Apply suggestions from Danny's code review

Co-authored-by: Danny Ryan <dannyjryan@gmail.com>

specs/phase0/weak-subjectivity.md

@@ -3,6 +3,7 @@
 **Notice**: This document is a work-in-progress for researchers and implementers.
 
 ## Table of contents
+
 <!-- TOC -->
 <!-- START doctoc generated TOC please keep comment here to allow auto update -->
 <!-- DON'T EDIT THIS SECTION, INSTEAD RE-RUN doctoc TO UPDATE -->
@@ -28,7 +29,7 @@ This document is a guide for implementing the Weak Subjectivity protections in P
 - [Proof of Stake: How I Learned to Love Weak Subjectivity](https://blog.ethereum.org/2014/11/25/proof-stake-learned-love-weak-subjectivity/)
 
 ## Prerequisites
-This document uses data structures, constants, functions, and terminology from [Phase 0 -- The Beacon Chain](https://github.com/ethereum/eth2.0-specs/blob/dev/specs/phase0/beacon-chain.md) and [Phase 0 -- Beacon Chain Fork Choice](https://github.com/ethereum/eth2.0-specs/blob/dev/specs/phase0/fork-choice.md).
+This document uses data structures, constants, functions, and terminology from [Phase 0 -- The Beacon Chain](./beacon-chain.md) and [Phase 0 -- Beacon Chain Fork Choice](./fork-choice.md).
 
 ## Constants
 | Name           | Value        |
@@ -40,20 +41,23 @@ This document uses data structures, constants, functions, and terminology from [
 Any `Checkpoint` can used be a Weak Subjectivity Checkpoint. These Weak Subjectivity Checkpoints are distributed by providers, downloaded by users and/or distributed as a part of clients, and used as input while syncing a client.
 
 ## Weak Subjectivity Period
-The Weak Subjectivity Period is the number of recent epochs within which there must be a Weak Subjectivity Checkpoint so that an attacker who takes control of the validator set at the beginning of the period is slashed at least a threshold amount in case a conflicting `Checkpoint` is finalized. `SAFETY_DECAY` is defined as the maximum percentage tolerable loss in the 1/3rd safety margin of FFG finality, which makes our threshold amount of slashing to be 1/3 - `SAFETY_DECAY/100`.
+The Weak Subjectivity Period is the number of recent epochs within which there must be a Weak Subjectivity Checkpoint to ensure that an attacker who takes control of the validator set at the beginning of the period is slashed at least a minimum threshold in the event that a conflicting `Checkpoint` is finalized.
+
+`SAFETY_DECAY` is defined as the maximum percentage tolerable loss in the one-third safety margin of FFG finality. Thus, any attack exploiting the Weak Subjectivity Period has a safety margin of at least `1/3 - SAFETY_DECAY/100`.
 
 ### Calculating the Weak Subjectivity Period
 For more information about this calculation, refer to [Weak Subjectivity in Eth2.0](https://notes.ethereum.org/@adiasg/weak-subjectvity-eth2).
 
-Note: `compute_weak_subjectivity_period()` is planned to be updated when a more accurate calculation is made.
+*Note*: `compute_weak_subjectivity_period()` is planned to be updated when a more accurate calculation is made.
+
 ```python
-  def compute_weak_subjectivity_period(state):
+  def compute_weak_subjectivity_period(state: BeaconState) -> uint64:
     weak_subjectivity_period = MIN_VALIDATOR_WITHDRAWABILITY_DELAY
-    val_count = len(get_active_validator_indices(state, get_current_epoch(state)))
+    validator_count = len(get_active_validator_indices(state, get_current_epoch(state)))
     if val_count >= MIN_PER_EPOCH_CHURN_LIMIT * CHURN_LIMIT_QUOTIENT:
-        weak_subjectivity_period += SAFETY_DECAY*CHURN_LIMIT_QUOTIENT/(2*100)
+        weak_subjectivity_period += SAFETY_DECAY * CHURN_LIMIT_QUOTIENT / (2 * 100)
     else:
-        weak_subjectivity_period += SAFETY_DECAY*val_count/(2*100*MIN_PER_EPOCH_CHURN_LIMIT)
+        weak_subjectivity_period += SAFETY_DECAY * val_count / (2 * 100 * MIN_PER_EPOCH_CHURN_LIMIT)
     return weak_subjectivity_period
 ```
 
@@ -73,10 +77,10 @@ A brief reference for what these values look like in practice:
 | 524288  | 3532 |
 
 ## Weak Subjectivity Sync
-Clients should allow users to input a Weak Subjectivity Checkpoint at startup, and guarantee that any successful sync leads to the given Weak Subjectivity Checkpoint being in the canonical chain. If such a sync is not possible, the client should treat this as a critical and irrecoverable failure.
+Clients should allow users to input a Weak Subjectivity Checkpoint at startup, and guarantee that any successful sync leads to the given Weak Subjectivity Checkpoint along the canonical chain. If such a sync is not possible, the client should treat this as a critical and irrecoverable failure.
 
 ### Weak Subjectivity Sync Procedure
-1. Take a Weak Subjectivity Checkpoint as a CLI parameter input in `block_root:epoch_number` format, where `block_root` and `epoch_number` represent a valid `Checkpoint`. Example of the format:
+1. Input a Weak Subjectivity Checkpoint as a CLI parameter in `block_root:epoch_number` format, where `block_root` (an "0x" prefixed 32-byte hex string) and `epoch_number` (an integer) represent a valid `Checkpoint`. Example of the format:
 ```
 0x8584188b86a9296932785cc2827b925f9deebacce6d72ad8d53171fa046b43d9:9544
 ```
@@ -86,7 +90,7 @@ Clients should allow users to input a Weak Subjectivity Checkpoint at startup, a
 ### Checking for Stale Weak Subjectivity Checkpoint
 Clients may choose to validate that the input Weak Subjectivity Checkpoint is not stale at the time of startup. To support this mechanism, the client needs to take the state at the Weak Subjectivity Checkpoint as a CLI parameter input (or fetch the state associated with the input Weak Subjectivity Checkpoint from some source). The check can be implemented in the following way:
 ```python
-  def is_within_weak_subjectivity_period(store, ws_state, ws_checkpoint):
+  def is_within_weak_subjectivity_period(store: Store, ws_state: BeaconState, ws_checkpoint: Checkpoint) -> bool:
     # Clients may choose to validate the input state against the input Weak Subjectivity Checkpoint
     assert ws_state.latest_block_header.state_root == ws_checkpoint.root
     assert compute_epoch_at_slot(ws_state.slot) == ws_checkpoint.epoch