diff --git a/specs/core/0_beacon-chain.md b/specs/core/0_beacon-chain.md
index c286891fb..1957f1be6 100644
--- a/specs/core/0_beacon-chain.md
+++ b/specs/core/0_beacon-chain.md
@@ -872,12 +872,12 @@ def get_beacon_proposer_index(state: BeaconState,
 #### `get_updated_ancestor_hashes`
 
 ```python
-def get_updated_ancestor_hashes(parent: BeaconBlock,
-                                parent_hash: Hash32) -> List[Hash32]:
-    new_ancestor_hashes = copy.deepcopy(parent.ancestor_hashes)
+def get_updated_ancestor_hashes(latest_block: BeaconBlock,
+                                latest_hash: Hash32) -> List[Hash32]:
+    new_ancestor_hashes = copy.deepcopy(latest_block.ancestor_hashes)
     for i in range(32):
-        if parent.slot % 2**i == 0:
-            new_ancestor_hashes[i] = parent_hash
+        if latest_block.slot % 2**i == 0:
+            new_ancestor_hashes[i] = latest_hash
     return new_ancestor_hashes
 ```
 
@@ -1205,31 +1205,28 @@ def exit_validator(index: int,
 
 Below are the processing steps that happen at every slot.
 
-* Let `parent_hash` be the hash of the latest beacon block that was processed in the chain.
-* Let `parent` be the `BeaconBlock` with the hash `parent_hash`.
+* Let `latest_hash` be the hash of the latest beacon block that was processed in the chain.
+* Let `latest_block` be the `BeaconBlock` with the hash `latest_hash`.
 * Set `state.slot += 1`
-* Set `state.latest_block_hashes = state.latest_block_hashes + [parent_hash]`. (The output of `get_block_hash` should not change, except that it will no longer throw for `state.slot - 1`).
+* Set `state.latest_block_hashes = state.latest_block_hashes + [latest_hash]`. (The output of `get_block_hash` should not change, except that it will no longer throw for `state.slot - 1`).
 
 If there is a block from the proposer for `state.slot`, we process that incoming block:
-* Let `slot_has_block = True`
 * Let `block` be that associated incoming block.
-* Verify that `block.ancestor_hashes` equals `get_updated_ancestor_hashes(parent, parent_hash)`.
+* Verify that `block.slot == state.slot`
+* Verify that `block.ancestor_hashes` equals `get_updated_ancestor_hashes(latest_block, latest_hash)`.
 
 If there is not a block from the proposer for `state.slot`, the slot is processed without a block:
-* Let `slot_has_block = False`
+* Let `state.validator_registry[get_beacon_proposer_index(state, state.slot)].randao_skips += 1`.
+* Skip all other per-slot processing. Move directly to [per-epoch processing](#per-epoch-processing).
 
 ### Proposer signature
 
-If `slot_has_block`:
-
 * Let `block_hash_without_sig` be the hash of `block` where `proposer_signature` is set to `[0, 0]`.
 * Let `proposal_hash = hash(ProposalSignedData(state.slot, BEACON_CHAIN_SHARD_NUMBER, block_hash_without_sig))`.
 * Verify that `BLSVerify(pubkey=state.validator_registry[get_beacon_proposer_index(state, state.slot)].pubkey, data=proposal_hash, sig=block.proposer_signature, domain=get_domain(state.fork_data, state.slot, DOMAIN_PROPOSAL))`.
 
 ### Attestations
 
-*If not `slot_has_block`, do not process attestations. Move to next section.*
-
 * Verify that `len(block.attestations) <= MAX_ATTESTATIONS_PER_BLOCK`.
 
 For each `attestation` in `block.attestations`:
@@ -1248,8 +1245,6 @@ For each `attestation` in `block.attestations`:
 
 ### RANDAO
 
-If `slot_has_block`:
-
 * Let `repeat_hash(x, n) = x if n == 0 else repeat_hash(hash(x), n-1)`.
 * Let `proposer = state.validator_registry[get_beacon_proposer_index(state, state.slot)]`.
 * Verify that `repeat_hash(block.randao_reveal, proposer.randao_skips + 1) == proposer.randao_commitment`.
@@ -1257,23 +1252,13 @@ If `slot_has_block`:
 * Set `proposer.randao_commitment = block.randao_reveal`.
 * Set `proposer.randao_skips = 0`.
 
-
-If not `slot_has_block`:
-
-* Let `state.validator_registry[get_beacon_proposer_index(state, state.slot)].randao_skips += 1`.
-
 ### PoW receipt root
 
-*If not `slot_has_block`, do not process PoW receipt root. Move to next section.*
-
-
 * If `block.candidate_pow_receipt_root` is `x.candidate_pow_receipt_root` for some `x` in `state.candidate_pow_receipt_roots`, set `x.votes += 1`.
 * Otherwise, append to `state.candidate_pow_receipt_roots` a new `CandidatePoWReceiptRootRecord(candidate_pow_receipt_root=block.candidate_pow_receipt_root, votes=1)`.
 
 ### Special objects
 
-*If not `slot_has_block`, do not process special objects. Move to next section.*
-
 * Verify that the quantity of each type of object in `block.specials` is less than or equal to its maximum (see table at the top).
 * Verify that objects are sorted in order of `kind`. That is, `block.specials[i+1].kind >= block.specials[i].kind` for `0 <= i < len(block.specials-1)`.
 
@@ -1607,9 +1592,8 @@ while len(state.persistent_committee_reassignments) > 0 and state.persistent_com
 
 ## State root processing
 
-*If not `slot_has_block`, do not process state root. Move to next section.*
-
-Verify `block.state_root == hash(state)`
+If there exists a `block` for the slot being processed:
+* Verify `block.state_root == hash(state)`
 
 # Appendix
 ## Appendix A - Hash function