docs: shares upon delegation

docs/core/accounting/SharesAccounting.md

@@ -162,6 +162,67 @@ See implementation in:
 * [`StrategyManager.depositIntoStrategy`](../../../src/contracts/core/StrategyManager.sol)
 * [`EigenPodManager.recordBeaconChainETHBalanceUpdate`](../../../src/contracts/pods/EigenPodManager.sol)
 
+
+---
+
+### Delegation
+
+Suppose we have an undelegated staker who decides to delegate to an operator.
+We have the following properties that should be preserved.
+
+#### Operator Level
+
+Operator shares should be increased by the amount of delegatable shares the staker has, this is synonymous to their withdrawable shares $a_n$. Therefore,
+
+$$
+op_{n+1} = op_{n} + a_n
+$$
+
+$$
+= op_{n} + s_n k_n l_n m_n
+$$
+
+
+#### Staker Level
+
+withdrawable shares should remain unchanged
+
+$$
+a_{n+1} = a_n
+$$
+
+deposit shares should remain unchanged
+
+$$
+s_{n+1} = s_n
+$$
+
+beaconChainSlashingFactor and maxMagnitude should also remain unchanged. In this case, since the staker is not delegated, then their maxMagnitude should by default be equal to 1.
+
+$$
+l_{n+1} = l_n
+$$
+
+Now the question is what is the new depositScalingFactor equal to?
+
+$$
+a_{n+1} = a_n
+$$
+
+$$
+=> s_{n+1} k_{n+1} l_{n+1} m_{n+1} = s_n k_n l_n m_n
+$$
+
+$$
+=> s_{n} k_{n+1} l_{n} m_{n+1} = s_n k_n l_n m_n
+$$
+
+$$
+=> k_{n+1} = \frac {k_n m_n} { m_{n+1} }
+$$
+
+Notice how the staker variables that update $k_{n+1}$ and $m_{n+1}$ do not affect previously queued withdrawals and shares received upon withdrawal completion. This is because the maxMagnitude that is looked up is dependent on the operator at the time of the queued withdrawal and the $k_n$ is effectively stored in the scaled shares field.
+
 ---
 
 ### Slashing