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\section{Reproducibility Details}
\label{app:reproducibility}
\begin{itemize}[leftmargin=1.5em]
\item \textbf{Environment:} Python 3.11, LanceDB 0.3.0, sentence-transformers
1.2.0 (all-MiniLM-L6-v2, $d=384$; we use $d=768$ in the paper via
all-mpnet-base-v2).
\item \textbf{Network simulation:} Discrete-event simulator with configurable
latency (uniform 10--100\,ms), packet loss ($p=0.01$), and node failures.
\item \textbf{Byzantine behavior:} Random noise ($\bm{s}_{i,m}^{(j)} \sim
\text{Unif}(\{-1,+1\}^g)$, $\alpha_{i,m}^{(j)} \sim \text{Unif}(0, 1)$).
\item \textbf{GRPO setup:} Group size $G = 4$, max iterations $K = 3$,
reward weights $\alpha = 0.7$, $\beta = 0.3$.
\item \textbf{Seeds:} Fixed seeds 42, 123, 456 for three independent runs;
all tables report mean $\pm$ std ($\leq 0.4\%$ in all cases).
\item \textbf{Hardware:} Simulated on a single 16-core x86 machine;
no GPU required for simulation.
\end{itemize}
% ============================================================================
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