diff --git a/specs/core/0_beacon-chain.md b/specs/core/0_beacon-chain.md
index 698f026c9..1d4a486a1 100644
--- a/specs/core/0_beacon-chain.md
+++ b/specs/core/0_beacon-chain.md
@@ -50,10 +50,10 @@
             - [`BeaconState`](#beaconstate)
     - [Helper functions](#helper-functions)
         - [Math](#math)
-            - [`int_to_bytes`](#int_to_bytes)
-            - [`bytes_to_int`](#bytes_to_int)
             - [`integer_squareroot`](#integer_squareroot)
             - [`xor`](#xor)
+            - [`int_to_bytes`](#int_to_bytes)
+            - [`bytes_to_int`](#bytes_to_int)
         - [Crypto](#crypto)
             - [`hash`](#hash)
             - [`hash_tree_root`](#hash_tree_root)
@@ -64,42 +64,39 @@
         - [Predicates](#predicates)
             - [`is_active_validator`](#is_active_validator)
             - [`is_slashable_validator`](#is_slashable_validator)
-            - [`is_valid_merkle_branch`](#is_valid_merkle_branch)
             - [`is_slashable_attestation_data`](#is_slashable_attestation_data)
+            - [`is_valid_merkle_branch`](#is_valid_merkle_branch)
+        - [Misc](#misc)
+            - [`shuffle_index`](#shuffle_index)
+            - [`compute_committee`](#compute_committee)
+            - [`validate_indexed_attestation`](#validate_indexed_attestation)
+            - [`slot_to_epoch`](#slot_to_epoch)
+            - [`epoch_first_slot`](#epoch_first_slot)
+            - [`delayed_activation_exit_epoch`](#delayed_activation_exit_epoch)
+            - [`bls_domain`](#bls_domain)
         - [Beacon state getters](#beacon-state-getters)
             - [`get_current_epoch`](#get_current_epoch)
             - [`get_previous_epoch`](#get_previous_epoch)
-            - [`get_committee_count`](#get_committee_count)
-            - [`get_start_shard`](#get_start_shard)
-            - [`get_active_validator_indices`](#get_active_validator_indices)
-
-
-            - [`bls_domain`](#bls_domain)
-            - [`slot_to_epoch`](#slot_to_epoch)
-            - [`epoch_start_slot`](#epoch_start_slot)
-
-            - [`increase_balance`](#increase_balance)
-            - [`decrease_balance`](#decrease_balance)
-            - [`get_shard_delta`](#get_shard_delta)
-            - [`get_attestation_data_slot`](#get_attestation_data_slot)
-            - [`get_block_root_at_slot`](#get_block_root_at_slot)
             - [`get_block_root`](#get_block_root)
+            - [`get_block_root_at_slot`](#get_block_root_at_slot)
             - [`get_randao_mix`](#get_randao_mix)
-            - [`get_compact_committees_root`](#get_compact_committees_root)
+            - [`get_active_validator_indices`](#get_active_validator_indices)
+            - [`get_churn_limit`](#get_churn_limit)
+            - [`get_committee_count`](#get_committee_count)
             - [`get_seed`](#get_seed)
-            - [`get_beacon_proposer_index`](#get_beacon_proposer_index)
-
-            - [`shuffle_index`](#shuffle_index)
-            - [`compute_committee`](#compute_committee)
             - [`get_crosslink_committee`](#get_crosslink_committee)
-            - [`get_attesting_indices`](#get_attesting_indices)
+            - [`get_start_shard`](#get_start_shard)
+            - [`get_shard_delta`](#get_shard_delta)
+            - [`get_proposer_index`](#get_proposer_index)
+            - [`get_attestation_data_slot`](#get_attestation_data_slot)
+            - [`get_compact_committees_root`](#get_compact_committees_root)
             - [`get_total_balance`](#get_total_balance)
             - [`get_domain`](#get_domain)
             - [`get_indexed_attestation`](#get_indexed_attestation)
-            - [`validate_indexed_attestation`](#validate_indexed_attestation)
-            - [`delayed_activation_exit_epoch`](#delayed_activation_exit_epoch)
-            - [`get_churn_limit`](#get_churn_limit)
-        - [Routines for updating validator status](#routines-for-updating-validator-status)
+            - [`get_attesting_indices`](#get_attesting_indices)
+        - [State mutators](#state-mutators)
+            - [`increase_balance`](#increase_balance)
+            - [`decrease_balance`](#decrease_balance)
             - [`initiate_validator_exit`](#initiate_validator_exit)
             - [`slash_validator`](#slash_validator)
     - [Genesis](#genesis)
@@ -201,6 +198,7 @@ The following values are (non-configurable) constants used throughout the specif
 | `MIN_GENESIS_ACTIVE_VALIDATOR_COUNT` | `2**16` (= 65,536) |
 | `MIN_GENESIS_TIME` | `1578009600` (Jan 3, 2020) |
 | `JUSTIFICATION_BITS_LENGTH` | `4` |
+| `ENDIANNESS` | `'little'` |
 
 * For the safety of crosslinks, `TARGET_COMMITTEE_SIZE` exceeds [the recommended minimum committee size of 111](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.)
 
@@ -559,18 +557,6 @@ class BeaconState(Container):
 
 #### `int_to_bytes`
 
-```python
-def int_to_bytes(integer: int, length: int) -> bytes:
-    return integer.to_bytes(length, 'little')
-```
-
-#### `bytes_to_int`
-
-```python
-def bytes_to_int(data: bytes) -> int:
-    return int.from_bytes(data, 'little')
-```
-
 #### `integer_squareroot`
 
 ```python
@@ -597,11 +583,29 @@ def xor(bytes1: Bytes32, bytes2: Bytes32) -> Bytes32:
     return Bytes32(a ^ b for a, b in zip(bytes1, bytes2))
 ```
 
+```python
+def int_to_bytes(integer: int, length: int) -> bytes:
+    """
+    Return the ``length``-byte serialization of ``integer``.
+    """
+    return integer.to_bytes(length, ENDIANNESS)
+```
+
+#### `bytes_to_int`
+
+```python
+def bytes_to_int(data: bytes) -> int:
+    """
+    Return the integer deserialization of ``data``.
+    """
+    return int.from_bytes(data, ENDIANNESS)
+```
+
 ### Crypto
 
 #### `hash`
 
-The `hash` function is SHA256.
+`def hash(data: bytes) -> Hash` is SHA256.
 
 #### `hash_tree_root`
 
@@ -625,22 +629,6 @@ The `hash` function is SHA256.
 
 ### Predicates
 
-#### `is_valid_merkle_branch`
-
-```python
-def is_valid_merkle_branch(leaf: Hash, branch: Sequence[Hash], depth: int, index: int, root: Hash) -> 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
-```
-
 #### `is_active_validator`
 
 ```python
@@ -676,6 +664,137 @@ def is_slashable_attestation_data(data_1: AttestationData, data_2: AttestationDa
     )
 ```
 
+#### `is_valid_merkle_branch`
+
+```python
+def is_valid_merkle_branch(leaf: Hash, branch: Sequence[Hash], depth: int, index: int, root: Hash) -> 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
+
+#### `shuffle_index`
+
+```python
+def shuffle_index(index: ValidatorIndex, index_count: int, seed: Hash) -> ValidatorIndex:
+    """
+    Return the shuffled validator index corresponding to ``seed`` (and ``index_count``).
+    """
+    assert index < index_count
+    assert index_count <= 2**40
+
+    # 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_int(hash(seed + int_to_bytes(current_round, length=1))[0:8]) % index_count
+        flip = ValidatorIndex((pivot + index_count - index) % index_count)
+        position = max(index, flip)
+        source = hash(
+            seed + int_to_bytes(current_round, length=1) +
+            int_to_bytes(position // 256, length=4)
+        )
+        byte = source[(position % 256) // 8]
+        bit = (byte >> (position % 8)) % 2
+        index = flip if bit else index
+
+    return ValidatorIndex(index)
+```
+
+#### `compute_committee`
+
+```python
+def compute_committee(indices: Sequence[ValidatorIndex],
+                      seed: Hash, index: int, count: int) -> Sequence[ValidatorIndex]:
+    """
+    Return the committee corresponding to ``indices``, ``seed``, ``index`` and committee ``count``.
+    """
+    start = (len(indices) * index) // count
+    end = (len(indices) * (index + 1)) // count
+    return [indices[shuffle_index(ValidatorIndex(i), len(indices), seed)] for i in range(start, end)]
+```
+
+#### `validate_indexed_attestation`
+
+```python
+def validate_indexed_attestation(state: BeaconState, indexed_attestation: IndexedAttestation) -> None:
+    """
+    Verify validity of ``indexed_attestation``.
+    """
+    bit_0_indices = indexed_attestation.custody_bit_0_indices
+    bit_1_indices = indexed_attestation.custody_bit_1_indices
+
+    # Verify no index has custody bit equal to 1 [to be removed in phase 1]
+    assert len(bit_1_indices) == 0
+    # Verify max number of indices
+    assert len(bit_0_indices) + len(bit_1_indices) <= MAX_VALIDATORS_PER_COMMITTEE
+    # Verify index sets are disjoint
+    assert len(set(bit_0_indices).intersection(bit_1_indices)) == 0
+    # Verify indices are sorted
+    assert bit_0_indices == sorted(bit_0_indices) and bit_1_indices == sorted(bit_1_indices)
+    # Verify aggregate signature
+    assert bls_verify_multiple(
+        pubkeys=[
+            bls_aggregate_pubkeys([state.validators[i].pubkey for i in bit_0_indices]),
+            bls_aggregate_pubkeys([state.validators[i].pubkey for i in bit_1_indices]),
+        ],
+        message_hashes=[
+            hash_tree_root(AttestationDataAndCustodyBit(data=indexed_attestation.data, custody_bit=0b0)),
+            hash_tree_root(AttestationDataAndCustodyBit(data=indexed_attestation.data, custody_bit=0b1)),
+        ],
+        signature=indexed_attestation.signature,
+        domain=get_domain(state, DOMAIN_ATTESTATION, indexed_attestation.data.target.epoch),
+    )
+```
+
+#### `slot_to_epoch`
+
+```python
+def slot_to_epoch(slot: Slot) -> Epoch:
+    """
+    Return the epoch number of ``slot``.
+    """
+    return Epoch(slot // SLOTS_PER_EPOCH)
+```
+
+#### `epoch_first_slot`
+
+```python
+def epoch_first_slot(epoch: Epoch) -> Slot:
+    """
+    Return the first slot of ``epoch``.
+    """
+    return Slot(epoch * SLOTS_PER_EPOCH)
+```
+
+#### `delayed_activation_exit_epoch`
+
+```python
+def delayed_activation_exit_epoch(epoch: Epoch) -> Epoch:
+    """
+    Return the epoch at which an activation or exit triggered in ``epoch`` takes effect.
+    """
+    return Epoch(epoch + 1 + ACTIVATION_EXIT_DELAY)
+```
+
+#### `bls_domain`
+
+```python
+def bls_domain(domain_type: int, fork_version: bytes=b'\x00' * 4) -> int:
+    """
+    Return the BLS domain for the ``domain_type`` and ``fork_version``.
+    """
+    return bytes_to_int(int_to_bytes(domain_type, length=4) + fork_version)
+```
+
 ### Beacon state getters
 
 #### `get_current_epoch`
@@ -706,7 +825,7 @@ def get_block_root(state: BeaconState, epoch: Epoch) -> Hash:
     """
     Return the block root at a recent ``epoch``.
     """
-    return get_block_root_at_slot(state, epoch_start_slot(epoch))
+    return get_block_root_at_slot(state, epoch_first_slot(epoch))
 ```
 
 #### `get_block_root_at_slot`
@@ -824,10 +943,10 @@ def get_shard_delta(state: BeaconState, epoch: Epoch) -> Shard:
     return Shard(min(get_committee_count(state, epoch), SHARD_COUNT - SHARD_COUNT // SLOTS_PER_EPOCH))
 ```
 
-#### `get_beacon_proposer_index`
+#### `get_proposer_index`
 
 ```python
-def get_beacon_proposer_index(state: BeaconState) -> ValidatorIndex:
+def get_proposer_index(state: BeaconState) -> ValidatorIndex:
     """
     Return the beacon proposer index at the current epoch.
     """
@@ -857,7 +976,7 @@ def get_attestation_data_slot(state: BeaconState, data: AttestationData) -> Slot
     """
     committee_count = get_committee_count(state, data.target.epoch)
     offset = (data.crosslink.shard + SHARD_COUNT - get_start_shard(state, data.target.epoch)) % SHARD_COUNT
-    return Slot(epoch_start_slot(data.target.epoch) + offset // (committee_count // SLOTS_PER_EPOCH))
+    return Slot(epoch_first_slot(data.target.epoch) + offset // (committee_count // SLOTS_PER_EPOCH))
 ```
 
 #### `get_compact_committees_root`
@@ -936,63 +1055,14 @@ def get_attesting_indices(state: BeaconState,
     return set(index for i, index in enumerate(committee) if bits[i])
 ```
 
-
-
-
-
-
-
-
-
-
-
-
-#### `bls_domain`
-
-```python
-def bls_domain(domain_type: int, fork_version: bytes=b'\x00\x00\x00\x00') -> int:
-    """
-    Return the bls domain given by the ``domain_type`` and optional 4 byte ``fork_version`` (defaults to zero).
-    """
-    return bytes_to_int(int_to_bytes(domain_type, length=4) + fork_version)
-```
-
-#### `slot_to_epoch`
-
-```python
-def slot_to_epoch(slot: Slot) -> Epoch:
-    """
-    Return the epoch number of the given ``slot``.
-    """
-    return Epoch(slot // SLOTS_PER_EPOCH)
-```
-
-#### `epoch_start_slot`
-
-```python
-def epoch_start_slot(epoch: Epoch) -> Slot:
-    """
-    Return the starting slot of the given ``epoch``.
-    """
-    return Slot(epoch * SLOTS_PER_EPOCH)
-```
-
-#### `delayed_activation_exit_epoch`
-
-```python
-def delayed_activation_exit_epoch(epoch: Epoch) -> Epoch:
-    """
-    Return the epoch at which an activation or exit triggered in ``epoch`` takes effect.
-    """
-    return Epoch(epoch + 1 + ACTIVATION_EXIT_DELAY)
-```
+### State mutators
 
 #### `increase_balance`
 
 ```python
 def increase_balance(state: BeaconState, index: ValidatorIndex, delta: Gwei) -> None:
     """
-    Increase validator balance by ``delta``.
+    Increase the validator balance at index ``index`` by ``delta``.
     """
     state.balances[index] += delta
 ```
@@ -1002,91 +1072,17 @@ def increase_balance(state: BeaconState, index: ValidatorIndex, delta: Gwei) ->
 ```python
 def decrease_balance(state: BeaconState, index: ValidatorIndex, delta: Gwei) -> None:
     """
-    Decrease validator balance by ``delta`` with underflow protection.
+    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
 ```
 
-#### `shuffle_index`
-
-```python
-def shuffle_index(index: ValidatorIndex, index_count: int, seed: Hash) -> ValidatorIndex:
-    """
-    Return the shuffled validator index corresponding to ``seed`` (and ``index_count``).
-    """
-    assert index < index_count
-    assert index_count <= 2**40
-
-    # 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_int(hash(seed + int_to_bytes(current_round, length=1))[0:8]) % index_count
-        flip = ValidatorIndex((pivot + index_count - index) % index_count)
-        position = max(index, flip)
-        source = hash(
-            seed + int_to_bytes(current_round, length=1) +
-            int_to_bytes(position // 256, length=4)
-        )
-        byte = source[(position % 256) // 8]
-        bit = (byte >> (position % 8)) % 2
-        index = flip if bit else index
-
-    return ValidatorIndex(index)
-```
-
-#### `compute_committee`
-
-```python
-def compute_committee(indices: Sequence[ValidatorIndex],
-                      seed: Hash, index: int, count: int) -> Sequence[ValidatorIndex]:
-    start = (len(indices) * index) // count
-    end = (len(indices) * (index + 1)) // count
-    return [indices[shuffle_index(ValidatorIndex(i), len(indices), seed)] for i in range(start, end)]
-```
-
-#### `validate_indexed_attestation`
-
-```python
-def validate_indexed_attestation(state: BeaconState, indexed_attestation: IndexedAttestation) -> None:
-    """
-    Verify validity of ``indexed_attestation``.
-    """
-    bit_0_indices = indexed_attestation.custody_bit_0_indices
-    bit_1_indices = indexed_attestation.custody_bit_1_indices
-
-    # Verify no index has custody bit equal to 1 [to be removed in phase 1]
-    assert len(bit_1_indices) == 0
-    # Verify max number of indices
-    assert len(bit_0_indices) + len(bit_1_indices) <= MAX_VALIDATORS_PER_COMMITTEE
-    # Verify index sets are disjoint
-    assert len(set(bit_0_indices).intersection(bit_1_indices)) == 0
-    # Verify indices are sorted
-    assert bit_0_indices == sorted(bit_0_indices) and bit_1_indices == sorted(bit_1_indices)
-    # Verify aggregate signature
-    assert bls_verify_multiple(
-        pubkeys=[
-            bls_aggregate_pubkeys([state.validators[i].pubkey for i in bit_0_indices]),
-            bls_aggregate_pubkeys([state.validators[i].pubkey for i in bit_1_indices]),
-        ],
-        message_hashes=[
-            hash_tree_root(AttestationDataAndCustodyBit(data=indexed_attestation.data, custody_bit=0b0)),
-            hash_tree_root(AttestationDataAndCustodyBit(data=indexed_attestation.data, custody_bit=0b1)),
-        ],
-        signature=indexed_attestation.signature,
-        domain=get_domain(state, DOMAIN_ATTESTATION, indexed_attestation.data.target.epoch),
-    )
-```
-
-### Routines for updating validator status
-
-*Note*: All functions in this section mutate `state`.
-
 #### `initiate_validator_exit`
 
 ```python
 def initiate_validator_exit(state: BeaconState, index: ValidatorIndex) -> None:
     """
-    Initiate the exit of the validator of the given ``index``.
+    Initiate the exit of the validator with index ``index``.
     """
     # Return if validator already initiated exit
     validator = state.validators[index]
@@ -1123,7 +1119,7 @@ def slash_validator(state: BeaconState,
     decrease_balance(state, slashed_index, validator.effective_balance // MIN_SLASHING_PENALTY_QUOTIENT)
 
     # Apply proposer and whistleblower rewards
-    proposer_index = get_beacon_proposer_index(state)
+    proposer_index = get_proposer_index(state)
     if whistleblower_index is None:
         whistleblower_index = proposer_index
     whistleblower_reward = Gwei(validator.effective_balance // WHISTLEBLOWER_REWARD_QUOTIENT)
@@ -1134,22 +1130,12 @@ def slash_validator(state: BeaconState,
 
 ## Genesis
 
-### Genesis state
-
-Before the Ethereum 2.0 genesis has been triggered, and for every Ethereum 1.0 block, call `initialize_beacon_state_from_eth1(eth1_block_hash, eth1_timestamp, deposits)` where:
+Before the Ethereum 2.0 genesis has been triggered, and for every Ethereum 1.0 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 1.0 block
 * `eth1_timestamp` is the Unix timestamp corresponding to `eth1_block_hash`
 * `deposits` is the sequence of all deposits, ordered chronologically, up to the block with hash `eth1_block_hash`
 
-The genesis state `genesis_state` is the return value of calling `initialize_beacon_state_from_eth1(eth1_block_hash, eth1_timestamp, deposits)` only if `is_valid_genesis_state(genesis_state) is True`.
-
-Implementations can choose to support different (more optimized) variations of the below initialization approach:
- - Build the `genesis_state` from a stream of deposits by incrementally updating the `state.eth1_data.deposit_root`.
- - Compute deposit proofs for the final `state.eth1_data.deposit_root`, and process as a pre-determined collection.
-
-*Note*: The two constants `MIN_GENESIS_TIME` and `MIN_GENESIS_ACTIVE_VALIDATOR_COUNT` have yet to be agreed upon by the community, and can be updated as necessary.
-
 ```python
 def initialize_beacon_state_from_eth1(eth1_block_hash: Hash,
                                       eth1_timestamp: uint64,
@@ -1175,22 +1161,27 @@ def initialize_beacon_state_from_eth1(eth1_block_hash: Hash,
             validator.activation_epoch = GENESIS_EPOCH
 
     # Populate compact_committees_roots
-    genesis_committee_root = get_compact_committees_root(state, GENESIS_EPOCH)
+    committee_root = get_compact_committees_root(state, GENESIS_EPOCH)
     for index in range(EPOCHS_PER_HISTORICAL_VECTOR):
-        state.compact_committees_roots[index] = genesis_committee_root
+        state.compact_committees_roots[index] = committee_root
     return state
 ```
 
+### 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
-    elif len(get_active_validator_indices(state, GENESIS_EPOCH)) < MIN_GENESIS_ACTIVE_VALIDATOR_COUNT:
+    if len(get_active_validator_indices(state, GENESIS_EPOCH)) < MIN_GENESIS_ACTIVE_VALIDATOR_COUNT:
         return False
-    else:
-        return True
+    return True
 ```
 
+*Note*: The `is_valid_genesis_state` function (including `MIN_GENESIS_TIME` and `MIN_GENESIS_ACTIVE_VALIDATOR_COUNT`) is a placeholder for testing. It has yet to be finalized by the community, and can be updated as necessary.
+
 ### Genesis block
 
 Let `genesis_block = BeaconBlock(state_root=hash_tree_root(genesis_state))`.
@@ -1287,7 +1278,7 @@ def get_matching_head_attestations(state: BeaconState, epoch: Epoch) -> Sequence
 ```python
 def get_unslashed_attesting_indices(state: BeaconState,
                                     attestations: Sequence[PendingAttestation]) -> Set[ValidatorIndex]:
-    output = set()  # type: Set[ValidatorIndex]
+    output = set()  # Type: Set[ValidatorIndex]
     for a in attestations:
         output = output.union(get_attesting_indices(state, a.data, a.aggregation_bits))
     return set(filter(lambda index: not state.validators[index].slashed, list(output)))
@@ -1566,7 +1557,7 @@ def process_block_header(state: BeaconState, block: BeaconBlock) -> None:
         body_root=hash_tree_root(block.body),
     )
     # Verify proposer is not slashed
-    proposer = state.validators[get_beacon_proposer_index(state)]
+    proposer = state.validators[get_proposer_index(state)]
     assert not proposer.slashed
     # Verify proposer signature
     assert bls_verify(proposer.pubkey, signing_root(block), block.signature, get_domain(state, DOMAIN_BEACON_PROPOSER))
@@ -1578,7 +1569,7 @@ def process_block_header(state: BeaconState, block: BeaconBlock) -> None:
 def process_randao(state: BeaconState, body: BeaconBlockBody) -> None:
     epoch = get_current_epoch(state)
     # Verify RANDAO reveal
-    proposer = state.validators[get_beacon_proposer_index(state)]
+    proposer = state.validators[get_proposer_index(state)]
     assert bls_verify(proposer.pubkey, hash_tree_root(epoch), body.randao_reveal, get_domain(state, DOMAIN_RANDAO))
     # Mix in RANDAO reveal
     mix = xor(get_randao_mix(state, epoch), hash(body.randao_reveal))
@@ -1620,9 +1611,6 @@ def process_operations(state: BeaconState, body: BeaconBlockBody) -> None:
 
 ```python
 def process_proposer_slashing(state: BeaconState, proposer_slashing: ProposerSlashing) -> None:
-    """
-    Process ``ProposerSlashing`` operation.
-    """
     proposer = state.validators[proposer_slashing.proposer_index]
     # Verify that the epoch is the same
     assert slot_to_epoch(proposer_slashing.header_1.slot) == slot_to_epoch(proposer_slashing.header_2.slot)
@@ -1642,9 +1630,6 @@ def process_proposer_slashing(state: BeaconState, proposer_slashing: ProposerSla
 
 ```python
 def process_attester_slashing(state: BeaconState, attester_slashing: AttesterSlashing) -> None:
-    """
-    Process ``AttesterSlashing`` operation.
-    """
     attestation_1 = attester_slashing.attestation_1
     attestation_2 = attester_slashing.attestation_2
     assert is_slashable_attestation_data(attestation_1.data, attestation_2.data)
@@ -1665,9 +1650,6 @@ def process_attester_slashing(state: BeaconState, attester_slashing: AttesterSla
 
 ```python
 def process_attestation(state: BeaconState, attestation: Attestation) -> None:
-    """
-    Process ``Attestation`` operation.
-    """
     data = attestation.data
     assert data.crosslink.shard < SHARD_COUNT
     assert data.target.epoch in (get_previous_epoch(state), get_current_epoch(state))
@@ -1679,7 +1661,7 @@ def process_attestation(state: BeaconState, attestation: Attestation) -> None:
         data=data,
         aggregation_bits=attestation.aggregation_bits,
         inclusion_delay=state.slot - attestation_slot,
-        proposer_index=get_beacon_proposer_index(state),
+        proposer_index=get_proposer_index(state),
     )
 
     if data.target.epoch == get_current_epoch(state):
@@ -1705,9 +1687,6 @@ def process_attestation(state: BeaconState, attestation: Attestation) -> None:
 
 ```python
 def process_deposit(state: BeaconState, deposit: Deposit) -> None:
-    """
-    Process an Eth1 deposit, registering a validator or increasing its balance.
-    """
     # Verify the Merkle branch
     assert is_valid_merkle_branch(
         leaf=hash_tree_root(deposit.data),
@@ -1754,9 +1733,6 @@ def process_deposit(state: BeaconState, deposit: Deposit) -> None:
 
 ```python
 def process_voluntary_exit(state: BeaconState, exit: VoluntaryExit) -> None:
-    """
-    Process ``VoluntaryExit`` operation.
-    """
     validator = state.validators[exit.validator_index]
     # Verify the validator is active
     assert is_active_validator(validator, get_current_epoch(state))
@@ -1777,9 +1753,6 @@ def process_voluntary_exit(state: BeaconState, exit: VoluntaryExit) -> None:
 
 ```python
 def process_transfer(state: BeaconState, transfer: Transfer) -> None:
-    """
-    Process ``Transfer`` operation.
-    """
     # Verify the balance the covers amount and fee (with overflow protection)
     assert state.balances[transfer.sender] >= max(transfer.amount + transfer.fee, transfer.amount, transfer.fee)
     # A transfer is valid in only one slot
@@ -1803,7 +1776,7 @@ def process_transfer(state: BeaconState, transfer: Transfer) -> None:
     # Process the transfer
     decrease_balance(state, transfer.sender, transfer.amount + transfer.fee)
     increase_balance(state, transfer.recipient, transfer.amount)
-    increase_balance(state, get_beacon_proposer_index(state), transfer.fee)
+    increase_balance(state, get_proposer_index(state), transfer.fee)
     # Verify balances are not dust
     assert not (0 < state.balances[transfer.sender] < MIN_DEPOSIT_AMOUNT)
     assert not (0 < state.balances[transfer.recipient] < MIN_DEPOSIT_AMOUNT)
diff --git a/specs/core/0_fork-choice.md b/specs/core/0_fork-choice.md
index 64afb3f6b..b2ae89e9f 100644
--- a/specs/core/0_fork-choice.md
+++ b/specs/core/0_fork-choice.md
@@ -124,7 +124,7 @@ def get_latest_attesting_balance(store: Store, root: Hash) -> Gwei:
 def get_head(store: Store) -> Hash:
     # Execute the LMD-GHOST fork choice
     head = store.justified_checkpoint.root
-    justified_slot = epoch_start_slot(store.justified_checkpoint.epoch)
+    justified_slot = epoch_first_slot(store.justified_checkpoint.epoch)
     while True:
         children = [
             root for root in store.blocks.keys()
@@ -162,7 +162,7 @@ def on_block(store: Store, block: BeaconBlock) -> None:
         store.finalized_checkpoint.root
     )
     # Check that block is later than the finalized epoch slot
-    assert block.slot > epoch_start_slot(store.finalized_checkpoint.epoch)
+    assert block.slot > epoch_first_slot(store.finalized_checkpoint.epoch)
     # Check the block is valid and compute the post-state
     state = state_transition(pre_state, block)
     # Add new state for this block to the store
@@ -190,11 +190,11 @@ def on_attestation(store: Store, attestation: Attestation) -> None:
 
     # Attestations cannot be from future epochs. If they are, delay consideration until the epoch arrivesr
     base_state = store.block_states[target.root].copy()
-    assert store.time >= base_state.genesis_time + epoch_start_slot(target.epoch) * SECONDS_PER_SLOT
+    assert store.time >= base_state.genesis_time + epoch_first_slot(target.epoch) * SECONDS_PER_SLOT
 
     # Store target checkpoint state if not yet seen
     if target not in store.checkpoint_states:
-        process_slots(base_state, epoch_start_slot(target.epoch))
+        process_slots(base_state, epoch_first_slot(target.epoch))
         store.checkpoint_states[target] = base_state
     target_state = store.checkpoint_states[target]
 
diff --git a/specs/core/1_custody-game.md b/specs/core/1_custody-game.md
index e588e9fdf..993a45b0f 100644
--- a/specs/core/1_custody-game.md
+++ b/specs/core/1_custody-game.md
@@ -382,7 +382,7 @@ def process_custody_key_reveal(state: BeaconState, reveal: CustodyKeyReveal) ->
     revealer.next_custody_reveal_period += 1
 
     # Reward Block Preposer
-    proposer_index = get_beacon_proposer_index(state)
+    proposer_index = get_proposer_index(state)
     increase_balance(
         state,
         proposer_index,
@@ -452,7 +452,7 @@ def process_early_derived_secret_reveal(state: BeaconState, reveal: EarlyDerived
         )
 
         # Apply penalty
-        proposer_index = get_beacon_proposer_index(state)
+        proposer_index = get_proposer_index(state)
         whistleblower_index = reveal.masker_index
         whistleblowing_reward = Gwei(penalty // WHISTLEBLOWER_REWARD_QUOTIENT)
         proposer_reward = Gwei(whistleblowing_reward // PROPOSER_REWARD_QUOTIENT)
@@ -493,7 +493,7 @@ def process_chunk_challenge(state: BeaconState, challenge: CustodyChunkChallenge
     # Add new chunk challenge record
     new_record = CustodyChunkChallengeRecord(
         challenge_index=state.custody_challenge_index,
-        challenger_index=get_beacon_proposer_index(state),
+        challenger_index=get_proposer_index(state),
         responder_index=challenge.responder_index,
         inclusion_epoch=get_current_epoch(state),
         data_root=challenge.attestation.data.crosslink.data_root,
@@ -610,7 +610,7 @@ def process_chunk_challenge_response(state: BeaconState,
     records = state.custody_chunk_challenge_records
     records[records.index(challenge)] = CustodyChunkChallengeRecord()
     # Reward the proposer
-    proposer_index = get_beacon_proposer_index(state)
+    proposer_index = get_proposer_index(state)
     increase_balance(state, proposer_index, Gwei(get_base_reward(state, proposer_index) // MINOR_REWARD_QUOTIENT))
 ```
 
diff --git a/specs/validator/0_beacon-chain-validator.md b/specs/validator/0_beacon-chain-validator.md
index f4a83b833..9921bf034 100644
--- a/specs/validator/0_beacon-chain-validator.md
+++ b/specs/validator/0_beacon-chain-validator.md
@@ -146,7 +146,7 @@ def get_committee_assignment(
     assert epoch <= next_epoch
 
     committees_per_slot = get_committee_count(state, epoch) // SLOTS_PER_EPOCH
-    start_slot = epoch_start_slot(epoch)
+    start_slot = epoch_first_slot(epoch)
     for slot in range(start_slot, start_slot + SLOTS_PER_EPOCH):
         offset = committees_per_slot * (slot % SLOTS_PER_EPOCH)
         slot_start_shard = (get_start_shard(state, epoch) + offset) % SHARD_COUNT
@@ -162,7 +162,7 @@ A validator can use the following function to see if they are supposed to propos
 ```python
 def is_proposer(state: BeaconState,
                 validator_index: ValidatorIndex) -> bool:
-    return get_beacon_proposer_index(state) == validator_index
+    return get_proposer_index(state) == validator_index
 ```
 
 *Note*: To see if a validator is assigned to propose during the slot, the beacon state must be in the epoch in question. At the epoch boundaries, the validator must run an epoch transition into the epoch to successfully check the proposal assignment of the first slot.
@@ -307,7 +307,7 @@ Set `attestation_data.beacon_block_root = signing_root(head_block)`.
 * Set `attestation_data.target_root = epoch_boundary_block_root` where `epoch_boundary_block_root` is the root of block at the most recent epoch boundary.
 
 *Note*: `epoch_boundary_block_root` can be looked up in the state using:
-* Let `start_slot = epoch_start_slot(get_current_epoch(head_state))`.
+* Let `start_slot = epoch_first_slot(get_current_epoch(head_state))`.
 * Let `epoch_boundary_block_root = signing_root(head_block) if start_slot == head_state.slot else get_block_root(state, start_slot)`.
 
 ##### Crosslink vote
diff --git a/test_libs/pyspec/eth2spec/test/helpers/attestations.py b/test_libs/pyspec/eth2spec/test/helpers/attestations.py
index 38635bafe..053446a2d 100644
--- a/test_libs/pyspec/eth2spec/test/helpers/attestations.py
+++ b/test_libs/pyspec/eth2spec/test/helpers/attestations.py
@@ -15,15 +15,15 @@ def build_attestation_data(spec, state, slot, shard):
     else:
         block_root = spec.get_block_root_at_slot(state, slot)
 
-    current_epoch_start_slot = spec.epoch_start_slot(spec.get_current_epoch(state))
-    if slot < current_epoch_start_slot:
+    current_epoch_first_slot = spec.epoch_first_slot(spec.get_current_epoch(state))
+    if slot < current_epoch_first_slot:
         epoch_boundary_root = spec.get_block_root(state, spec.get_previous_epoch(state))
-    elif slot == current_epoch_start_slot:
+    elif slot == current_epoch_first_slot:
         epoch_boundary_root = block_root
     else:
         epoch_boundary_root = spec.get_block_root(state, spec.get_current_epoch(state))
 
-    if slot < current_epoch_start_slot:
+    if slot < current_epoch_first_slot:
         source_epoch = state.previous_justified_checkpoint.epoch
         source_root = state.previous_justified_checkpoint.root
     else:
diff --git a/test_libs/pyspec/eth2spec/test/helpers/block.py b/test_libs/pyspec/eth2spec/test/helpers/block.py
index 16249fe93..324c5bbe7 100644
--- a/test_libs/pyspec/eth2spec/test/helpers/block.py
+++ b/test_libs/pyspec/eth2spec/test/helpers/block.py
@@ -12,7 +12,7 @@ def sign_block(spec, state, block, proposer_index=None):
 
     if proposer_index is None:
         if block.slot == state.slot:
-            proposer_index = spec.get_beacon_proposer_index(state)
+            proposer_index = spec.get_proposer_index(state)
         else:
             if spec.slot_to_epoch(state.slot) + 1 > spec.slot_to_epoch(block.slot):
                 print("warning: block slot far away, and no proposer index manually given."
@@ -20,7 +20,7 @@ def sign_block(spec, state, block, proposer_index=None):
             # use stub state to get proposer index of future slot
             stub_state = deepcopy(state)
             spec.process_slots(stub_state, block.slot)
-            proposer_index = spec.get_beacon_proposer_index(stub_state)
+            proposer_index = spec.get_proposer_index(stub_state)
 
     privkey = privkeys[proposer_index]
 
diff --git a/test_libs/pyspec/eth2spec/test/phase_0/block_processing/test_process_attester_slashing.py b/test_libs/pyspec/eth2spec/test/phase_0/block_processing/test_process_attester_slashing.py
index 7a6030157..7f539e3b9 100644
--- a/test_libs/pyspec/eth2spec/test/phase_0/block_processing/test_process_attester_slashing.py
+++ b/test_libs/pyspec/eth2spec/test/phase_0/block_processing/test_process_attester_slashing.py
@@ -30,7 +30,7 @@ def run_attester_slashing_processing(spec, state, attester_slashing, valid=True)
         + attester_slashing.attestation_1.custody_bit_1_indices
     )
 
-    proposer_index = spec.get_beacon_proposer_index(state)
+    proposer_index = spec.get_proposer_index(state)
     pre_proposer_balance = get_balance(state, proposer_index)
     pre_slashings = {slashed_index: get_balance(state, slashed_index) for slashed_index in slashed_indices}
     pre_withdrawalable_epochs = {
diff --git a/test_libs/pyspec/eth2spec/test/phase_0/block_processing/test_process_block_header.py b/test_libs/pyspec/eth2spec/test/phase_0/block_processing/test_process_block_header.py
index a2306ef4d..c348e57e1 100644
--- a/test_libs/pyspec/eth2spec/test/phase_0/block_processing/test_process_block_header.py
+++ b/test_libs/pyspec/eth2spec/test/phase_0/block_processing/test_process_block_header.py
@@ -75,7 +75,7 @@ def test_proposer_slashed(spec, state):
     # use stub state to get proposer index of next slot
     stub_state = deepcopy(state)
     next_slot(spec, stub_state)
-    proposer_index = spec.get_beacon_proposer_index(stub_state)
+    proposer_index = spec.get_proposer_index(stub_state)
 
     # set proposer to slashed
     state.validators[proposer_index].slashed = True
diff --git a/test_libs/pyspec/eth2spec/test/phase_0/block_processing/test_process_transfer.py b/test_libs/pyspec/eth2spec/test/phase_0/block_processing/test_process_transfer.py
index 6903f0666..5ea8cbacf 100644
--- a/test_libs/pyspec/eth2spec/test/phase_0/block_processing/test_process_transfer.py
+++ b/test_libs/pyspec/eth2spec/test/phase_0/block_processing/test_process_transfer.py
@@ -21,7 +21,7 @@ def run_transfer_processing(spec, state, transfer, valid=True):
         yield 'post', None
         return
 
-    proposer_index = spec.get_beacon_proposer_index(state)
+    proposer_index = spec.get_proposer_index(state)
     pre_transfer_sender_balance = state.balances[transfer.sender]
     pre_transfer_recipient_balance = state.balances[transfer.recipient]
     pre_transfer_proposer_balance = state.balances[proposer_index]
diff --git a/test_libs/pyspec/eth2spec/test/phase_0/epoch_processing/test_process_justification_and_finalization.py b/test_libs/pyspec/eth2spec/test/phase_0/epoch_processing/test_process_justification_and_finalization.py
index f59da1fc5..a308fe3d2 100644
--- a/test_libs/pyspec/eth2spec/test/phase_0/epoch_processing/test_process_justification_and_finalization.py
+++ b/test_libs/pyspec/eth2spec/test/phase_0/epoch_processing/test_process_justification_and_finalization.py
@@ -33,7 +33,7 @@ def add_mock_attestations(spec, state, epoch, source, target, sufficient_support
     total_balance = spec.get_total_active_balance(state)
     remaining_balance = total_balance * 2 // 3
 
-    start_slot = spec.epoch_start_slot(epoch)
+    start_slot = spec.epoch_first_slot(epoch)
     for slot in range(start_slot, start_slot + spec.SLOTS_PER_EPOCH):
         for shard in get_shards_for_slot(spec, state, slot):
             # Check if we already have had sufficient balance. (and undone if we don't want it).
@@ -80,7 +80,7 @@ def get_checkpoints(spec, epoch):
 
 def put_checkpoints_in_block_roots(spec, state, checkpoints):
     for c in checkpoints:
-        state.block_roots[spec.epoch_start_slot(c.epoch) % spec.SLOTS_PER_HISTORICAL_ROOT] = c.root
+        state.block_roots[spec.epoch_first_slot(c.epoch) % spec.SLOTS_PER_HISTORICAL_ROOT] = c.root
 
 
 def finalize_on_234(spec, state, epoch, sufficient_support):
diff --git a/test_libs/pyspec/eth2spec/test/sanity/test_blocks.py b/test_libs/pyspec/eth2spec/test/sanity/test_blocks.py
index b2eb19244..086d141a5 100644
--- a/test_libs/pyspec/eth2spec/test/sanity/test_blocks.py
+++ b/test_libs/pyspec/eth2spec/test/sanity/test_blocks.py
@@ -214,7 +214,7 @@ def test_attester_slashing(spec, state):
     # lost whistleblower reward
     assert get_balance(state, validator_index) < get_balance(pre_state, validator_index)
 
-    proposer_index = spec.get_beacon_proposer_index(state)
+    proposer_index = spec.get_proposer_index(state)
     # gained whistleblower reward
     assert (
         get_balance(state, proposer_index) >
diff --git a/test_libs/pyspec/eth2spec/test/test_finality.py b/test_libs/pyspec/eth2spec/test/test_finality.py
index 5ff0ed1ef..d572b05fb 100644
--- a/test_libs/pyspec/eth2spec/test/test_finality.py
+++ b/test_libs/pyspec/eth2spec/test/test_finality.py
@@ -43,7 +43,7 @@ def next_epoch_with_attestations(spec,
         block = build_empty_block_for_next_slot(spec, post_state)
         if fill_cur_epoch and post_state.slot >= spec.MIN_ATTESTATION_INCLUSION_DELAY:
             slot_to_attest = post_state.slot - spec.MIN_ATTESTATION_INCLUSION_DELAY + 1
-            if slot_to_attest >= spec.epoch_start_slot(spec.get_current_epoch(post_state)):
+            if slot_to_attest >= spec.epoch_first_slot(spec.get_current_epoch(post_state)):
                 cur_attestation = get_valid_attestation(spec, post_state, slot_to_attest)
                 block.body.attestations.append(cur_attestation)