diff --git a/specs/beacon-chain.md b/specs/beacon-chain.md
index cc4e0b57a..676ea0600 100644
--- a/specs/beacon-chain.md
+++ b/specs/beacon-chain.md
@@ -147,7 +147,7 @@ An `AttestationSignedData` has the following fields:
     'slot': 'uint64',
     # Shard number
     'shard': 'uint16',
-    # 31 parent hashes
+    # CYCLE_LENGTH parent hashes
     'parent_hashes': ['hash32'],
     # Shard block hash
     'shard_block_hash': 'hash32',
@@ -498,7 +498,8 @@ def on_startup(initial_validator_entries: List[Any]) -> Tuple[CrystallizedState,
             withdrawal_shard=withdrawal_shard,
             withdrawal_address=withdrawal_address,
             randao_commitment=randao_commitment,
-            current_slot=0
+            current_slot=0,
+            status=ACTIVE,
         )
     # Setup crystallized state
     x = get_new_shuffling(bytes([0] * 32), validators, 0)
@@ -545,7 +546,19 @@ The `CrystallizedState()` and `ActiveState()` constructors should initialize all
 
 ### Routine for adding a validator
 
-This routine should be run for every validator that is inducted as part of a log created on the PoW chain [TODO: explain where to check for these logs]. These logs should be processed in the order in which they are emitted by the PoW chain. Define `min_empty_validator(validators)` as a function that returns the lowest validator index `i` such that `validators[i].status == WITHDRAWN`, otherwise `None`.
+This routine should be run for every validator that is inducted as part of a log created on the PoW chain [TODO: explain where to check for these logs]. The status of the validators added after genesis is `PENDING_ACTIVATION`. These logs should be processed in the order in which they are emitted by the PoW chain.
+
+First, a helper function:
+
+```python
+def min_empty_validator(validators: List[ValidatorRecord]):
+    for i, v in enumerate(validators):
+        if v.status == WITHDRAWN:
+            return i
+    return None
+```
+
+Now, to add a validator:
 
 ```python
 def add_validator(validators: List[ValidatorRecord],
@@ -554,6 +567,7 @@ def add_validator(validators: List[ValidatorRecord],
                   withdrawal_shard: int,
                   withdrawal_address: Address,
                   randao_commitment: Hash32,
+                  status: int,
                   current_slot: int) -> int:
     # if following assert fails, validator induction failed
     # move on to next validator registration log
@@ -566,8 +580,8 @@ def add_validator(validators: List[ValidatorRecord],
         withdrawal_address=withdrawal_address,
         randao_commitment=randao_commitment,
         randao_last_change=current_slot,
-        balance=DEPOSIT_SIZE * GWEI_PER_ETH,
-        status=PENDING_ACTIVATION,
+        balance=DEPOSIT_SIZE * GWEI_PER_ETH, # in Gwei
+        status=status,
         exit_slot=0
     )
     index = min_empty_validator(validators)
@@ -665,7 +679,7 @@ For every `(shard, shard_block_hash)` tuple:
 
 * Let `total_balance_attesting_to_h` be the total balance of validators that attested to the shard block with hash `shard_block_hash`.
 * Let `total_committee_balance` be the total balance in the committee of validators that could have attested to the shard block with hash `shard_block_hash`.
-* If `3 * total_balance_attesting_to_h >= 2 * total_committee_balance` and `recently_changed is False`, set `crosslinks[shard] = CrosslinkRecord(recently_changed=True, slot=block.last_state_recalculation_slot + CYCLE_LENGTH, hash=shard_block_hash)`.
+* If `3 * total_balance_attesting_to_h >= 2 * total_committee_balance` and `recently_changed is False`, set `crosslinks[shard] = CrosslinkRecord(recently_changed=True, slot=last_state_recalculation_slot + CYCLE_LENGTH, hash=shard_block_hash)`.
 
 #### Balance recalculations related to FFG rewards
 
diff --git a/specs/simple-serialize.md b/specs/simple-serialize.md
index be58a68dd..f508e8298 100644
--- a/specs/simple-serialize.md
+++ b/specs/simple-serialize.md
@@ -186,6 +186,8 @@ return byte_length + value
 
 #### List/Vectors
 
+Lists are a collection of elements of the same homogeneous type.
+
 | Check to perform                            | Code                        |
 |:--------------------------------------------|:----------------------------|
 | Length of serialized list fits into 4 bytes | ``len(serialized) < 2**32`` |
@@ -327,7 +329,7 @@ return rawbytes[bytes_start:bytes_end], new_index
 
 #### List/Vectors
 
-Deserialize each object in the list.
+Deserialize each element in the list.
 1. Get the length of the serialized list.
 2. Loop through deserializing each item in the list until you reach the
 entire length of the list.