Cosmetic genesis cleanups

specs/core/0_beacon-chain.md

@@ -93,7 +93,10 @@
         - [Routines for updating validator status](#routines-for-updating-validator-status)
             - [`initiate_validator_exit`](#initiate_validator_exit)
             - [`slash_validator`](#slash_validator)
-    - [On genesis](#on-genesis)
+    - [Genesis](#genesis)
+        - [`Eth2Genesis`](#eth2genesis)
+        - [Genesis state](#genesis-state)
+        - [Genesis block](#genesis-block)
     - [Beacon chain state transition function](#beacon-chain-state-transition-function)
         - [State caching](#state-caching)
         - [Per-epoch processing](#per-epoch-processing)
@@ -1171,30 +1174,29 @@ def slash_validator(state: BeaconState, slashed_index: ValidatorIndex, whistlebl
     decrease_balance(state, slashed_index, whistleblowing_reward)
 ```
 
-## On genesis
+## Genesis
 
-When enough full deposits have been made to the deposit contract, an `Eth2Genesis` log is emitted. Construct a corresponding `genesis_state` and `genesis_block` as follows:
+### `Eth2Genesis`
 
-* Let `genesis_validator_deposits` be the list of deposits, ordered chronologically, up to and including the deposit that triggered the `Eth2Genesis` log.
-* Let `genesis_time` be the timestamp specified in the `Eth2Genesis` log.
-* Let `genesis_eth1_data` be the `Eth1Data` object where:
-    * `genesis_eth1_data.deposit_root` is the `deposit_root` contained in the `Eth2Genesis` log.
-    * `genesis_eth1_data.deposit_count` is the `deposit_count` contained in the `Eth2Genesis` log.
-    * `genesis_eth1_data.block_hash` is the hash of the Ethereum 1.0 block that emitted the `Eth2Genesis` log.
-* Let `genesis_state = get_genesis_beacon_state(genesis_validator_deposits, genesis_time, genesis_eth1_data)`.
-* Let `genesis_block = BeaconBlock(state_root=hash_tree_root(genesis_state))`.
+When enough deposits of size `MAX_EFFECTIVE_BALANCE` have been made to the deposit contract an `Eth2Genesis` log is emitted triggering the genesis of the beacon chain. Let:
+
+* `eth2genesis` be the object corresponding to `Eth2Genesis`
+* `genesis_eth1_data` be object of type `Eth1Data` where
+    * `genesis_eth1_data.deposit_root = eth2genesis.deposit_root`
+    * `genesis_eth1_data.deposit_count = eth2genesis.deposit_count`
+    * `genesis_eth1_data.block_hash` is the hash of the Ethereum 1.0 block that emitted the `Eth2Genesis` log
+* `genesis_deposits` be the object of type `List[Deposit]` with deposits ordered chronologically up to and including the deposit that triggered the `Eth2Genesis` log
+
+### Genesis state
+
+Let `genesis_state = get_genesis_beacon_state(eth2genesis.genesis_time, genesis_eth1_data, genesis_deposits)`.
 
 ```python
-def get_genesis_beacon_state(genesis_validator_deposits: List[Deposit],
-                             genesis_time: int,
-                             genesis_eth1_data: Eth1Data) -> BeaconState:
-    """
-    Get the genesis ``BeaconState``.
-    """
+def get_genesis_beacon_state(genesis_time: int, eth1_data: Eth1Data, deposits: List[Deposit]) -> BeaconState:
     state = BeaconState(genesis_time=genesis_time, latest_eth1_data=genesis_eth1_data)
 
     # Process genesis deposits
-    for deposit in genesis_validator_deposits:
+    for deposit in deposits:
         process_deposit(state, deposit)
 
     # Process genesis activations
@@ -1203,6 +1205,7 @@ def get_genesis_beacon_state(genesis_validator_deposits: List[Deposit],
             validator.activation_eligibility_epoch = GENESIS_EPOCH
             validator.activation_epoch = GENESIS_EPOCH
 
+    # Populate latest_active_index_roots
     genesis_active_index_root = hash_tree_root(get_active_validator_indices(state, GENESIS_EPOCH))
     for index in range(LATEST_ACTIVE_INDEX_ROOTS_LENGTH):
         state.latest_active_index_roots[index] = genesis_active_index_root
@@ -1210,6 +1213,10 @@ def get_genesis_beacon_state(genesis_validator_deposits: List[Deposit],
     return state
 ```
 
+### Genesis block
+
+Let `genesis_block = BeaconBlock(state_root=hash_tree_root(genesis_state))`.
+
 ## Beacon chain state transition function
 
 We now define the state transition function. At a high level, the state transition is made up of four parts: