\newcommand{\BoardAbstract}{On all 395 leaderboard curves of rank $24$--$31$, with primes below $10^{10}$, the optimised kernel certifies $\ran\le r$ on 379 curves and the fixed kernel on 372; where both succeed the fixed kernel needs a median of 4.0 times as many primes.}
\newcommand{\BoardBrief}{On the 395 leaderboard curves of rank $24$--$31$ ($p<10^{10}$) the optimised kernel certifies $\ran\le r$ on 379 curves, the fixed kernel on 372; 7 only by the optimised kernel, none only by the fixed one (Section~\ref{sec:board}).}
\newcommand{\BoardDetail}{On 16 curves neither kernel reaches the target with $p<10^{10}$; on all of them the certified bound of the optimised kernel is the smaller one; their certified bounds at the cap are listed in the repository.}
\newcommand{\BoardTrend}{The median ratio grows with the rank, though not monotonically, from 3.1 at rank $24$ to 6.9 at rank $31$ (Table~\ref{tab:board}).}