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

# Altair -- The Beacon Chain

## Table of contents

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- [Introduction](#introduction)
- [Custom types](#custom-types)
- [Constants](#constants)
  - [Participation flag indices](#participation-flag-indices)
  - [Incentivization weights](#incentivization-weights)
  - [Domain types](#domain-types)
  - [Misc](#misc)
- [Preset](#preset)
  - [Updated penalty values](#updated-penalty-values)
  - [Sync committee](#sync-committee)
- [Configuration](#configuration)
  - [Inactivity penalties](#inactivity-penalties)
- [Containers](#containers)
  - [Modified containers](#modified-containers)
    - [`BeaconBlockBody`](#beaconblockbody)
    - [`BeaconState`](#beaconstate)
  - [New containers](#new-containers)
    - [`SyncAggregate`](#syncaggregate)
    - [`SyncCommittee`](#synccommittee)
- [Helper functions](#helper-functions)
  - [Crypto](#crypto)
  - [Misc](#misc-1)
    - [`add_flag`](#add_flag)
    - [`has_flag`](#has_flag)
    - [`get_index_for_new_validator`](#get_index_for_new_validator)
    - [`set_or_append_list`](#set_or_append_list)
  - [Beacon state accessors](#beacon-state-accessors)
    - [`get_next_sync_committee_indices`](#get_next_sync_committee_indices)
    - [`get_next_sync_committee`](#get_next_sync_committee)
    - [`get_base_reward_per_increment`](#get_base_reward_per_increment)
    - [`get_base_reward`](#get_base_reward)
    - [`get_unslashed_participating_indices`](#get_unslashed_participating_indices)
    - [`get_attestation_participation_flag_indices`](#get_attestation_participation_flag_indices)
    - [`get_flag_index_deltas`](#get_flag_index_deltas)
    - [Modified `get_inactivity_penalty_deltas`](#modified-get_inactivity_penalty_deltas)
  - [Beacon state mutators](#beacon-state-mutators)
    - [Modified `slash_validator`](#modified-slash_validator)
  - [Block processing](#block-processing)
    - [Modified `process_attestation`](#modified-process_attestation)
    - [Modified `add_validator_to_registry`](#modified-add_validator_to_registry)
    - [Sync aggregate processing](#sync-aggregate-processing)
  - [Epoch processing](#epoch-processing)
    - [Justification and finalization](#justification-and-finalization)
    - [Inactivity scores](#inactivity-scores)
    - [Rewards and penalties](#rewards-and-penalties)
    - [Slashings](#slashings)
    - [Participation flags updates](#participation-flags-updates)
    - [Sync committee updates](#sync-committee-updates)
- [Initialize state for pure Altair testnets and test vectors](#initialize-state-for-pure-altair-testnets-and-test-vectors)

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## Introduction

Altair is the first beacon chain hard fork. Its main features are:

* sync committees to support light clients
* incentive accounting reforms to reduce spec complexity
* penalty parameter updates towards their planned maximally punitive values

## Custom types

| Name | SSZ equivalent | Description |
| - | - | - |
| `ParticipationFlags` | `uint8` | a succinct representation of 8 boolean participation flags |

## Constants

### Participation flag indices

| Name | Value |
| - | - |
| `TIMELY_SOURCE_FLAG_INDEX` | `0` |
| `TIMELY_TARGET_FLAG_INDEX` | `1` |
| `TIMELY_HEAD_FLAG_INDEX` | `2` |

### Incentivization weights

| Name | Value |
| - | - |
| `TIMELY_SOURCE_WEIGHT` | `uint64(14)` |
| `TIMELY_TARGET_WEIGHT` | `uint64(26)` |
| `TIMELY_HEAD_WEIGHT` | `uint64(14)` |
| `SYNC_REWARD_WEIGHT` | `uint64(2)` |
| `PROPOSER_WEIGHT` | `uint64(8)` |
| `WEIGHT_DENOMINATOR` | `uint64(64)` |

*Note*: The sum of the weights equal `WEIGHT_DENOMINATOR`.

### Domain types

| Name | Value |
| - | - |
| `DOMAIN_SYNC_COMMITTEE` | `DomainType('0x07000000')` |
| `DOMAIN_SYNC_COMMITTEE_SELECTION_PROOF` | `DomainType('0x08000000')` |
| `DOMAIN_CONTRIBUTION_AND_PROOF` | `DomainType('0x09000000')` |

### Misc

| Name | Value |
| - | - |
| `PARTICIPATION_FLAG_WEIGHTS` | `[TIMELY_SOURCE_WEIGHT, TIMELY_TARGET_WEIGHT, TIMELY_HEAD_WEIGHT]` |

## Preset

### Updated penalty values

This patch updates a few configuration values to move penalty parameters closer to their final, maximum security values.

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

| Name | Value |
| - | - |
| `INACTIVITY_PENALTY_QUOTIENT_ALTAIR` | `uint64(3 * 2**24)` (= 50,331,648) |
| `MIN_SLASHING_PENALTY_QUOTIENT_ALTAIR` | `uint64(2**6)` (= 64) |
| `PROPORTIONAL_SLASHING_MULTIPLIER_ALTAIR` | `uint64(2)` |

### Sync committee

| Name | Value | Unit | Duration |
| - | - | - | - |
| `SYNC_COMMITTEE_SIZE` | `uint64(2**9)` (= 512) | validators | |
| `EPOCHS_PER_SYNC_COMMITTEE_PERIOD` | `uint64(2**8)` (= 256) | epochs | ~27 hours |

## Configuration

### Inactivity penalties

| Name | Value | Description |
| - | - | - |
| `INACTIVITY_SCORE_BIAS` | `uint64(2**2)` (= 4) | score points per inactive epoch |
| `INACTIVITY_SCORE_RECOVERY_RATE` | `uint64(2**4)` (= 16) | score points per leak-free epoch |

## Containers

### Modified containers

#### `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]
    sync_aggregate: SyncAggregate  # [New in Altair]
```

#### `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
    # Participation
    previous_epoch_participation: List[ParticipationFlags, VALIDATOR_REGISTRY_LIMIT]  # [Modified in Altair]
    current_epoch_participation: List[ParticipationFlags, VALIDATOR_REGISTRY_LIMIT]  # [Modified in Altair]
    # Finality
    justification_bits: Bitvector[JUSTIFICATION_BITS_LENGTH]  # Bit set for every recent justified epoch
    previous_justified_checkpoint: Checkpoint
    current_justified_checkpoint: Checkpoint
    finalized_checkpoint: Checkpoint
    # Inactivity
    inactivity_scores: List[uint64, VALIDATOR_REGISTRY_LIMIT]  # [New in Altair]
    # Sync
    current_sync_committee: SyncCommittee  # [New in Altair]
    next_sync_committee: SyncCommittee  # [New in Altair]
```

### New containers

#### `SyncAggregate`

```python
class SyncAggregate(Container):
    sync_committee_bits: Bitvector[SYNC_COMMITTEE_SIZE]
    sync_committee_signature: BLSSignature
```

#### `SyncCommittee`

```python
class SyncCommittee(Container):
    pubkeys: Vector[BLSPubkey, SYNC_COMMITTEE_SIZE]
    aggregate_pubkey: BLSPubkey
```

## Helper functions

### Crypto

Refer to the definitions in the [phase 0 document regarding BLS signatures](../phase0/beacon-chain.md#bls-signatures)
and the extensions defined in the [Altair BLS document](./bls.md). This specification assumes knowledge of
the functionality described in those documents.

### Misc

#### `add_flag`

```python
def add_flag(flags: ParticipationFlags, flag_index: int) -> ParticipationFlags:
    """
    Return a new ``ParticipationFlags`` adding ``flag_index`` to ``flags``.
    """
    flag = ParticipationFlags(2**flag_index)
    return flags | flag
```

#### `has_flag`

```python
def has_flag(flags: ParticipationFlags, flag_index: int) -> bool:
    """
    Return whether ``flags`` has ``flag_index`` set.
    """
    flag = ParticipationFlags(2**flag_index)
    return flags & flag == flag
```

#### `get_index_for_new_validator`

```python
def get_index_for_new_validator(state: BeaconState) -> ValidatorIndex:
    return ValidatorIndex(len(state.validators))
```

#### `set_or_append_list`

```python
def set_or_append_list(list: List, index: ValidatorIndex, value: Any) -> None:
    if index == len(list):
        list.append(value)
    else:
        list[index] = value
```

### Beacon state accessors

#### `get_next_sync_committee_indices`

```python
def get_next_sync_committee_indices(state: BeaconState) -> Sequence[ValidatorIndex]:
    """
    Return the sync committee indices, with possible duplicates, for the next sync committee.
    """
    epoch = Epoch(get_current_epoch(state) + 1)

    MAX_RANDOM_BYTE = 2**8 - 1
    active_validator_indices = get_active_validator_indices(state, epoch)
    active_validator_count = uint64(len(active_validator_indices))
    seed = get_seed(state, epoch, DOMAIN_SYNC_COMMITTEE)
    i = 0
    sync_committee_indices: List[ValidatorIndex] = []
    while len(sync_committee_indices) < SYNC_COMMITTEE_SIZE:
        shuffled_index = compute_shuffled_index(uint64(i % active_validator_count), active_validator_count, seed)
        candidate_index = active_validator_indices[shuffled_index]
        random_byte = hash(seed + uint_to_bytes(uint64(i // 32)))[i % 32]
        effective_balance = state.validators[candidate_index].effective_balance
        if effective_balance * MAX_RANDOM_BYTE >= MAX_EFFECTIVE_BALANCE * random_byte:
            sync_committee_indices.append(candidate_index)
        i += 1
    return sync_committee_indices
```

#### `get_next_sync_committee`

*Note*: The function `get_next_sync_committee` should only be called at sync committee period boundaries and when [upgrading state to Altair](./fork.md#upgrading-the-state).

```python
def get_next_sync_committee(state: BeaconState) -> SyncCommittee:
    """
    Return the next sync committee, with possible pubkey duplicates.
    """
    indices = get_next_sync_committee_indices(state)
    pubkeys = [state.validators[index].pubkey for index in indices]
    aggregate_pubkey = eth_aggregate_pubkeys(pubkeys)
    return SyncCommittee(pubkeys=pubkeys, aggregate_pubkey=aggregate_pubkey)
```

#### `get_base_reward_per_increment`

```python
def get_base_reward_per_increment(state: BeaconState) -> Gwei:
    return Gwei(EFFECTIVE_BALANCE_INCREMENT * BASE_REWARD_FACTOR // integer_squareroot(get_total_active_balance(state)))
```

#### `get_base_reward`

*Note*: The function `get_base_reward` is modified with the removal of `BASE_REWARDS_PER_EPOCH` and the use of increment based accounting.

*Note*: On average an optimally performing validator earns one base reward per epoch.

```python
def get_base_reward(state: BeaconState, index: ValidatorIndex) -> Gwei:
    """
    Return the base reward for the validator defined by ``index`` with respect to the current ``state``.
    """
    increments = state.validators[index].effective_balance // EFFECTIVE_BALANCE_INCREMENT
    return Gwei(increments * get_base_reward_per_increment(state))
```

#### `get_unslashed_participating_indices`

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

#### `get_attestation_participation_flag_indices`

```python
def get_attestation_participation_flag_indices(state: BeaconState,
                                               data: AttestationData,
                                               inclusion_delay: uint64) -> Sequence[int]:
    """
    Return the flag indices that are satisfied by an attestation.
    """
    if data.target.epoch == get_current_epoch(state):
        justified_checkpoint = state.current_justified_checkpoint
    else:
        justified_checkpoint = state.previous_justified_checkpoint

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

    participation_flag_indices = []
    if is_matching_source and inclusion_delay <= integer_squareroot(SLOTS_PER_EPOCH):
        participation_flag_indices.append(TIMELY_SOURCE_FLAG_INDEX)
    if is_matching_target and inclusion_delay <= SLOTS_PER_EPOCH:
        participation_flag_indices.append(TIMELY_TARGET_FLAG_INDEX)
    if is_matching_head and inclusion_delay == MIN_ATTESTATION_INCLUSION_DELAY:
        participation_flag_indices.append(TIMELY_HEAD_FLAG_INDEX)

    return participation_flag_indices
```

#### `get_flag_index_deltas`

```python
def get_flag_index_deltas(state: BeaconState, flag_index: int) -> Tuple[Sequence[Gwei], Sequence[Gwei]]:
    """
    Return the deltas for a given ``flag_index`` by scanning through the participation flags.
    """
    rewards = [Gwei(0)] * len(state.validators)
    penalties = [Gwei(0)] * len(state.validators)
    previous_epoch = get_previous_epoch(state)
    unslashed_participating_indices = get_unslashed_participating_indices(state, flag_index, previous_epoch)
    weight = PARTICIPATION_FLAG_WEIGHTS[flag_index]
    unslashed_participating_balance = get_total_balance(state, unslashed_participating_indices)
    unslashed_participating_increments = unslashed_participating_balance // EFFECTIVE_BALANCE_INCREMENT
    active_increments = get_total_active_balance(state) // EFFECTIVE_BALANCE_INCREMENT
    for index in get_eligible_validator_indices(state):
        base_reward = get_base_reward(state, index)
        if index in unslashed_participating_indices:
            if not is_in_inactivity_leak(state):
                reward_numerator = base_reward * weight * unslashed_participating_increments
                rewards[index] += Gwei(reward_numerator // (active_increments * WEIGHT_DENOMINATOR))
        elif flag_index != TIMELY_HEAD_FLAG_INDEX:
            penalties[index] += Gwei(base_reward * weight // WEIGHT_DENOMINATOR)
    return rewards, penalties
```

#### Modified `get_inactivity_penalty_deltas`

```python
def get_inactivity_penalty_deltas(state: BeaconState) -> Tuple[Sequence[Gwei], Sequence[Gwei]]:
    """
    Return the inactivity penalty deltas by considering timely target participation flags and inactivity scores.
    """
    rewards = [Gwei(0) for _ in range(len(state.validators))]
    penalties = [Gwei(0) for _ in range(len(state.validators))]
    previous_epoch = get_previous_epoch(state)
    matching_target_indices = get_unslashed_participating_indices(state, TIMELY_TARGET_FLAG_INDEX, previous_epoch)
    for index in get_eligible_validator_indices(state):
        if index not in matching_target_indices:
            penalty_numerator = state.validators[index].effective_balance * state.inactivity_scores[index]
            penalty_denominator = INACTIVITY_SCORE_BIAS * INACTIVITY_PENALTY_QUOTIENT_ALTAIR
            penalties[index] += Gwei(penalty_numerator // penalty_denominator)
    return rewards, penalties
```

### Beacon state mutators

#### Modified `slash_validator`

*Note*: The function `slash_validator` is modified to use `MIN_SLASHING_PENALTY_QUOTIENT_ALTAIR`
and use `PROPOSER_WEIGHT` when calculating the proposer reward.

```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_ALTAIR)

    # 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_WEIGHT // WEIGHT_DENOMINATOR)
    increase_balance(state, proposer_index, proposer_reward)
    increase_balance(state, whistleblower_index, Gwei(whistleblower_reward - proposer_reward))
```

### 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 Altair]
    process_sync_aggregate(state, block.body.sync_aggregate)  # [New in Altair]
```

#### Modified `process_attestation`

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

```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)

    # Participation flag indices
    participation_flag_indices = get_attestation_participation_flag_indices(state, data, state.slot - data.slot)

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

    # Update epoch participation flags
    if data.target.epoch == get_current_epoch(state):
        epoch_participation = state.current_epoch_participation
    else:
        epoch_participation = state.previous_epoch_participation

    proposer_reward_numerator = 0
    for index in get_attesting_indices(state, data, attestation.aggregation_bits):
        for flag_index, weight in enumerate(PARTICIPATION_FLAG_WEIGHTS):
            if flag_index in participation_flag_indices and not has_flag(epoch_participation[index], flag_index):
                epoch_participation[index] = add_flag(epoch_participation[index], flag_index)
                proposer_reward_numerator += get_base_reward(state, index) * weight

    # Reward proposer
    proposer_reward_denominator = (WEIGHT_DENOMINATOR - PROPOSER_WEIGHT) * WEIGHT_DENOMINATOR // PROPOSER_WEIGHT
    proposer_reward = Gwei(proposer_reward_numerator // proposer_reward_denominator)
    increase_balance(state, get_beacon_proposer_index(state), proposer_reward)
```

#### Modified `add_validator_to_registry`

*Note*: The function `add_validator_to_registry` is modified to initialize `inactivity_scores`, `previous_epoch_participation`, and `current_epoch_participation`.

```python
def add_validator_to_registry(state: BeaconState,
                              pubkey: BLSPubkey,
                              withdrawal_credentials: Bytes32,
                              amount: uint64) -> None:
    index = get_index_for_new_validator(state)
    validator = get_validator_from_deposit(pubkey, withdrawal_credentials, amount)
    set_or_append_list(state.validators, index, validator)
    set_or_append_list(state.balances, index, amount)
    # [New in Altair]
    set_or_append_list(state.previous_epoch_participation, index, ParticipationFlags(0b0000_0000))
    set_or_append_list(state.current_epoch_participation, index, ParticipationFlags(0b0000_0000))
    set_or_append_list(state.inactivity_scores, index, uint64(0))
```

#### Sync aggregate processing

*Note*: The function `process_sync_aggregate` is new.

```python
def process_sync_aggregate(state: BeaconState, sync_aggregate: SyncAggregate) -> None:
    # Verify sync committee aggregate signature signing over the previous slot block root
    committee_pubkeys = state.current_sync_committee.pubkeys
    participant_pubkeys = [pubkey for pubkey, bit in zip(committee_pubkeys, sync_aggregate.sync_committee_bits) if bit]
    previous_slot = max(state.slot, Slot(1)) - Slot(1)
    domain = get_domain(state, DOMAIN_SYNC_COMMITTEE, compute_epoch_at_slot(previous_slot))
    signing_root = compute_signing_root(get_block_root_at_slot(state, previous_slot), domain)
    assert eth_fast_aggregate_verify(participant_pubkeys, signing_root, sync_aggregate.sync_committee_signature)

    # Compute participant and proposer rewards
    total_active_increments = get_total_active_balance(state) // EFFECTIVE_BALANCE_INCREMENT
    total_base_rewards = Gwei(get_base_reward_per_increment(state) * total_active_increments)
    max_participant_rewards = Gwei(total_base_rewards * SYNC_REWARD_WEIGHT // WEIGHT_DENOMINATOR // SLOTS_PER_EPOCH)
    participant_reward = Gwei(max_participant_rewards // SYNC_COMMITTEE_SIZE)
    proposer_reward = Gwei(participant_reward * PROPOSER_WEIGHT // (WEIGHT_DENOMINATOR - PROPOSER_WEIGHT))

    # Apply participant and proposer rewards
    all_pubkeys = [v.pubkey for v in state.validators]
    committee_indices = [ValidatorIndex(all_pubkeys.index(pubkey)) for pubkey in state.current_sync_committee.pubkeys]
    for participant_index, participation_bit in zip(committee_indices, sync_aggregate.sync_committee_bits):
        if participation_bit:
            increase_balance(state, participant_index, participant_reward)
            increase_balance(state, get_beacon_proposer_index(state), proposer_reward)
        else:
            decrease_balance(state, participant_index, participant_reward)
```

### Epoch processing

```python
def process_epoch(state: BeaconState) -> None:
    process_justification_and_finalization(state)  # [Modified in Altair]
    process_inactivity_updates(state)  # [New in Altair]
    process_rewards_and_penalties(state)  # [Modified in Altair]
    process_registry_updates(state)
    process_slashings(state)  # [Modified in Altair]
    process_eth1_data_reset(state)
    process_effective_balance_updates(state)
    process_slashings_reset(state)
    process_randao_mixes_reset(state)
    process_historical_roots_update(state)
    process_participation_flag_updates(state)  # [New in Altair]
    process_sync_committee_updates(state)  # [New in Altair]
```

#### Justification and finalization

*Note*: The function `process_justification_and_finalization` is modified to adapt to the new participation records.

```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_indices = get_unslashed_participating_indices(state, TIMELY_TARGET_FLAG_INDEX, get_previous_epoch(state))
    current_indices = get_unslashed_participating_indices(state, TIMELY_TARGET_FLAG_INDEX, get_current_epoch(state))
    total_active_balance = get_total_active_balance(state)
    previous_target_balance = get_total_balance(state, previous_indices)
    current_target_balance = get_total_balance(state, current_indices)
    weigh_justification_and_finalization(state, total_active_balance, previous_target_balance, current_target_balance)
```

#### Inactivity scores

*Note*: The function `process_inactivity_updates` is new.

```python
def process_inactivity_updates(state: BeaconState) -> None:
    # Skip the genesis epoch as score updates are based on the previous epoch participation
    if get_current_epoch(state) == GENESIS_EPOCH:
        return

    for index in get_eligible_validator_indices(state):
        # Increase the inactivity score of inactive validators
        if index in get_unslashed_participating_indices(state, TIMELY_TARGET_FLAG_INDEX, get_previous_epoch(state)):
            state.inactivity_scores[index] -= min(1, state.inactivity_scores[index])
        else:
            state.inactivity_scores[index] += INACTIVITY_SCORE_BIAS
        # Decrease the inactivity score of all eligible validators during a leak-free epoch
        if not is_in_inactivity_leak(state):
            state.inactivity_scores[index] -= min(INACTIVITY_SCORE_RECOVERY_RATE, state.inactivity_scores[index])
```

#### Rewards and penalties

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

```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

    flag_deltas = [get_flag_index_deltas(state, flag_index) for flag_index in range(len(PARTICIPATION_FLAG_WEIGHTS))]
    deltas = flag_deltas + [get_inactivity_penalty_deltas(state)]
    for (rewards, penalties) in deltas:
        for index in range(len(state.validators)):
            increase_balance(state, ValidatorIndex(index), rewards[index])
            decrease_balance(state, ValidatorIndex(index), penalties[index])
```

#### Slashings

*Note*: The function `process_slashings` is modified to use `PROPORTIONAL_SLASHING_MULTIPLIER_ALTAIR`.

```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_ALTAIR, total_balance)
    for index, validator in enumerate(state.validators):
        if validator.slashed and epoch + EPOCHS_PER_SLASHINGS_VECTOR // 2 == validator.withdrawable_epoch:
            increment = EFFECTIVE_BALANCE_INCREMENT  # Factored out from penalty numerator to avoid uint64 overflow
            penalty_numerator = validator.effective_balance // increment * adjusted_total_slashing_balance
            penalty = penalty_numerator // total_balance * increment
            decrease_balance(state, ValidatorIndex(index), penalty)
```

#### Participation flags updates

*Note*: The function `process_participation_flag_updates` is new.

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

#### Sync committee updates

*Note*: The function `process_sync_committee_updates` is new.

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

## Initialize state for pure Altair testnets and test vectors

This helper function is only for initializing the state for pure Altair testnets and tests.

*Note*: The function `initialize_beacon_state_from_eth1` is modified: (1) using `ALTAIR_FORK_VERSION` as the previous and current fork version, (2) utilizing the Altair `BeaconBlockBody` when constructing the initial `latest_block_header`, and (3) adding initial sync committees.

```python
def initialize_beacon_state_from_eth1(eth1_block_hash: Hash32,
                                      eth1_timestamp: uint64,
                                      deposits: Sequence[Deposit]) -> BeaconState:
    fork = Fork(
        previous_version=ALTAIR_FORK_VERSION,  # [Modified in Altair] for testing only
        current_version=ALTAIR_FORK_VERSION,  # [Modified in Altair]
        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)

    # [New in Altair] Fill in sync committees
    # Note: A duplicate committee is assigned for the current and next committee at genesis
    state.current_sync_committee = get_next_sync_committee(state)
    state.next_sync_committee = get_next_sync_committee(state)

    return state
```