys, signing_root, indexed_attestation.signature)
```
#### `is_valid_merkle_branch`
```python
def is_valid_merkle_branch(leaf: Bytes32, branch: Sequence[Bytes32], depth: uint64, index: uint64, root: Root) -> bool:
"""
Check if ``leaf`` at ``index`` verifies against the Merkle ``root`` and ``branch``.
"""
value = leaf
for i in range(depth):
if index // (2**i) % 2:
value = hash(branch[i] + value)
else:
value = hash(value + branch[i])
return value == root
```
### Misc
#### `compute_shuffled_index`
```python
def compute_shuffled_index(index: uint64, index_count: uint64, seed: Bytes32) -> uint64:
"""
Return the shuffled index corresponding to ``seed`` (and ``index_count``).
"""
assert index < index_count
# Swap or not (https://link.springer.com/content/pdf/10.1007%2F978-3-642-32009-5_1.pdf)
# See the 'generalized domain' algorithm on page 3
for current_round in range(SHUFFLE_ROUND_COUNT):
pivot = bytes_to_uint64(hash(seed + uint_to_bytes(uint8(current_round)))[0:8]) % index_count
flip = (pivot + index_count - index) % index_count
position = max(index, flip)
source = hash(
seed
+ uint_to_bytes(uint8(current_round))
+ uint_to_bytes(uint32(position // 256))
)
byte = uint8(source[(position % 256) // 8])
bit = (byte >> (position % 8)) % 2
index = flip if bit else index
return index
```
#### `compute_proposer_index`
```python
def compute_proposer_index(state: BeaconState, indices: Sequence[ValidatorIndex], seed: Bytes32) -> 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 = state.validators[candidate_index].effective_balance
if effective_balance * MAX_RANDOM_BYTE >= MAX_EFFECTIVE_BALANCE * random_byte:
return candidate_index
i += 1
```
#### `compute_committee`
```python
def compute_committee(indices: Sequence[ValidatorIndex],
seed: Bytes32,
index: uint64,
count: uint64) -> Sequence[ValidatorIndex]:
"""
Return the committee corresponding to ``indices``, ``seed``, ``index``, and committee ``count``.
"""
start = (len(indices) * index) // count
end = (len(indices) * uint64(index + 1)) // count
return [indices[compute_shuffled_index(uint64(i), uint64(len(indices)), seed)] for i in range(start, end)]
```
#### `compute_epoch_at_slot`
```python
def compute_epoch_at_slot(slot: Slot) -> Epoch:
"""
Return the epoch number at ``slot``.
"""
return Epoch(slot // SLOTS_PER_EPOCH)
```
#### `compute_start_slot_at_epoch`
```python
def compute_start_slot_at_epoch(epoch: Epoch) -> Slot:
"""
Return the start slot of ``epoch``.
"""
return Slot(epoch * SLOTS_PER_EPOCH)
```
#### `compute_activation_exit_epoch`
```python
def compute_activation_exit_epoch(epoch: Epoch) -> Epoch:
"""
Return the epoch during which validator activations and exits initiated in ``epoch`` take effect.
"""
return Epoch(epoch + 1 + MAX_SEED_LOOKAHEAD)
```
#### `compute_fork_data_root`
```python
def compute_fork_data_root(current_version: Version, genesis_validators_root: Root) -> Root:
"""
Return the 32-byte fork data root for the ``current_version`` and ``genesis_validators_root``.
This is used primarily in signature domains to avoid collisions across forks/chains.
"""
return hash_tree_root(ForkData(
current_version=current_version,
genesis_validators_root=genesis_validators_root,
))
```
#### `compute_fork_digest`
```python
def compute_fork_digest(current_version: Version, genesis_validators_root: Root) -> ForkDigest:
"""
Return the 4-byte fork digest for the ``current_version`` and ``genesis_validators_root``.
This is a digest primarily used for domain separation on the p2p layer.
4-bytes suffices for practical separation of forks/chains.
"""
return ForkDigest(compute_fork_data_root(current_version, genesis_validators_root)[:4])
```
#### `compute_domain`
```python
def compute_domain(domain_type: DomainType, fork_version: Version=None, genesis_validators_root: Root=None) -> Domain:
"""
Return the domain for the ``domain_type`` and ``fork_version``.
"""
if fork_version is None:
fork_version = GENESIS_FORK_VERSION
if genesis_validators_root is None:
genesis_validators_root = Root() # all bytes zero by default
fork_data_root = compute_fork_data_root(fork_version, genesis_validators_root)
return Domain(domain_type + fork_data_root[:28])
```
#### `compute_signing_root`
```python
def compute_signing_root(ssz_object: SSZObject, domain: Domain) -> Root:
"""
Return the signing root for the corresponding signing data.
"""
return hash_tree_root(SigningData(
object_root=hash_tree_root(ssz_object),
domain=domain,
))
```
### Beacon state accessors
#### `get_current_epoch`
```python
def get_current_epoch(state: BeaconState) -> Epoch:
"""
Return the current epoch.
"""
return compute_epoch_at_slot(state.slot)
```
#### `get_previous_epoch`
```python
def get_previous_epoch(state: BeaconState) -> Epoch:
"""`
Return the previous epoch (unless the current epoch is ``GENESIS_EPOCH``).
"""
current_epoch = get_current_epoch(state)
return GENESIS_EPOCH if current_epoch == GENESIS_EPOCH else Epoch(current_epoch - 1)
```
#### `get_block_root`
```python
def get_block_root(state: BeaconState, epoch: Epoch) -> Root:
"""
Return the block root at the start of a recent ``epoch``.
"""
return get_block_root_at_slot(state, compute_start_slot_at_epoch(epoch))
```
#### `get_block_root_at_slot`
```python
def get_block_root_at_slot(state: BeaconState, slot: Slot) -> Root:
"""
Return the block root at a recent ``slot``.
"""
assert slot < state.slot <= slot + SLOTS_PER_HISTORICAL_ROOT
return state.block_roots[slot % SLOTS_PER_HISTORICAL_ROOT]
```
#### `get_randao_mix`
```python
def get_randao_mix(state: BeaconState, epoch: Epoch) -> Bytes32:
"""
Return the randao mix at a recent ``epoch``.
"""
return state.randao_mixes[epoch % EPOCHS_PER_HISTORICAL_VECTOR]
```
#### `get_active_validator_indices`
```python
def get_active_validator_indices(state: BeaconState, epoch: Epoch) -> Sequence[ValidatorIndex]:
"""
Return the sequence of active validator indices at ``epoch``.
"""
return [ValidatorIndex(i) for i, v in enumerate(state.validators) if is_active_validator(v, epoch)]
```
#### `get_validator_churn_limit`
```python
def get_validator_churn_limit(state: BeaconState) -> uint64:
"""
Return the validator churn limit for the current epoch.
"""
active_validator_indices = get_active_validator_indices(state, get_current_epoch(state))
return max(MIN_PER_EPOCH_CHURN_LIMIT, uint64(len(active_validator_indices)) // CHURN_LIMIT_QUOTIENT)
```
#### `get_seed`
```python
def get_seed(state: BeaconState, epoch: Epoch, domain_type: DomainType) -> Bytes32:
"""
Return the seed at ``epoch``.
"""
mix = get_randao_mix(state, Epoch(epoch + EPOCHS_PER_HISTORICAL_VECTOR - MIN_SEED_LOOKAHEAD - 1)) # Avoid underflow
return hash(domain_type + uint_to_bytes(epoch) + mix)
```
#### `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(
MAX_COMMITTEES_PER_SLOT,
uint64(len(get_active_validator_indices(state, epoch))) // SLOTS_PER_EPOCH // TARGET_COMMITTEE_SIZE,
))
```
#### `get_beacon_committee`
```python
def get_beacon_committee(state: BeaconState, slot: Slot, index: CommitteeIndex) -> Sequence[ValidatorIndex]:
"""
Return the beacon committee at ``slot`` for ``index``.
"""
epoch = compute_epoch_at_slot(slot)
committees_per_slot = get_committee_count_per_slot(state, epoch)
return compute_committee(
indices=get_active_validator_indices(state, epoch),
seed=get_seed(state, epoch, DOMAIN_BEACON_ATTESTER),
index=(slot % SLOTS_PER_EPOCH) * committees_per_slot + index,
count=committees_per_slot * SLOTS_PER_EPOCH,
)
```
#### `get_beacon_proposer_index`
```python
def get_beacon_proposer_index(state: BeaconState) -> ValidatorIndex:
"""
Return the beacon proposer index at the current slot.
"""
epoch = get_current_epoch(state)
seed = hash(get_seed(state, epoch, DOMAIN_BEACON_PROPOSER) + uint_to_bytes(state.slot))
indices = get_active_validator_indices(state, epoch)
return compute_proposer_index(state, indices, seed)
```
#### `get_total_balance`
```python
def get_total_balance(state: BeaconState, indices: Set[ValidatorIndex]) -> Gwei:
"""
Return the combined effective balance of the ``indices``.
``EFFECTIVE_BALANCE_INCREMENT`` Gwei minimum to avoid divisions by zero.
Math safe up to ~10B ETH, after which this overflows uint64.
"""
return Gwei(max(EFFECTIVE_BALANCE_INCREMENT, sum([state.validators[index].effective_balance for index in indices])))
```
#### `get_total_active_balance`
```python
def get_total_active_balance(state: BeaconState) -> Gwei:
"""
Return the combined effective balance of the active validators.
Note: ``get_total_balance`` returns ``EFFECTIVE_BALANCE_INCREMENT`` Gwei minimum to avoid divisions by zero.
"""
return get_total_balance(state, set(get_active_validator_indices(state, get_current_epoch(state))))
```
#### `get_domain`
```python
def get_domain(state: BeaconState, domain_type: DomainType, epoch: Epoch=None) -> Domain:
"""
Return the signature domain (fork version concatenated with domain type) of a message.
"""
epoch = get_current_epoch(state) if epoch is None else epoch
fork_version = state.fork.previous_version if epoch < state.fork.epoch else state.fork.current_version
return compute_domain(domain_type, fork_version, state.genesis_validators_root)
```
#### `get_indexed_attestation`
```python
def get_indexed_attestation(state: BeaconState, attestation: Attestation) -> IndexedAttestation:
"""
Return the indexed attestation corresponding to ``attestation``.
"""
attesting_indices = get_attesting_indices(state, attestation)
return IndexedAttestation(
attesting_indices=sorted(attesting_indices),
data=attestation.data,
signature=attestation.signature,
)
```
#### `get_attesting_indices`
```python
def get_attesting_indices(state: BeaconState, attestation: Attestation) -> Set[ValidatorIndex]:
"""
Return the set of attesting indices corresponding to ``data`` and ``bits``.
"""
committee = get_beacon_committee(state, attestation.data.slot, attestation.data.index)
return set(index for i, index in enumerate(committee) if attestation.aggregation_bits[i])
```
### Beacon state mutators
#### `increase_balance`
```python
def increase_balance(state: BeaconState, index: ValidatorIndex, delta: Gwei) -> None:
"""
Increase the validator balance at index ``index`` by ``delta``.
"""
state.balances[index] += delta
```
#### `decrease_balance`
```python
def decrease_balance(state: BeaconState, index: ValidatorIndex, delta: Gwei) -> None:
"""
Decrease the validator balance at index ``index`` by ``delta``, with underflow protection.
"""
state.balances[index] = 0 if delta > state.balances[index] else state.balances[index] - delta
```
#### `initiate_validator_exit`
```python
def initiate_validator_exit(state: BeaconState, index: ValidatorIndex) -> None:
"""
Initiate the exit of the validator with index ``index``.
"""
# Return if validator already initiated exit
validator = state.validators[index]
if validator.exit_epoch != FAR_FUTURE_EPOCH:
return
# Compute exit queue epoch
exit_epochs = [v.exit_epoch for v in state.validators if v.exit_epoch != FAR_FUTURE_EPOCH]
exit_queue_epoch = max(exit_epochs + [compute_activation_exit_epoch(get_current_epoch(state))])
exit_queue_churn = len([v for v in state.validators if v.exit_epoch == exit_queue_epoch])
if exit_queue_churn >= get_validator_churn_limit(state):
exit_queue_epoch += Epoch(1)
# Set validator exit epoch and withdrawable epoch
validator.exit_epoch = exit_queue_epoch
validator.withdrawable_epoch = Epoch(validator.exit_epoch + MIN_VALIDATOR_WITHDRAWABILITY_DELAY)
```
#### `slash_validator`
```python
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 // 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))
```
## Genesis
Before the Ethereum beacon chain genesis has been triggered, and for every Ethereum proof-of-work block, let `candidate_state = initialize_beacon_state_from_eth1(eth1_block_hash, eth1_timestamp, deposits)` where:
- `eth1_block_hash` is the hash of the Ethereum proof-of-work block
- `eth1_timestamp` is the Unix timestamp corresponding to `eth1_block_hash`
- `deposits` is the sequence of all deposits, ordered chronologically, up to (and including) the block with hash `eth1_block_hash`
Proof-of-work blocks must only be considered once they are at least `SECONDS_PER_ETH1_BLOCK * ETH1_FOLLOW_DISTANCE` seconds old (i.e. `eth1_timestamp + SECONDS_PER_ETH1_BLOCK * ETH1_FOLLOW_DISTANCE <= current_unix_time`). Due to this constraint, if `GENESIS_DELAY < SECONDS_PER_ETH1_BLOCK * ETH1_FOLLOW_DISTANCE`, then the `genesis_time` can happen before the time/state is first known. Values should be configured to avoid this case.
```python
def initialize_beacon_state_from_eth1(eth1_block_hash: Hash32,
eth1_timestamp: uint64,
deposits: Sequence[Deposit]) -> BeaconState:
fork = Fork(
previous_version=GENESIS_FORK_VERSION,
current_version=GENESIS_FORK_VERSION,
epoch=GENESIS_EPOCH,
)
state = BeaconState(
genesis_time=eth1_timestamp + GENESIS_DELAY,
fork=fork,
eth1_data=Eth1Data(block_hash=eth1_block_hash, deposit_count=uint64(len(deposits))),
latest_block_header=BeaconBlockHeader(body_root=hash_tree_root(BeaconBlockBody())),
randao_mixes=[eth1_block_hash] * EPOCHS_PER_HISTORICAL_VECTOR, # Seed RANDAO with Eth1 entropy
)
# Process deposits
leaves = list(map(lambda deposit: deposit.data, deposits))
for index, deposit in enumerate(deposits):
deposit_data_list = List[DepositData, 2**DEPOSIT_CONTRACT_TREE_DEPTH](*leaves[:index + 1])
state.eth1_data.deposit_root = hash_tree_root(deposit_data_list)
process_deposit(state, deposit)
# Process activations
for index, validator in enumerate(state.validators):
balance = state.balances[index]
validator.effective_balance = min(balance - balance % EFFECTIVE_BALANCE_INCREMENT, MAX_EFFECTIVE_BALANCE)
if validator.effective_balance == MAX_EFFECTIVE_BALANCE:
validator.activation_eligibility_epoch = GENESIS_EPOCH
validator.activation_epoch = GENESIS_EPOCH
# Set genesis validators root for domain separation and chain versioning
state.genesis_validators_root = hash_tree_root(state.validators)
return state
```
*Note*: The ETH1 block with `eth1_timestamp` meeting the minimum genesis active validator count criteria can also occur before `MIN_GENESIS_TIME`.
### Genesis state
Let `genesis_state = candidate_state` whenever `is_valid_genesis_state(candidate_state) is True` for the first time.
```python
def is_valid_genesis_state(state: BeaconState) -> bool:
if state.genesis_time < MIN_GENESIS_TIME:
return False
if len(get_active_validator_indices(state, GENESIS_EPOCH)) < MIN_GENESIS_ACTIVE_VALIDATOR_COUNT:
return False
return True
```
### Genesis block
Let `genesis_block = BeaconBlock(state_root=hash_tree_root(genesis_state))`.
## Beacon chain state transition function
The post-state corresponding to a pre-state `state` and a signed block `signed_block` is defined as `state_transition(state, signed_block)`. State transitions that trigger an unhandled exception (e.g. a failed `assert` or an out-of-range list access) are considered invalid. State transitions that cause a `uint64` overflow or underflow are also considered invalid.
```python
def state_transition(state: BeaconState, signed_block: SignedBeaconBlock, validate_result: bool=True) -> None:
block = signed_block.message
# Process slots (including those with no blocks) since block
process_slots(state, block.slot)
# Verify signature
if validate_result:
assert verify_block_signature(state, signed_block)
# Process block
process_block(state, block)
# Verify state root
if validate_result:
assert block.state_root == hash_tree_root(state)
```
```python
def verify_block_signature(state: BeaconState, signed_block: SignedBeaconBlock) -> bool:
proposer = state.validators[signed_block.message.proposer_index]
signing_root = compute_signing_root(signed_block.message, get_domain(state, DOMAIN_BEACON_PROPOSER))
return bls.Verify(proposer.pubkey, signing_root, signed_block.signature)
```
```python
def process_slots(state: BeaconState, slot: Slot) -> None:
assert state.slot < slot
while state.slot < slot:
process_slot(state)
# Process epoch on the start slot of the next epoch
if (state.slot + 1) % SLOTS_PER_EPOCH == 0:
process_epoch(state)
state.slot = Slot(state.slot + 1)
```
```python
def process_slot(state: BeaconState) -> None:
# Cache state root
previous_state_root = hash_tree_root(state)
state.state_roots[state.slot % SLOTS_PER_HISTORICAL_ROOT] = previous_state_root
# Cache latest block header state root
if state.latest_block_header.state_root == Bytes32():
state.latest_block_header.state_root = previous_state_root
# Cache block root
previous_block_root = hash_tree_root(state.latest_block_header)
state.block_roots[state.slot % SLOTS_PER_HISTORICAL_ROOT] = previous_block_root
```
### Epoch processing
```python
def process_epoch(state: BeaconState) -> None:
process_justification_and_finalization(state)
process_rewards_and_penalties(state)
process_registry_updates(state)
process_slashings(state)
process_eth1_data_reset(state)
process_effective_balance_updates(state)
process_slashings_reset(state)
process_randao_mixes_reset(state)
process_historical_roots_update(state)
process_participation_record_updates(state)
```
#### Helper functions
```python
def get_matching_source_attestations(state: BeaconState, epoch: Epoch) -> Sequence[PendingAttestation]:
assert epoch in (get_previous_epoch(state), get_current_epoch(state))
return state.current_epoch_attestations if epoch == get_current_epoch(state) else state.previous_epoch_attestations
```
```python
def get_matching_target_attestations(state: BeaconState, epoch: Epoch) -> Sequence[PendingAttestation]:
return [
a for a in get_matching_source_attestations(state, epoch)
if a.data.target.root == get_block_root(state, epoch)
]
```
```python
def get_matching_head_attestations(state: BeaconState, epoch: Epoch) -> Sequence[PendingAttestation]:
return [
a for a in get_matching_target_attestations(state, epoch)
if a.data.beacon_block_root == get_block_root_at_slot(state, a.data.slot)
]
```
```python
def get_unslashed_attesting_indices(state: BeaconState,
attestations: Sequence[PendingAttestation]) -> Set[ValidatorIndex]:
output = set() # type: Set[ValidatorIndex]
for a in attestations:
output = output.union(get_attesting_indices(state, a))
return set(filter(lambda index: not state.validators[index].slashed, output))
```
```python
def get_attesting_balance(state: BeaconState, attestations: Sequence[PendingAttestation]) -> Gwei:
"""
Return the combined effective balance of the set of unslashed validators participating in ``attestations``.
Note: ``get_total_balance`` returns ``EFFECTIVE_BALANCE_INCREMENT`` Gwei minimum to avoid divisions by zero.
"""
return get_total_balance(state, get_unslashed_attesting_indices(state, attestations))
```
#### Justification and finalization
```python
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_attestations = get_matching_target_attestations(state, get_previous_epoch(state))
current_attestations = get_matching_target_attestations(state, get_current_epoch(state))
total_active_balance = get_total_active_balance(state)
previous_target_balance = get_attesting_balance(state, previous_attestations)
current_target_balance = get_attesting_balance(state, current_attestations)
weigh_justification_and_finalization(state, total_active_balance, previous_target_balance, current_target_balance)
```
```python
def weigh_justification_and_finalization(state: BeaconState,
total_active_balance: Gwei,
previous_epoch_target_balance: Gwei,
current_epoch_target_balance: Gwei) -> None:
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
if previous_epoch_target_balance * 3 >= total_active_balance * 2:
state.current_justified_checkpoint = Checkpoint(epoch=previous_epoch,
root=get_block_root(state, previous_epoch))
state.justification_bits[1] = 0b1
if current_epoch_target_balance * 3 >= total_active_balance * 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
```
#### Rewards and penalties
##### Helpers
```python
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) // BASE_REWARDS_PER_EPOCH)
```
```python
def get_proposer_reward(state: BeaconState, attesting_index: ValidatorIndex) -> Gwei:
return Gwei(get_base_reward(state, attesting_index) // PROPOSER_REWARD_QUOTIENT)
```
```python
def get_finality_delay(state: BeaconState) -> uint64:
return get_previous_epoch(state) - state.finalized_checkpoint.epoch
```
```python
def is_in_inactivity_leak(state: BeaconState) -> bool:
return get_finality_delay(state) > MIN_EPOCHS_TO_INACTIVITY_PENALTY
```
```python
def get_eligible_validator_indices(state: BeaconState) -> Sequence[ValidatorIndex]:
previous_epoch = get_previous_epoch(state)
return [
ValidatorIndex(index) for index, v in enumerate(state.validators)
if is_active_validator(v, previous_epoch) or (v.slashed and previous_epoch + 1 < v.withdrawable_epoch)
]
```
```python
def get_attestation_component_deltas(state: BeaconState,
attestations: Sequence[PendingAttestation]
) -> Tuple[Sequence[Gwei], Sequence[Gwei]]:
"""
Helper with shared logic for use by get source, target, and head deltas functions
"""
rewards = [Gwei(0)] * len(state.validators)
penalties = [Gwei(0)] * len(state.validators)
total_balance = get_total_active_balance(state)
unslashed_attesting_indices = get_unslashed_attesting_indices(state, attestations)
attesting_balance = get_total_balance(state, unslashed_attesting_indices)
for index in get_eligible_validator_indices(state):
if index in unslashed_attesting_indices:
increment = EFFECTIVE_BALANCE_INCREMENT # Factored out from balance totals to avoid uint64 overflow
if is_in_inactivity_leak(state):
# Since full base reward will be canceled out by inactivity penalty deltas,
# optimal participation receives full base reward compensation here.
rewards[index] += get_base_reward(state, index)
else:
reward_numerator = get_base_reward(state, index) * (attesting_balance // increment)
rewards[index] += reward_numerator // (total_balance // increment)
else:
penalties[index] += get_base_reward(state, index)
return rewards, penalties
```
##### Components of attestation deltas
```python
def get_source_deltas(state: BeaconState) -> Tuple[Sequence[Gwei], Sequence[Gwei]]:
"""
Return attester micro-rewards/penalties for source-vote for each validator.
"""
matching_source_attestations = get_matching_source_attestations(state, get_previous_epoch(state))
return get_attestation_component_deltas(state, matching_source_attestations)
```
```python
def get_target_deltas(state: BeaconState) -> Tuple[Sequence[Gwei], Sequence[Gwei]]:
"""
Return attester micro-rewards/penalties for target-vote for each validator.
"""
matching_target_attestations = get_matching_target_attestations(state, get_previous_epoch(state))
return get_attestation_component_deltas(state, matching_target_attestations)
```
```python
def get_head_deltas(state: BeaconState) -> Tuple[Sequence[Gwei], Sequence[Gwei]]:
"""
Return attester micro-rewards/penalties for head-vote for each validator.
"""
matching_head_attestations = get_matching_head_attestations(state, get_previous_epoch(state))
return get_attestation_component_deltas(state, matching_head_attestations)
```
```python
def get_inclusion_delay_deltas(state: BeaconState) -> Tuple[Sequence[Gwei], Sequence[Gwei]]:
"""
Return proposer and inclusion delay micro-rewards/penalties for each validator.
"""
rewards = [Gwei(0) for _ in range(len(state.validators))]
matching_source_attestations = get_matching_source_attestations(state, get_previous_epoch(state))
for index in get_unslashed_attesting_indices(state, matching_source_attestations):
attestation = min([
a for a in matching_source_attestations
if index in get_attesting_indices(state, a)
], key=lambda a: a.inclusion_delay)
rewards[attestation.proposer_index] += get_proposer_reward(state, index)
max_attester_reward = Gwei(get_base_reward(state, index) - get_proposer_reward(state, index))
rewards[index] += Gwei(max_attester_reward // attestation.inclusion_delay)
# No penalties associated with inclusion delay
penalties = [Gwei(0) for _ in range(len(state.validators))]
return rewards, penalties
```
```python
def get_inactivity_penalty_deltas(state: BeaconState) -> Tuple[Sequence[Gwei], Sequence[Gwei]]:
"""
Return inactivity reward/penalty deltas for each validator.
"""
penalties = [Gwei(0) for _ in range(len(state.validators))]
if is_in_inactivity_leak(state):
matching_target_attestations = get_matching_target_attestations(state, get_previous_epoch(state))
matching_target_attesting_indices = get_unslashed_attesting_indices(state, matching_target_attestations)
for index in get_eligible_validator_indices(state):
# If validator is performing optimally this cancels all rewards for a neutral balance
base_reward = get_base_reward(state, index)
penalties[index] += Gwei(BASE_REWARDS_PER_EPOCH * base_reward - get_proposer_reward(state, index))
if index not in matching_target_attesting_indices:
effective_balance = state.validators[index].effective_balance
penalties[index] += Gwei(effective_balance * get_finality_delay(state) // INACTIVITY_PENALTY_QUOTIENT)
# No rewards associated with inactivity penalties
rewards = [Gwei(0) for _ in range(len(state.validators))]
return rewards, penalties
```
##### `get_attestation_deltas`
```python
def get_attestation_deltas(state: BeaconState) -> Tuple[Sequence[Gwei], Sequence[Gwei]]:
"""
Return attestation reward/penalty deltas for each validator.
"""
source_rewards, source_penalties = get_source_deltas(state)
target_rewards, target_penalties = get_target_deltas(state)
head_rewards, head_penalties = get_head_deltas(state)
inclusion_delay_rewards, _ = get_inclusion_delay_deltas(state)
_, inactivity_penalties = get_inactivity_penalty_deltas(state)
rewards = [
source_rewards[i] + target_rewards[i] + head_rewards[i] + inclusion_delay_rewards[i]
for i in range(len(state.validators))
]
penalties = [
source_penalties[i] + target_penalties[i] + head_penalties[i] + inactivity_penalties[i]
for i in range(len(state.validators))
]
return rewards, penalties
```
##### `process_rewards_and_penalties`
```python
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
rewards, penalties = get_attestation_deltas(state)
for index in range(len(state.validators)):
increase_balance(state, ValidatorIndex(index), rewards[index])
decrease_balance(state, ValidatorIndex(index), penalties[index])
```
#### Registry updates
```python
def process_registry_updates(state: BeaconState) -> None:
# Process activation eligibility and ejections
for index, validator in enumerate(state.validators):
if is_eligible_for_activation_queue(validator):
validator.activation_eligibility_epoch = get_current_epoch(state) + 1
if (
is_active_validator(validator, get_current_epoch(state))
and validator.effective_balance <= EJECTION_BALANCE
):
initiate_validator_exit(state, ValidatorIndex(index))
# Queue validators eligible for activation and not yet dequeued for activation
activation_queue = sorted([
index for index, validator in enumerate(state.validators)
if is_eligible_for_activation(state, validator)
# Order by the sequence of activation_eligibility_epoch setting and then index
], key=lambda index: (state.validators[index].activation_eligibility_epoch, index))
# Dequeued validators for activation up to churn limit
for index in activation_queue[:get_validator_churn_limit(state)]:
validator = state.validators[index]
validator.activation_epoch = compute_activation_exit_epoch(get_current_epoch(state))
```
#### Slashings
```python
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) * 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)
```
#### Eth1 data votes updates
```python
def process_eth1_data_reset(state: BeaconState) -> None:
next_epoch = Epoch(get_current_epoch(state) + 1)
# Reset eth1 data votes
if next_epoch % EPOCHS_PER_ETH1_VOTING_PERIOD == 0:
state.eth1_data_votes = []
```
#### Effective balances updates
```python
def process_effective_balance_updates(state: BeaconState) -> None:
# Update effective balances with hysteresis
for index, validator in enumerate(state.validators):
balance = state.balances[index]
HYSTERESIS_INCREMENT = uint64(EFFECTIVE_BALANCE_INCREMENT // HYSTERESIS_QUOTIENT)
DOWNWARD_THRESHOLD = HYSTERESIS_INCREMENT * HYSTERESIS_DOWNWARD_MULTIPLIER
UPWARD_THRESHOLD = HYSTERESIS_INCREMENT * HYSTERESIS_UPWARD_MULTIPLIER
if (
balance + DOWNWARD_THRESHOLD < validator.effective_balance
or validator.effective_balance + UPWARD_THRESHOLD < balance
):
validator.effective_balance = min(balance - balance % EFFECTIVE_BALANCE_INCREMENT, MAX_EFFECTIVE_BALANCE)
```
#### Slashings balances updates
```python
def process_slashings_reset(state: BeaconState) -> None:
next_epoch = Epoch(get_current_epoch(state) + 1)
# Reset slashings
state.slashings[next_epoch % EPOCHS_PER_SLASHINGS_VECTOR] = Gwei(0)
```
#### Randao mixes updates
```python
def process_randao_mixes_reset(state: BeaconState) -> None:
current_epoch = get_current_epoch(state)
next_epoch = Epoch(current_epoch + 1)
# Set randao mix
state.randao_mixes[next_epoch % EPOCHS_PER_HISTORICAL_VECTOR] = get_randao_mix(state, current_epoch)
```
#### Historical roots updates
```python
def process_historical_roots_update(state: BeaconState) -> None:
# Set historical root accumulator
next_epoch = Epoch(get_current_epoch(state) + 1)
if next_epoch % (SLOTS_PER_HISTORICAL_ROOT // SLOTS_PER_EPOCH) == 0:
historical_batch = HistoricalBatch(block_roots=state.block_roots, state_roots=state.state_roots)
state.historical_roots.append(hash_tree_root(historical_batch))
```
#### Participation records rotation
```python
def process_participation_record_updates(state: BeaconState) -> None:
# Rotate current/previous epoch attestations
state.previous_epoch_attestations = state.current_epoch_attestations
state.current_epoch_attestations = []
```
### 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)
```
#### Block header
```python
def process_block_header(state: BeaconState, block: BeaconBlock) -> None:
# Verify that the slots match
assert block.slot == state.slot
# Verify that the block is newer than latest block header
assert block.slot > state.latest_block_header.slot
# Verify that proposer index is the correct index
assert block.proposer_index == get_beacon_proposer_index(state)
# Verify that the parent matches
assert block.parent_root == hash_tree_root(state.latest_block_header)
# Cache current block as the new latest block
state.latest_block_header = BeaconBlockHeader(
slot=block.slot,
proposer_index=block.proposer_index,
parent_root=block.parent_root,
state_root=Bytes32(), # Overwritten in the next process_slot call
body_root=hash_tree_root(block.body),
)
# Verify proposer is not slashed
proposer = state.validators[block.proposer_index]
assert not proposer.slashed
```
#### RANDAO
```python
def process_randao(state: BeaconState, body: BeaconBlockBody) -> None:
epoch = get_current_epoch(state)
# Verify RANDAO reveal
proposer = state.validators[get_beacon_proposer_index(state)]
signing_root = compute_signing_root(epoch, get_domain(state, DOMAIN_RANDAO))
assert bls.Verify(proposer.pubkey, signing_root, body.randao_reveal)
# Mix in RANDAO reveal
mix = xor(get_randao_mix(state, epoch), hash(body.randao_reveal))
state.randao_mixes[epoch % EPOCHS_PER_HISTORICAL_VECTOR] = mix
```
#### Eth1 data
```python
def process_eth1_data(state: BeaconState, body: BeaconBlockBody) -> None:
state.eth1_data_votes.append(body.eth1_data)
if state.eth1_data_votes.count(body.eth1_data) * 2 > EPOCHS_PER_ETH1_VOTING_PERIOD * SLOTS_PER_EPOCH:
state.eth1_data = body.eth1_data
```
#### 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)
for_ops(body.attestations, process_attestation)
for_ops(body.deposits, process_deposit)
for_ops(body.voluntary_exits, process_voluntary_exit)
```
##### Proposer slashings
```python
def process_proposer_slashing(state: BeaconState, proposer_slashing: ProposerSlashing) -> None:
header_1 = proposer_slashing.signed_header_1.message
header_2 = proposer_slashing.signed_header_2.message
# Verify header slots match
assert header_1.slot == header_2.slot
# Verify header proposer indices match
assert header_1.proposer_index == header_2.proposer_index
# Verify the headers are different
assert header_1 != header_2
# Verify the proposer is slashable
proposer = state.validators[header_1.proposer_index]
assert is_slashable_validator(proposer, get_current_epoch(state))
# Verify signatures
for signed_header in (proposer_slashing.signed_header_1, proposer_slashing.signed_header_2):
domain = get_domain(state, DOMAIN_BEACON_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, header_1.proposer_index)
```
##### Attester slashings
```python
def process_attester_slashing(state: BeaconState, attester_slashing: AttesterSlashing) -> None:
attestation_1 = attester_slashing.attestation_1
attestation_2 = attester_slashing.attestation_2
assert is_slashable_attestation_data(attestation_1.data, attestation_2.data)
assert is_valid_indexed_attestation(state, attestation_1)
assert is_valid_indexed_attestation(state, attestation_2)
slashed_any = False
indices = set(attestation_1.attesting_indices).intersection(attestation_2.attesting_indices)
for index in sorted(indices):
if is_slashable_validator(state.validators[index], get_current_epoch(state)):
slash_validator(state, index)
slashed_any = True
assert slashed_any
```
##### Attestations
```python
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)
pending_attestation = PendingAttestation(
data=data,
aggregation_bits=attestation.aggregation_bits,
inclusion_delay=state.slot - data.slot,
proposer_index=get_beacon_proposer_index(state),
)
if data.target.epoch == get_current_epoch(state):
assert data.source == state.current_justified_checkpoint
state.current_epoch_attestations.append(pending_attestation)
else:
assert data.source == state.previous_justified_checkpoint
state.previous_epoch_attestations.append(pending_attestation)
# Verify signature
assert is_valid_indexed_attestation(state, get_indexed_attestation(state, attestation))
```
##### Deposits
```python
def get_validator_from_deposit(pubkey: BLSPubkey, withdrawal_credentials: Bytes32, amount: uint64) -> Validator:
effective_balance = min(amount - amount % EFFECTIVE_BALANCE_INCREMENT, MAX_EFFECTIVE_BALANCE)
return Validator(
pubkey=pubkey,
withdrawal_credentials=withdrawal_credentials,
activation_eligibility_epoch=FAR_FUTURE_EPOCH,
activation_epoch=FAR_FUTURE_EPOCH,
exit_epoch=FAR_FUTURE_EPOCH,
withdrawable_epoch=FAR_FUTURE_EPOCH,
effective_balance=effective_balance,
)
```
```python
def add_validator_to_registry(state: BeaconState,
pubkey: BLSPubkey,
withdrawal_credentials: Bytes32,
amount: uint64) -> None:
state.validators.append(get_validator_from_deposit(pubkey, withdrawal_credentials, amount))
state.balances.append(amount)
```
```python
def apply_deposit(state: BeaconState,
pubkey: BLSPubkey,
withdrawal_credentials: Bytes32,
amount: uint64,
signature: BLSSignature) -> None:
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=pubkey,
withdrawal_credentials=withdrawal_credentials,
amount=amount,
)
domain = compute_domain(DOMAIN_DEPOSIT) # Fork-agnostic domain since deposits are valid across forks
signing_root = compute_signing_root(deposit_message, domain)
if bls.Verify(pubkey, signing_root, signature):
add_validator_to_registry(state, pubkey, withdrawal_credentials, amount)
else:
# Increase balance by deposit amount
index = ValidatorIndex(validator_pubkeys.index(pubkey))
increase_balance(state, index, amount)
```
```python
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
apply_deposit(
state=state,
pubkey=deposit.data.pubkey,
withdrawal_credentials=deposit.data.withdrawal_credentials,
amount=deposit.data.amount,
signature=deposit.data.signature,
)
```
##### Voluntary exits
```python
def process_voluntary_exit(state: BeaconState, signed_voluntary_exit: SignedVoluntaryExit) -> None:
voluntary_exit = signed_voluntary_exit.message
validator = state.validators[voluntary_exit.validator_index]
# Verify the validator is active
assert is_active_validator(validator, get_current_epoch(state))
# Verify exit has not been initiated
assert validator.exit_epoch == FAR_FUTURE_EPOCH
# Exits must specify an epoch when they become valid; they are not valid before then
assert get_current_epoch(state) >= voluntary_exit.epoch
# Verify the validator has been active long enough
assert get_current_epoch(state) >= validator.activation_epoch + SHARD_COMMITTEE_PERIOD
# Verify signature
domain = get_domain(state, DOMAIN_VOLUNTARY_EXIT, voluntary_exit.epoch)
signing_root = compute_signing_root(voluntary_exit, domain)
assert bls.Verify(validator.pubkey, signing_root, signed_voluntary_exit.signature)
# Initiate exit
initiate_validator_exit(state, voluntary_exit.validator_index)
```
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