diff --git a/specs/das/das-core.md b/specs/das/das-core.md
index ee73a6150..ce39565a1 100644
--- a/specs/das/das-core.md
+++ b/specs/das/das-core.md
@@ -12,7 +12,7 @@
 - [Configuration](#configuration)
   - [Misc](#misc)
 - [New containers](#new-containers)
-  - [DASSample](#dassample)
+  - [`DASSample`](#dassample)
 - [Helper functions](#helper-functions)
   - [Reverse bit ordering](#reverse-bit-ordering)
     - [`reverse_bit_order`](#reverse_bit_order)
@@ -45,7 +45,7 @@ We define the following Python custom types for type hinting and readability:
 
 ## New containers
 
-### DASSample
+### `DASSample`
 
 ```python
 class DASSample(Container):
diff --git a/specs/sharding/beacon-chain.md b/specs/sharding/beacon-chain.md
index 673cd7744..c0dab3ad9 100644
--- a/specs/sharding/beacon-chain.md
+++ b/specs/sharding/beacon-chain.md
@@ -70,7 +70,7 @@ We define the following Python custom types for type hinting and readability:
 | Name | SSZ equivalent | Description |
 | - | - | - |
 | `Shard` | `uint64` | A shard number |
-| `BLSCommitment` | `bytes48` | A G1 curve point |
+| `BLSCommitment` | `Bytes48` | A G1 curve point |
 | `BLSPoint` | `uint256` | A number `x` in the range `0 <= x < MODULUS` |
 
 ## Constants
@@ -108,7 +108,7 @@ The following values are (non-configurable) constants used throughout the specif
 | - | - |
 | `G1_SETUP` | Type `List[G1]`. The G1-side trusted setup `[G, G*s, G*s**2....]`; note that the first point is the generator. |
 | `G2_SETUP` | Type `List[G2]`. The G2-side trusted setup `[G, G*s, G*s**2....]` |
-| `ROOT_OF_UNITY` | `pow(PRIMITIVE_ROOT_OF_UNITY, (MODULUS - 1) // (MAX_SAMPLES_PER_BLOCK * POINTS_PER_SAMPLE, MODULUS)` |
+| `ROOT_OF_UNITY` | `pow(PRIMITIVE_ROOT_OF_UNITY, (MODULUS - 1) // (MAX_SAMPLES_PER_BLOCK * POINTS_PER_SAMPLE), MODULUS)` |
 
 ### Gwei values
 
@@ -223,7 +223,7 @@ class PendingShardHeader(Container):
     # Who voted for the header
     votes: Bitlist[MAX_VALIDATORS_PER_COMMITTEE]
     # Has this header been confirmed?
-    confirmed: bool
+    confirmed: boolean
 ```
 
 ## Helper functions
@@ -514,7 +514,7 @@ def process_shard_header(state: BeaconState,
         assert header.degree_proof == G1_SETUP[0]
     assert (
         bls.Pairing(header.degree_proof, G2_SETUP[0])
-        == bls.Pairing(header.commitment.point, G2_SETUP[-header.commitment.length]))
+        == bls.Pairing(header.commitment.point, G2_SETUP[-header.commitment.length])
     )
 
     # Get the correct pending header list
@@ -618,7 +618,7 @@ def process_pending_headers(state: BeaconState) -> None:
     for slot_index in range(SLOTS_PER_EPOCH):
         for shard in range(SHARD_COUNT):
             state.grandparent_epoch_confirmed_commitments[shard][slot_index] = DataCommitment()
-    confirmed_headers = [candidate in state.previous_epoch_pending_shard_headers if candidate.confirmed]
+    confirmed_headers = [candidate for candidate in state.previous_epoch_pending_shard_headers if candidate.confirmed]
     for header in confirmed_headers:
         state.grandparent_epoch_confirmed_commitments[c.shard][c.slot % SLOTS_PER_EPOCH] = c.commitment
 ```
@@ -666,7 +666,7 @@ def reset_pending_headers(state: BeaconState) -> None:
     next_epoch = get_current_epoch(state) + 1
     next_epoch_start_slot = compute_start_slot_at_epoch(next_epoch)
     for slot in range(next_epoch_start_slot, next_epoch_start_slot + SLOTS_IN_EPOCH):
-        for index in range(get_committee_count_per_slot(next_epoch):
+        for index in range(get_committee_count_per_slot(next_epoch)):
             shard = compute_shard_from_committee_index(state, slot, index)
             committee_length = len(get_beacon_committee(state, slot, shard))
             state.current_epoch_pending_shard_headers.append(PendingShardHeader(