# Ethereum 2.0 Phase 1 -- Custody Game **Notice**: This document is a work-in-progress for researchers and implementers. ## Table of contents - [Ethereum 2.0 Phase 1 -- Custody Game](#ethereum-20-phase-1----custody-game) - [Table of contents](#table-of-contents) - [Introduction](#introduction) - [Terminology](#terminology) - [Constants](#constants) - [Misc](#misc) - [Custody game parameters](#custody-game-parameters) - [Time parameters](#time-parameters) - [Max operations per block](#max-operations-per-block) - [Reward and penalty quotients](#reward-and-penalty-quotients) - [Signature domain types](#signature-domain-types) - [Data structures](#data-structures) - [Custody objects](#custody-objects) - [`CustodyChunkChallenge`](#custodychunkchallenge) - [`CustodyBitChallenge`](#custodybitchallenge) - [`CustodyChunkChallengeRecord`](#custodychunkchallengerecord) - [`CustodyBitChallengeRecord`](#custodybitchallengerecord) - [`CustodyResponse`](#custodyresponse) - [New beacon operations](#new-beacon-operations) - [`CustodyKeyReveal`](#custodykeyreveal) - [`EarlyDerivedSecretReveal`](#earlyderivedsecretreveal) - [Phase 0 container updates](#phase-0-container-updates) - [`Validator`](#validator) - [`BeaconState`](#beaconstate) - [`BeaconBlockBody`](#beaconblockbody) - [Helpers](#helpers) - [`ceillog2`](#ceillog2) - [`is_valid_merkle_branch_with_mixin`](#is_valid_merkle_branch_with_mixin) - [`get_crosslink_chunk_count`](#get_crosslink_chunk_count) - [`legendre_bit`](#legendre_bit) - [`custody_subchunkify`](#custody_subchunkify) - [`get_custody_chunk_bit`](#get_custody_chunk_bit) - [`get_chunk_bits_root`](#get_chunk_bits_root) - [`get_randao_epoch_for_custody_period`](#get_randao_epoch_for_custody_period) - [`get_custody_period_for_validator`](#get_custody_period_for_validator) - [`replace_empty_or_append`](#replace_empty_or_append) - [Per-block processing](#per-block-processing) - [Operations](#operations) - [Custody key reveals](#custody-key-reveals) - [Early derived secret reveals](#early-derived-secret-reveals) - [Chunk challenges](#chunk-challenges) - [Bit challenges](#bit-challenges) - [Custody responses](#custody-responses) - [Per-epoch processing](#per-epoch-processing) - [Handling of custody-related deadlines](#handling-of-custody-related-deadlines) ## Introduction This document details the beacon chain additions and changes in Phase 1 of Ethereum 2.0 to support the shard data custody game, building upon the [Phase 0](0_beacon-chain.md) specification. ## Terminology - **Custody game**— - **Custody period**— - **Custody chunk**— - **Custody chunk bit**— - **Custody chunk challenge**— - **Custody bit**— - **Custody bit challenge**— - **Custody key**— - **Custody key reveal**— - **Custody key mask**— ## Constants ### Misc | Name | Value | | - | - | | `BLS12_381_Q` | `4002409555221667393417789825735904156556882819939007885332058136124031650490837864442687629129015664037894272559787` | | `MINOR_REWARD_QUOTIENT` | `2**8` (= 256) | | `MAX_EPOCHS_PER_CROSSLINK` | `2**6` (= 64) | epochs | ~7 hours | ### Custody game parameters | Name | Value | | - | - | | `BYTES_PER_SHARD_BLOCK` | `2**14` (= 16,384) | | `BYTES_PER_CUSTODY_CHUNK` | `2**9` (= 512) | | `BYTES_PER_CUSTODY_SUBCHUNK` | `48` | | `CHUNKS_PER_EPOCH` | `2 * BYTES_PER_SHARD_BLOCK * SLOTS_PER_EPOCH // BYTES_PER_CUSTODY_CHUNK` | | `MAX_CUSTODY_CHUNKS` | `MAX_EPOCHS_PER_CROSSLINK * CHUNKS_PER_EPOCH` | | `CUSTODY_DATA_DEPTH` | `ceillog2(MAX_CUSTODY_CHUNKS) + 1` | | `CUSTODY_CHUNK_BIT_DEPTH` | `ceillog2(MAX_EPOCHS_PER_CROSSLINK * CHUNKS_PER_EPOCH // 256) + 2` | ### Time parameters | Name | Value | Unit | Duration | | - | - | :-: | :-: | | `MAX_CHUNK_CHALLENGE_DELAY` | `2**11` (= 2,048) | epochs | ~9 days | | `CUSTODY_RESPONSE_DEADLINE` | `2**14` (= 16,384) | epochs | ~73 days | | `RANDAO_PENALTY_EPOCHS` | `2**1` (= 2) | epochs | 12.8 minutes | | `EARLY_DERIVED_SECRET_PENALTY_MAX_FUTURE_EPOCHS` | `2**14` | epochs | ~73 days | | `EPOCHS_PER_CUSTODY_PERIOD` | `2**11` (= 2,048) | epochs | ~9 days | | `CUSTODY_PERIOD_TO_RANDAO_PADDING` | `2**11` (= 2,048) | epochs | ~9 days | | `MAX_REVEAL_LATENESS_DECREMENT` | `2**7` (= 128) | epochs | ~14 hours | ### Max operations per block | Name | Value | | - | - | | `MAX_CUSTODY_KEY_REVEALS` | `2**4` (= 16) | | `MAX_EARLY_DERIVED_SECRET_REVEALS` | `1` | | `MAX_CUSTODY_CHUNK_CHALLENGES` | `2**2` (= 4) | | `MAX_CUSTODY_BIT_CHALLENGES` | `2**2` (= 4) | ### Reward and penalty quotients | Name | Value | | - | - | | `EARLY_DERIVED_SECRET_REVEAL_SLOT_REWARD_MULTIPLE` | `2**1` (= 2) | ### Signature domain types The following types are defined, mapping into `DomainType` (little endian): | Name | Value | | - | - | | `DOMAIN_CUSTODY_BIT_CHALLENGE` | `6` | ## Data structures ### Custody objects #### `CustodyChunkChallenge` ```python class CustodyChunkChallenge(Container): responder_index: ValidatorIndex attestation: Attestation chunk_index: uint64 ``` #### `CustodyBitChallenge` ```python class CustodyBitChallenge(Container): responder_index: ValidatorIndex attestation: Attestation challenger_index: ValidatorIndex responder_key: BLSSignature chunk_bits: Bitlist[MAX_CUSTODY_CHUNKS] signature: BLSSignature ``` #### `CustodyChunkChallengeRecord` ```python class CustodyChunkChallengeRecord(Container): challenge_index: uint64 challenger_index: ValidatorIndex responder_index: ValidatorIndex inclusion_epoch: Epoch data_root: Root depth: uint64 chunk_index: uint64 ``` #### `CustodyBitChallengeRecord` ```python class CustodyBitChallengeRecord(Container): challenge_index: uint64 challenger_index: ValidatorIndex responder_index: ValidatorIndex inclusion_epoch: Epoch data_root: Root chunk_count: uint64 chunk_bits_merkle_root: Root responder_key: BLSSignature ``` ### New Beacon Chain operations #### `CustodyKeyReveal` ```python class CustodyKeyReveal(Container): # Index of the validator whose key is being revealed revealer_index: ValidatorIndex # Reveal (masked signature) reveal: BLSSignature ``` #### `EarlyDerivedSecretReveal` Represents an early (punishable) reveal of one of the derived secrets, where derived secrets are RANDAO reveals and custody reveals (both are part of the same domain). ```python class EarlyDerivedSecretReveal(Container): # Index of the validator whose key is being revealed revealed_index: ValidatorIndex # RANDAO epoch of the key that is being revealed epoch: Epoch # Reveal (masked signature) reveal: BLSSignature # Index of the validator who revealed (whistleblower) masker_index: ValidatorIndex # Mask used to hide the actual reveal signature (prevent reveal from being stolen) mask: Bytes32 ``` ## Helpers ### `ceillog2` ```python def ceillog2(x: uint64) -> int: return (x - 1).bit_length() ``` ### `is_valid_merkle_branch_with_mixin` ```python def is_valid_merkle_branch_with_mixin(leaf: Bytes32, branch: Sequence[Bytes32], depth: uint64, index: uint64, root: Root, mixin: uint64) -> bool: value = leaf for i in range(depth): if index // (2**i) % 2: value = hash(branch[i] + value) else: value = hash(value + branch[i]) value = hash(value + mixin.to_bytes(32, "little")) return value == root ``` ### `get_crosslink_chunk_count` ```python def get_custody_chunk_count(crosslink: Crosslink) -> int: crosslink_length = min(MAX_EPOCHS_PER_CROSSLINK, crosslink.end_epoch - crosslink.start_epoch) return crosslink_length * CHUNKS_PER_EPOCH ``` ### `legendre_bit` Returns the Legendre symbol `(a/q)` normalizes as a bit (i.e. `((a/q) + 1) // 2`). In a production implementation, a well-optimized library (e.g. GMP) should be used for this. ```python def legendre_bit(a: int, q: int) -> int: if a >= q: return legendre_bit(a % q, q) if a == 0: return 0 assert(q > a > 0 and q % 2 == 1) t = 1 n = q while a != 0: while a % 2 == 0: a //= 2 r = n % 8 if r == 3 or r == 5: t = -t a, n = n, a if a % 4 == n % 4 == 3: t = -t a %= n if n == 1: return (t + 1) // 2 else: return 0 ``` ### `custody_subchunkify` Given one proof of custody chunk, returns the proof of custody subchunks of the correct sizes. ```python def custody_subchunkify(bytez: bytes) -> Sequence[bytes]: bytez += b'\x00' * (-len(bytez) % BYTES_PER_CUSTODY_SUBCHUNK) return [bytez[i:i + BYTES_PER_CUSTODY_SUBCHUNK] for i in range(0, len(bytez), BYTES_PER_CUSTODY_SUBCHUNK)] ``` ### `get_custody_chunk_bit` ```python def get_custody_chunk_bit(key: BLSSignature, chunk: bytes) -> bool: full_G2_element = bls_signature_to_G2(key) s = full_G2_element[0].coeffs bits = [legendre_bit((i + 1) * s[i % 2] + int.from_bytes(subchunk, "little"), BLS12_381_Q) for i, subchunk in enumerate(custody_subchunkify(chunk))] return bool(sum(bits) % 2) ``` ### `get_chunk_bits_root` ```python def get_chunk_bits_root(chunk_bits: Bitlist[MAX_CUSTODY_CHUNKS]) -> bit: aggregated_bits = 0 for i, b in enumerate(chunk_bits): aggregated_bits += 2**i * b return legendre_bit(aggregated_bits, BLS12_381_Q) ``` ### `get_randao_epoch_for_custody_period` ```python def get_randao_epoch_for_custody_period(period: uint64, validator_index: ValidatorIndex) -> Epoch: next_period_start = (period + 1) * EPOCHS_PER_CUSTODY_PERIOD - validator_index % EPOCHS_PER_CUSTODY_PERIOD return Epoch(next_period_start + CUSTODY_PERIOD_TO_RANDAO_PADDING) ``` ### `get_custody_period_for_validator` ```python def get_custody_period_for_validator(validator_index: ValidatorIndex, epoch: Epoch=None) -> int: ''' Return the reveal period for a given validator. ''' epoch = if epoch is None else epoch return (epoch + validator_index % EPOCHS_PER_CUSTODY_PERIOD) // EPOCHS_PER_CUSTODY_PERIOD ``` ### `replace_empty_or_append` ```python def replace_empty_or_append(list: MutableSequence[Any], new_element: Any) -> int: for i in range(len(list)): if is_zero(list[i]): list[i] = new_element return i list.append(new_element) return len(list) - 1 ``` ## Per-block processing ### Custody Game Operations ```python def process_custody_game_operations(state: BeaconState, body: BeaconBlockBody) -> None: def for_ops(operations, fn): for operation in operations: fn(state, operation) for_ops(body.custody_key_reveals, process_custody_key_reveal) for_ops(body.early_derived_secret_reveals, process_early_derived_secret_reveal) for_ops(body.custody_chunk_challenges, process_chunk_challenge) for_ops(body.custody_bit_challenges, process_bit_challenge) ``` #### Custody key reveals ```python def process_custody_key_reveal(state: BeaconState, reveal: CustodyKeyReveal) -> None: """ Process ``CustodyKeyReveal`` operation. Note that this function mutates ``state``. """ revealer = state.validators[reveal.revealer_index] epoch_to_sign = get_randao_epoch_for_custody_period(revealer.next_custody_secret_to_reveal, reveal.revealer_index) assert revealer.next_custody_secret_to_reveal < get_custody_period_for_validator(reveal.revealer_index, get_current_epoch(state)) # Revealed validator is active or exited, but not withdrawn assert is_slashable_validator(revealer, get_current_epoch(state)) # Verify signature assert bls_verify( pubkey=revealer.pubkey, message_hash=hash_tree_root(epoch_to_sign), signature=reveal.reveal, domain=get_domain( state=state, domain_type=DOMAIN_RANDAO, message_epoch=epoch_to_sign, ), ) # Decrement max reveal lateness if response is timely if epoch_to_sign + EPOCHS_PER_CUSTODY_PERIOD >= get_current_epoch(state): if revealer.max_reveal_lateness >= MAX_REVEAL_LATENESS_DECREMENT: revealer.max_reveal_lateness -= MAX_REVEAL_LATENESS_DECREMENT else: revealer.max_reveal_lateness = 0 else: revealer.max_reveal_lateness = max( revealer.max_reveal_lateness, get_current_epoch(state) - epoch_to_sign - EPOCHS_PER_CUSTODY_PERIOD ) # Process reveal revealer.next_custody_secret_to_reveal += 1 # Reward Block Preposer proposer_index = get_beacon_proposer_index(state) increase_balance( state, proposer_index, Gwei(get_base_reward(state, reveal.revealer_index) // MINOR_REWARD_QUOTIENT) ) ``` #### Early derived secret reveals ```python def process_early_derived_secret_reveal(state: BeaconState, reveal: EarlyDerivedSecretReveal) -> None: """ Process ``EarlyDerivedSecretReveal`` operation. Note that this function mutates ``state``. """ revealed_validator = state.validators[reveal.revealed_index] derived_secret_location = reveal.epoch % EARLY_DERIVED_SECRET_PENALTY_MAX_FUTURE_EPOCHS assert reveal.epoch >= get_current_epoch(state) + RANDAO_PENALTY_EPOCHS assert reveal.epoch < get_current_epoch(state) + EARLY_DERIVED_SECRET_PENALTY_MAX_FUTURE_EPOCHS assert not revealed_validator.slashed assert reveal.revealed_index not in state.exposed_derived_secrets[derived_secret_location] # Verify signature correctness masker = state.validators[reveal.masker_index] pubkeys = [revealed_validator.pubkey, masker.pubkey] message_hashes = [ hash_tree_root(reveal.epoch), reveal.mask, ] assert bls_verify_multiple( pubkeys=pubkeys, message_hashes=message_hashes, signature=reveal.reveal, domain=get_domain( state=state, domain_type=DOMAIN_RANDAO, message_epoch=reveal.epoch, ), ) if reveal.epoch >= get_current_epoch(state) + CUSTODY_PERIOD_TO_RANDAO_PADDING: # Full slashing when the secret was revealed so early it may be a valid custody # round key slash_validator(state, reveal.revealed_index, reveal.masker_index) else: # Only a small penalty proportional to proposer slot reward for RANDAO reveal # that does not interfere with the custody period # The penalty is proportional to the max proposer reward # Calculate penalty max_proposer_slot_reward = ( get_base_reward(state, reveal.revealed_index) * SLOTS_PER_EPOCH // len(get_active_validator_indices(state, get_current_epoch(state))) // PROPOSER_REWARD_QUOTIENT ) penalty = Gwei( max_proposer_slot_reward * EARLY_DERIVED_SECRET_REVEAL_SLOT_REWARD_MULTIPLE * (len(state.exposed_derived_secrets[derived_secret_location]) + 1) ) # Apply penalty proposer_index = get_beacon_proposer_index(state) whistleblower_index = reveal.masker_index whistleblowing_reward = Gwei(penalty // WHISTLEBLOWER_REWARD_QUOTIENT) proposer_reward = Gwei(whistleblowing_reward // PROPOSER_REWARD_QUOTIENT) increase_balance(state, proposer_index, proposer_reward) increase_balance(state, whistleblower_index, whistleblowing_reward - proposer_reward) decrease_balance(state, reveal.revealed_index, penalty) # Mark this derived secret as exposed so validator cannot be punished repeatedly state.exposed_derived_secrets[derived_secret_location].append(reveal.revealed_index) ``` #### Chunk challenges ```python def process_chunk_challenge(state: BeaconState, challenge: CustodyChunkChallenge) -> None: # Verify the attestation assert is_valid_indexed_attestation(state, get_indexed_attestation(state, challenge.attestation)) # Verify it is not too late to challenge assert (compute_epoch_at_slot(challenge.attestation.data.slot) >= get_current_epoch(state) - MAX_CHUNK_CHALLENGE_DELAY) responder = state.validators[challenge.responder_index] assert responder.exit_epoch >= get_current_epoch(state) - MAX_CHUNK_CHALLENGE_DELAY # Verify the responder participated in the attestation attesters = get_attesting_indices(state, challenge.attestation.data, challenge.attestation.aggregation_bits) assert challenge.responder_index in attesters # Verify the challenge is not a duplicate for record in state.custody_chunk_challenge_records: assert ( record.data_root != challenge.attestation.data.crosslink.data_root or record.chunk_index != challenge.chunk_index ) # Verify depth depth = ceillog2(get_custody_chunk_count(challenge.attestation.data.crosslink)) assert challenge.chunk_index < 2**depth # Add new chunk challenge record new_record = CustodyChunkChallengeRecord( challenge_index=state.custody_challenge_index, challenger_index=get_beacon_proposer_index(state), responder_index=challenge.responder_index, inclusion_epoch=get_current_epoch(state), data_root=challenge.attestation.data.crosslink.data_root, depth=depth, chunk_index=challenge.chunk_index, ) replace_empty_or_append(state.custody_chunk_challenge_records, new_record) state.custody_challenge_index += 1 # Postpone responder withdrawability responder.withdrawable_epoch = FAR_FUTURE_EPOCH ``` TODO: immediate challenge processing, no state records. ```python def process_chunk_challenge_response(state: BeaconState, response: CustodyResponse, challenge: CustodyChunkChallengeRecord) -> None: # Verify chunk index assert response.chunk_index == challenge.chunk_index # Verify bit challenge data is null assert response.chunk_bits_branch == [] and response.chunk_bits_leaf == Hash() # Verify minimum delay assert get_current_epoch(state) >= challenge.inclusion_epoch + MAX_SEED_LOOKAHEAD # Verify the chunk matches the crosslink data root assert is_valid_merkle_branch( leaf=hash_tree_root(response.chunk), branch=response.data_branch, depth=challenge.depth, index=response.chunk_index, root=challenge.data_root, ) # Clear the challenge records = state.custody_chunk_challenge_records records[records.index(challenge)] = CustodyChunkChallengeRecord() # Reward the proposer proposer_index = get_beacon_proposer_index(state) increase_balance(state, proposer_index, Gwei(get_base_reward(state, proposer_index) // MINOR_REWARD_QUOTIENT)) ``` #### Bit challenges ```python def process_bit_challenge(state: BeaconState, challenge: CustodyBitChallenge) -> None: attestation = challenge.attestation epoch = attestation.data.target.epoch shard = attestation.data.crosslink.shard # Verify challenge signature challenger = state.validators[challenge.challenger_index] domain = get_domain(state, DOMAIN_CUSTODY_BIT_CHALLENGE, get_current_epoch(state)) # TODO incorrect hash-tree-root, but this changes with phase 1 PR #1483 assert bls_verify(challenger.pubkey, hash_tree_root(challenge), challenge.signature, domain) # Verify challenger is slashable assert is_slashable_validator(challenger, get_current_epoch(state)) # Verify attestation assert is_valid_indexed_attestation(state, get_indexed_attestation(state, attestation)) # Verify attestation is eligible for challenging responder = state.validators[challenge.responder_index] assert get_current_epoch(state) <= get_randao_epoch_for_custody_period( get_custody_period_for_validator(challenge.responder_index, epoch), challenge.responder_index ) + 2 * EPOCHS_PER_CUSTODY_PERIOD + responder.max_reveal_lateness # Verify the responder participated in the attestation attesters = get_attesting_indices(state, attestation.data, attestation.aggregation_bits) assert challenge.responder_index in attesters # Verifier challenger is not already challenging for record in state.custody_bit_challenge_records: assert record.challenger_index != challenge.challenger_index # Verify the responder custody key epoch_to_sign = get_randao_epoch_for_custody_period( get_custody_period_for_validator(challenge.responder_index, epoch), challenge.responder_index, ) domain = get_domain(state, DOMAIN_RANDAO, epoch_to_sign) assert bls_verify(responder.pubkey, hash_tree_root(epoch_to_sign), challenge.responder_key, domain) # Verify the chunk count chunk_count = get_custody_chunk_count(attestation.data.crosslink) assert chunk_count == len(challenge.chunk_bits) # Verify custody bit is incorrect committee = get_beacon_committee(state, epoch, shard) custody_bit = attestation.custody_bits[committee.index(challenge.responder_index)] assert custody_bit != get_chunk_bits_root(challenge.chunk_bits) # Add new bit challenge record new_record = CustodyBitChallengeRecord( challenge_index=state.custody_challenge_index, challenger_index=challenge.challenger_index, responder_index=challenge.responder_index, inclusion_epoch=get_current_epoch(state), data_root=attestation.data.crosslink.data_root, chunk_count=chunk_count, chunk_bits_merkle_root=hash_tree_root(challenge.chunk_bits), responder_key=challenge.responder_key, ) replace_empty_or_append(state.custody_bit_challenge_records, new_record) state.custody_challenge_index += 1 # Postpone responder withdrawability responder.withdrawable_epoch = FAR_FUTURE_EPOCH ``` TODO: immediate challenge processing, no state records. ```python def process_bit_challenge_response(state: BeaconState, response: CustodyResponse, challenge: CustodyBitChallengeRecord) -> None: # Verify chunk index assert response.chunk_index < challenge.chunk_count # Verify responder has not been slashed responder = state.validators[challenge.responder_index] assert not responder.slashed # Verify the chunk matches the crosslink data root assert is_valid_merkle_branch( leaf=hash_tree_root(response.chunk), branch=response.data_branch, depth=ceillog2(challenge.chunk_count), index=response.chunk_index, root=challenge.data_root, ) # Verify the chunk bit leaf matches the challenge data assert is_valid_merkle_branch_with_mixin( leaf=hash_tree_root(response.chunk_bits_leaf), branch=response.chunk_bits_branch, depth=ceillog2(MAX_CUSTODY_CHUNKS // 256), index=response.chunk_index // 256, root=challenge.chunk_bits_merkle_root, mixin=challenge.chunk_count, ) # Verify the chunk bit does not match the challenge chunk bit assert (get_custody_chunk_bit(challenge.responder_key, response.chunk) != response.chunk_bits_leaf[response.chunk_index % 256]) # Clear the challenge records = state.custody_bit_challenge_records records[records.index(challenge)] = CustodyBitChallengeRecord() # Slash challenger slash_validator(state, challenge.challenger_index, challenge.responder_index) ``` ## Per-epoch processing ### Handling of custody-related deadlines Run `process_reveal_deadlines(state)` after `process_registry_updates(state)`: ```python def process_reveal_deadlines(state: BeaconState) -> None: for index, validator in enumerate(state.validators): deadline = validator.next_custody_secret_to_reveal + (CUSTODY_RESPONSE_DEADLINE // EPOCHS_PER_CUSTODY_PERIOD) if get_custody_period_for_validator(state, ValidatorIndex(index)) > deadline: slash_validator(state, ValidatorIndex(index)) ``` After `process_final_updates(state)`, additional updates are made for the custody game: ```python def process_custody_final_updates(state: BeaconState) -> None: current_epoch = get_current_epoch(state) # Clean up exposed RANDAO key reveals state.exposed_derived_secrets[current_epoch % EARLY_DERIVED_SECRET_PENALTY_MAX_FUTURE_EPOCHS] = [] # Reset withdrawable epochs if challenge records are empty records = state.custody_chunk_challenge_records + state.custody_bit_challenge_records validator_indices_in_records = set( [record.challenger_index for record in records] + [record.responder_index for record in records] ) for index, validator in enumerate(state.validators): if index not in validator_indices_in_records: if validator.exit_epoch != FAR_FUTURE_EPOCH and validator.withdrawable_epoch == FAR_FUTURE_EPOCH: validator.withdrawable_epoch = Epoch(validator.exit_epoch + MIN_VALIDATOR_WITHDRAWABILITY_DELAY) ```