# Bellatrix -- The Beacon Chain

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- [Introduction](#introduction)
- [Types](#types)
  - [New `ExtraData`](#new-extradata)
  - [New `LogsBloom`](#new-logsbloom)
  - [New `Transaction`](#new-transaction)
  - [New `Transactions`](#new-transactions)
- [Constants](#constants)
- [Presets](#presets)
  - [Rewards and penalties](#rewards-and-penalties)
  - [Execution](#execution)
- [Configs](#configs)
  - [Transition settings](#transition-settings)
- [Containers](#containers)
  - [Modified containers](#modified-containers)
    - [`BeaconBlockBody`](#beaconblockbody)
    - [`BeaconState`](#beaconstate)
  - [New containers](#new-containers)
    - [`ExecutionPayload`](#executionpayload)
    - [`ExecutionPayloadHeader`](#executionpayloadheader)
    - [`NewPayloadRequest`](#newpayloadrequest)
- [Helpers](#helpers)
  - [Predicates](#predicates)
    - [`is_merge_transition_complete`](#is_merge_transition_complete)
    - [`is_merge_transition_block`](#is_merge_transition_block)
    - [`is_execution_enabled`](#is_execution_enabled)
  - [Beacon state accessors](#beacon-state-accessors)
    - [Modified `get_inactivity_penalty_deltas`](#modified-get_inactivity_penalty_deltas)
  - [Beacon state mutators](#beacon-state-mutators)
    - [Modified `slash_validator`](#modified-slash_validator)
- [Beacon chain state transition function](#beacon-chain-state-transition-function)
  - [Execution engine](#execution-engine)
    - [Engine APIs](#engine-apis)
    - [`notify_new_payload`](#notify_new_payload)
    - [`is_valid_block_hash`](#is_valid_block_hash)
    - [`verify_and_notify_new_payload`](#verify_and_notify_new_payload)
  - [Block processing](#block-processing)
    - [Execution payload](#execution-payload)
      - [`process_execution_payload`](#process_execution_payload)
  - [Epoch processing](#epoch-processing)
    - [Slashings](#slashings)

<!-- mdformat-toc end -->

## Introduction

Bellatrix is a consensus-layer upgrade containing a number of features.
Including:

- Transaction execution
- Penalty parameter updates to their planned maximally punitive values

## Types

### New `ExtraData`

```python
class ExtraData(ByteList):
    """
    Arbitrary extra data included in an execution payload.
    """

    LIMIT = MAX_EXTRA_DATA_BYTES
```

### New `LogsBloom`

```python
class LogsBloom(ByteVector):
    """
    A Bloom filter aggregating the logs emitted by an execution payload.
    """

    LENGTH = BYTES_PER_LOGS_BLOOM
```

### New `Transaction`

*Note*: The `Transaction` type is a stub which is not final.

*Note*: A `Transaction` is either a
[typed transaction envelope](https://eips.ethereum.org/EIPS/eip-2718#opaque-byte-array-rather-than-an-rlp-array)
or a legacy transaction.

```python
class Transaction(ByteList):
    """
    An opaque execution-layer transaction, either a typed transaction
    envelope or a legacy RLP-encoded transaction.
    """

    LIMIT = MAX_BYTES_PER_TRANSACTION
```

### New `Transactions`

```python
class Transactions(List[Transaction]):
    """
    A list of execution-layer transactions.
    """

    LIMIT = MAX_TRANSACTIONS_PER_PAYLOAD
```

## Constants

| Name               | Value      |
| ------------------ | ---------- |
| `EMPTY_BLOCK_HASH` | `Hash32()` |

## Presets

### Rewards and penalties

Bellatrix updates a few configuration values to move penalty parameters to their
final, maximum security values.

| Name                                         | Value                          |
| -------------------------------------------- | ------------------------------ |
| `INACTIVITY_PENALTY_QUOTIENT_BELLATRIX`      | `Uint64(2**24)` (= 16,777,216) |
| `MIN_SLASHING_PENALTY_QUOTIENT_BELLATRIX`    | `Uint64(2**5)` (= 32)          |
| `PROPORTIONAL_SLASHING_MULTIPLIER_BELLATRIX` | `Uint64(3)`                    |

### Execution

| Name                           | Value                             |
| ------------------------------ | --------------------------------- |
| `MAX_BYTES_PER_TRANSACTION`    | `Uint64(2**30)` (= 1,073,741,824) |
| `MAX_TRANSACTIONS_PER_PAYLOAD` | `Uint64(2**20)` (= 1,048,576)     |
| `BYTES_PER_LOGS_BLOOM`         | `Uint64(2**8)` (= 256)            |
| `MAX_EXTRA_DATA_BYTES`         | `Uint64(2**5)` (= 32)             |

## Configs

### Transition settings

| Name                                   | Value                              |
| -------------------------------------- | ---------------------------------- |
| `TERMINAL_TOTAL_DIFFICULTY`            | `Uint256(58750000000000000000000)` |
| `TERMINAL_BLOCK_HASH`                  | `Hash32()`                         |
| `TERMINAL_BLOCK_HASH_ACTIVATION_EPOCH` | `Epoch(FAR_FUTURE_EPOCH)`          |

## Containers

### Modified containers

#### `BeaconBlockBody`

```python
class BeaconBlockBody(Container):
    randao_reveal: BLSSignature
    eth1_data: Eth1Data
    graffiti: Bytes32
    proposer_slashings: ProposerSlashings
    attester_slashings: AttesterSlashings
    attestations: Attestations
    deposits: Deposits
    voluntary_exits: VoluntaryExits
    sync_aggregate: SyncAggregate
    # [New in Bellatrix]
    execution_payload: ExecutionPayload
```

#### `BeaconState`

```python
class BeaconState(Container):
    genesis_time: Uint64
    genesis_validators_root: Root
    slot: Slot
    fork: Fork
    latest_block_header: BeaconBlockHeader
    block_roots: BlockRoots
    state_roots: StateRoots
    historical_roots: HistoricalRoots
    eth1_data: Eth1Data
    eth1_data_votes: Eth1DataVotes
    eth1_deposit_index: Uint64
    validators: Validators
    balances: Balances
    randao_mixes: RandaoMixes
    slashings: Slashings
    previous_epoch_participation: EpochParticipation
    current_epoch_participation: EpochParticipation
    justification_bits: JustificationBits
    previous_justified_checkpoint: Checkpoint
    current_justified_checkpoint: Checkpoint
    finalized_checkpoint: Checkpoint
    inactivity_scores: InactivityScores
    current_sync_committee: SyncCommittee
    next_sync_committee: SyncCommittee
    # [New in Bellatrix]
    latest_execution_payload_header: ExecutionPayloadHeader
```

### New containers

#### `ExecutionPayload`

*Note*: `fee_recipient`, `prev_randao`, and `block_number` correspond to
`beneficiary`, `difficulty`, and `number` in
[the yellow paper](https://ethereum.github.io/yellowpaper/paper.pdf),
respectively.

```python
class ExecutionPayload(Container):
    parent_hash: Hash32
    fee_recipient: ExecutionAddress
    state_root: Bytes32
    receipts_root: Bytes32
    logs_bloom: LogsBloom
    prev_randao: Bytes32
    block_number: Uint64
    gas_limit: Uint64
    gas_used: Uint64
    timestamp: Uint64
    extra_data: ExtraData
    base_fee_per_gas: Uint256
    block_hash: Hash32
    transactions: Transactions
```

#### `ExecutionPayloadHeader`

*Note*: `block_hash` is the hash of the execution block.

```python
class ExecutionPayloadHeader(Container):
    parent_hash: Hash32
    fee_recipient: ExecutionAddress
    state_root: Bytes32
    receipts_root: Bytes32
    logs_bloom: LogsBloom
    prev_randao: Bytes32
    block_number: Uint64
    gas_limit: Uint64
    gas_used: Uint64
    timestamp: Uint64
    extra_data: ExtraData
    base_fee_per_gas: Uint256
    block_hash: Hash32
    transactions_root: Root
```

#### `NewPayloadRequest`

```python
class NewPayloadRequest(Container):
    execution_payload: ExecutionPayload
```

## Helpers

### Predicates

#### `is_merge_transition_complete`

```python
def is_merge_transition_complete(state: BeaconState) -> bool:
    return state.latest_execution_payload_header != ExecutionPayloadHeader.empty()
```

#### `is_merge_transition_block`

```python
def is_merge_transition_block(state: BeaconState, body: BeaconBlockBody) -> bool:
    return (
        not is_merge_transition_complete(state)
        and body.execution_payload != ExecutionPayload.empty()
    )
```

#### `is_execution_enabled`

```python
def is_execution_enabled(state: BeaconState, body: BeaconBlockBody) -> bool:
    return is_merge_transition_block(state, body) or is_merge_transition_complete(state)
```

### Beacon state accessors

#### Modified `get_inactivity_penalty_deltas`

*Note*: The function `get_inactivity_penalty_deltas` is modified to use
`INACTIVITY_PENALTY_QUOTIENT_BELLATRIX`.

```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)] * len(state.validators)
    penalties = [Gwei(0)] * 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]
            )
            # [Modified in Bellatrix]
            penalty_denominator = INACTIVITY_SCORE_BIAS * INACTIVITY_PENALTY_QUOTIENT_BELLATRIX
            penalties[index] += 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_BELLATRIX`.

```python
def slash_validator(
    state: BeaconState,
    slashed_index: ValidatorIndex,
    whistleblower_index: ValidatorIndex | None = 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 = Boolean(True)
    validator.withdrawable_epoch = max(
        validator.withdrawable_epoch, epoch + EPOCHS_PER_SLASHINGS_VECTOR
    )
    state.slashings[epoch % EPOCHS_PER_SLASHINGS_VECTOR] += validator.effective_balance
    # [Modified in Bellatrix]
    slashing_penalty = validator.effective_balance // MIN_SLASHING_PENALTY_QUOTIENT_BELLATRIX
    decrease_balance(state, slashed_index, slashing_penalty)

    # Apply proposer and whistleblower rewards
    proposer_index = get_beacon_proposer_index(state)
    if whistleblower_index is None:
        whistleblower_index = proposer_index
    whistleblower_reward = validator.effective_balance // WHISTLEBLOWER_REWARD_QUOTIENT
    proposer_reward = whistleblower_reward * PROPOSER_WEIGHT // WEIGHT_DENOMINATOR
    increase_balance(state, proposer_index, proposer_reward)
    increase_balance(state, whistleblower_index, whistleblower_reward - proposer_reward)
```

## Beacon chain state transition function

### Execution engine

#### Engine APIs

The implementation-dependent `ExecutionEngine` protocol encapsulates the
execution sub-system logic via:

- a state object `self.execution_state` of type `ExecutionState`
- a notification function `self.notify_new_payload` which may apply changes to
  the `self.execution_state`

The body of these functions are implementation dependent. The Engine API may be
used to implement this and similarly defined functions via an external execution
engine.

#### `notify_new_payload`

`notify_new_payload` is a function accessed through the `EXECUTION_ENGINE`
module which instantiates the `ExecutionEngine` protocol.

```python
def notify_new_payload(self: ExecutionEngine, execution_payload: ExecutionPayload) -> bool:
    """
    Return ``True`` if and only if ``execution_payload`` is valid with respect to ``self.execution_state``.
    """
```

#### `is_valid_block_hash`

```python
def is_valid_block_hash(self: ExecutionEngine, execution_payload: ExecutionPayload) -> bool:
    """
    Return ``True`` if and only if ``execution_payload.block_hash`` is computed correctly.
    """
```

#### `verify_and_notify_new_payload`

```python
def verify_and_notify_new_payload(
    self: ExecutionEngine, new_payload_request: NewPayloadRequest
) -> bool:
    """
    Return ``True`` if and only if ``new_payload_request`` is valid with respect to ``self.execution_state``.
    """
    execution_payload = new_payload_request.execution_payload

    if b"" in execution_payload.transactions:
        return False

    if not self.is_valid_block_hash(execution_payload):
        return False

    if not self.notify_new_payload(execution_payload):
        return False

    return True
```

### Block processing

*Note*: The call to the `process_execution_payload` must happen before the call
to the `process_randao` as the former depends on the `randao_mix` computed with
the reveal of the previous block.

```python
def process_block(state: BeaconState, block: BeaconBlock) -> None:
    process_block_header(state, block)
    if is_execution_enabled(state, block.body):
        # [New in Bellatrix]
        process_execution_payload(state, block.body, EXECUTION_ENGINE)
    process_randao(state, block.body)
    process_eth1_data(state, block.body)
    process_operations(state, block.body)
    process_sync_aggregate(state, block.body.sync_aggregate)
```

#### Execution payload

##### `process_execution_payload`

```python
def process_execution_payload(
    state: BeaconState, body: BeaconBlockBody, execution_engine: ExecutionEngine
) -> None:
    payload = body.execution_payload

    # Verify consistency of the parent hash with respect to the previous execution payload header
    if is_merge_transition_complete(state):
        assert payload.parent_hash == state.latest_execution_payload_header.block_hash
    # Verify prev_randao
    assert payload.prev_randao == get_randao_mix(state, get_current_epoch(state))
    # Verify timestamp
    assert payload.timestamp == compute_time_at_slot(state.genesis_time, state.slot)
    # Verify the execution payload is valid
    assert execution_engine.verify_and_notify_new_payload(
        NewPayloadRequest(execution_payload=payload)
    )
    # Cache execution payload header
    state.latest_execution_payload_header = ExecutionPayloadHeader(
        parent_hash=payload.parent_hash,
        fee_recipient=payload.fee_recipient,
        state_root=payload.state_root,
        receipts_root=payload.receipts_root,
        logs_bloom=payload.logs_bloom,
        prev_randao=payload.prev_randao,
        block_number=payload.block_number,
        gas_limit=payload.gas_limit,
        gas_used=payload.gas_used,
        timestamp=payload.timestamp,
        extra_data=payload.extra_data,
        base_fee_per_gas=payload.base_fee_per_gas,
        block_hash=payload.block_hash,
        transactions_root=hash_tree_root(payload.transactions),
    )
```

### Epoch processing

#### Slashings

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

```python
def process_slashings(state: BeaconState) -> None:
    epoch = get_current_epoch(state)
    total_balance = get_total_active_balance(state)
    adjusted_total_slashing_balance = min(
        Gwei(sum(state.slashings))
        # [Modified in Bellatrix]
        * PROPORTIONAL_SLASHING_MULTIPLIER_BELLATRIX,
        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)
```