papers/lux-validator-economics/sections/10-validator-lifecycle-management.tex

\section{Validator Lifecycle Management}
\label{sec:lifecycle}

\subsection{Registration and Activation}

\begin{algorithm}[H]
\caption{Validator Registration}
\label{alg:registration}
\begin{algorithmic}[1]
\Procedure{RegisterValidator}{operator, selfStake, blsKey, commission}
    \State \textbf{require} $\mathsf{selfStake} \geq s^{\min}_{\text{val}} = 2{,}000$ LUX
    \State \textbf{require} $\mathsf{commission} \in [c^{\min}, c^{\max}]$
    \State \textbf{require} BLS proof-of-possession for $\mathsf{blsKey}$
    \State Lock $\mathsf{selfStake}$ in staking contract
    \State $\mathsf{activationEpoch} \gets e_{\text{current}} + 1$
    \State Add to pending validator queue
\EndProcedure
\end{algorithmic}
\end{algorithm}

\subsection{Commission Rate Changes}

Validators may adjust their commission rate with restrictions:

\begin{definition}[Commission Change Rules]
\begin{enumerate}
    \item Maximum increase: 2 percentage points per epoch.
    \item No decrease restriction (can lower freely).
    \item Change takes effect after a 1-epoch notice period.
    \item Delegators are notified and can redelegate during the notice period.
\end{enumerate}
\end{definition}

This prevents validators from attracting delegators with low commissions and then suddenly raising rates.

\subsection{Voluntary Exit}

\begin{algorithm}[H]
\caption{Voluntary Validator Exit}
\label{alg:exit}
\begin{algorithmic}[1]
\Procedure{ExitValidator}{validator $v_i$}
    \State Begin unbonding for all delegators of $v_i$
    \State Remove $v_i$ from active set at epoch $e_{\text{current}} + 1$
    \State $v_i$'s self-stake enters unbonding ($\tau_{\text{unbond}} = 14$ days)
    \State Pending rewards distributed at epoch boundary
    \State After $\tau_{\text{unbond}}$: release self-stake to operator
\EndProcedure
\end{algorithmic}
\end{algorithm}

\subsection{Validator Rotation and Churn}

\begin{definition}[Churn Limit]
At most $\mathsf{maxChurn} = \max(4, |\mathcal{V}| / 64)$ validators can enter or exit per epoch, preventing rapid validator set changes that could destabilize consensus.
\end{definition}

\begin{proposition}[Churn Safety]
With churn limit $C$ and epoch length $E$ blocks, the minimum time for an adversary to accumulate $1/3$ of stake through new validator registrations is:
\begin{equation}
    T_{\text{takeover}} = \frac{|\mathcal{V}| / 3}{C} \cdot E \text{ blocks}
\end{equation}
For $|\mathcal{V}| = 2{,}800$, $C = 44$, $E = 8{,}640$: $T \approx 182{,}000$ blocks ($\approx 21$ days).
\end{proposition}

\subsection{Performance Scoring}

Validators are scored on a composite metric used for delegation recommendations:

\begin{definition}[Validator Performance Score]
\begin{equation}
    \text{Score}_i = 0.40 \cdot u_i + 0.25 \cdot (1 - c_i / c^{\max}) + 0.20 \cdot \text{AppchainCoverage}_i + 0.15 \cdot \text{Tenure}_i
\end{equation}
where $\text{AppchainCoverage}_i = |\mathcal{K}_i| / |\mathcal{K}|$ and $\text{Tenure}_i = \min(1, \text{epochs active} / 365)$.
\end{definition}

\begin{table}[H]
\centering
\caption{Performance score distribution at epoch 500.}
\label{tab:scores}
\begin{tabular}{lrrr}
\toprule
\textbf{Score Range} & \textbf{Validators} & \textbf{Avg Stake (LUX)} & \textbf{Avg Commission} \\
\midrule
0.90--1.00 & 420 & 185,000 & 5.2\% \\
0.75--0.90 & 1,100 & 110,000 & 7.1\% \\
0.50--0.75 & 850 & 65,000 & 10.8\% \\
$< 0.50$ & 330 & 25,000 & 18.3\% \\
\bottomrule
\end{tabular}
\end{table}