diff --git a/specs/core/0_beacon-chain.md b/specs/core/0_beacon-chain.md
index fa95dc871..3ee0a1646 100644
--- a/specs/core/0_beacon-chain.md
+++ b/specs/core/0_beacon-chain.md
@@ -43,7 +43,6 @@ The primary source of load on the beacon chain are "attestations". Attestations
 | `MIN_VALIDATOR_SET_CHANGE_INTERVAL` | 2**8 (= 256) | slots | ~25 minutes |
 | `SHARD_PERSISTENT_COMMITTEE_CHANGE_PERIOD` | 2**17 (= 131,072) | slots | ~9 days |
 | `MIN_ATTESTATION_INCLUSION_DELAY` | 2**2 (= 4) | slots | ~24 seconds |
-| `RANDAO_SLOTS_PER_LAYER` | 2**12 (= 4,096) | slots | ~7 hours |
 | `SQRT_E_DROP_TIME` | 2**18 (= 262,144) | slots | ~18 days |
 | `WITHDRAWALS_PER_CYCLE` | 2**2 (=4) | validators | 5.2m ETH in ~6 months |
 | `MIN_WITHDRAWAL_PERIOD` | 2**13 (= 8,192) | slots | ~14 hours |
@@ -54,6 +53,8 @@ The primary source of load on the beacon chain are "attestations". Attestations
 | `BASE_REWARD_QUOTIENT` | 2**15 (= 32,768) | — |
 | `MAX_VALIDATOR_CHURN_QUOTIENT` | 2**5 (= 32) | — |
 | `POW_CONTRACT_MERKLE_TREE_DEPTH` | 2**5 (= 32) | - |
+| `MAX_ATTESTATION_COUNT` | 2**7 (= 128) | - |
+| `LOGOUT_MESSAGE` | `"LOGOUT"` | — |
 | `INITIAL_FORK_VERSION` | 0 | — |
 
 **Notes**
@@ -266,8 +267,8 @@ A `ValidatorRecord` has the following fields:
     'withdrawal_credentials': 'hash32',
     # RANDAO commitment
     'randao_commitment': 'hash32',
-    # Slot the RANDAO commitment was last changed
-    'randao_last_change': 'uint64',
+    # Slot the proposer has skipped (ie. layers of RANDAO expected)
+    'randao_skips': 'uint64',
     # Balance in Gwei
     'balance': 'uint64',
     # Status code
@@ -581,6 +582,9 @@ def int_sqrt(n: int) -> int:
 The beacon chain is initialized when a condition is met inside a contract on the existing PoW chain. This contract's code in Vyper is as follows:
 
 ```python
+SECONDS_PER_DAY: constant(uint256) = 86400
+POW_CONTRACT_MERKLE_TREE_DEPTH: constant(int128) = 32
+
 HashChainValue: event({previous_receipt_root: bytes32, data: bytes[2064], total_deposit_count: int128})
 ChainStart: event({receipt_root: bytes32, time: bytes[8]})
 
@@ -591,19 +595,21 @@ total_deposit_count: int128
 @public
 def deposit(deposit_params: bytes[2048]):
     index:int128 = self.total_deposit_count + 2**POW_CONTRACT_MERKLE_TREE_DEPTH
-    msg_gwei_bytes8: bytes[8] = slice(convert(msg.value / 10**9, 'bytes32'), 24, 8)
-    timestamp_bytes8: bytes[8] = slice(convert(block.timestamp, 'bytes32'), 24, 8)
+    msg_gwei_bytes8: bytes[8] = slice(concat("", convert(msg.value / 10**9, bytes32)), start=24, len=8)
+    timestamp_bytes8: bytes[8] = slice(concat("", convert(block.timestamp, bytes32)), start=24, len=8)
     deposit_data: bytes[2064] = concat(deposit_params, msg_gwei_bytes8, timestamp_bytes8)
 
     log.HashChainValue(self.receipt_tree[1], deposit_data, self.total_deposit_count)    
 
     self.receipt_tree[index] = sha3(deposit_data)
     for i in range(POW_CONTRACT_MERKLE_TREE_DEPTH):
-        index //= 2
+        index /= 2
         self.receipt_tree[index] = sha3(concat(self.receipt_tree[index * 2], self.receipt_tree[index * 2 + 1]))
     self.total_deposit_count += 1
     if self.total_deposit_count == 16384:
-        log.ChainStart(self.receipt_tree[1], timestamp_bytes8)
+        timestamp_day_boundary: uint256 = as_unitless_number(block.timestamp) - as_unitless_number(block.timestamp) % SECONDS_PER_DAY + SECONDS_PER_DAY
+        timestamp_day_boundary_bytes8: bytes[8] = slice(concat("", convert(timestamp_day_boundary, bytes32)), start=24, len=8)
+        log.ChainStart(self.receipt_tree[1], timestamp_day_boundary_bytes8)
 
 @public
 @constant
@@ -748,7 +754,7 @@ def add_validator(state: State,
         pubkey=pubkey,
         withdrawal_credentials=withdrawal_credentials,
         randao_commitment=randao_commitment,
-        randao_last_change=current_slot,
+        randao_skips=0,
         balance=DEPOSIT_SIZE * GWEI_PER_ETH,
         status=status,
         last_status_change_slot=current_slot,
@@ -817,7 +823,7 @@ def update_ancestor_hashes(parent_ancestor_hashes: List[Hash32],
 
 ### Verify attestations
 
-For each `AttestationRecord` object:
+Verify that there are at most `MAX_ATTESTATION_COUNT` `AttestationRecord` objects. For each `AttestationRecord` object:
 
 * Verify that `slot <= block.slot - MIN_ATTESTATION_INCLUSION_DELAY` and `slot >= max(parent.slot - CYCLE_LENGTH + 1, 0)`.
 * Verify that `justified_slot` is equal to or earlier than `last_justified_slot`.
@@ -841,10 +847,20 @@ Verify that `BLSVerify(pubkey=get_beacon_proposer(state, block.slot).pubkey, dat
 
 ### Verify and process RANDAO reveal
 
+First run the following state transition to update `randao_skips` variables for the missing slots.
+
+```python
+for slot in range(parent.slot + 1, block.slot):
+    proposer = get_beacon_proposer(state, slot)
+    proposer.randao_skips += 1
+```
+
+Then:
+
 * Let `repeat_hash(x, n) = x if n == 0 else repeat_hash(hash(x), n-1)`.
 * Let `V = get_beacon_proposer(state, block.slot)`.
-* Verify that `repeat_hash(block.randao_reveal, (block.slot - V.randao_last_change) // RANDAO_SLOTS_PER_LAYER + 1) == V.randao_commitment`
-* Set `state.randao_mix = xor(state.randao_mix, block.randao_reveal)`, `V.randao_commitment = block.randao_reveal`, `V.randao_last_change = block.slot`
+* Verify that `repeat_hash(block.randao_reveal, V.randao_skips + 1) == V.randao_commitment`
+* Set `state.randao_mix = xor(state.randao_mix, block.randao_reveal)`, `V.randao_commitment = block.randao_reveal`, `V.randao_skips = 0`
 
 ### Process PoW receipt root