\section{Parameter reference}\label{app:parameters}

Table~\ref{tab:parameters} collects the parameters of the adversary and its
analysis. The last two columns
distinguish where a parameter's role is introduced from where its value
is chosen and explained. All choices are fixed before the first query.
Appendix~\ref{app:coupling} gives explicit choices for the digit alphabet,
number of sweeps, and neighborhood radius in the local enclosure theorem.

\begin{center}
\begin{minipage}{\linewidth}
\captionsetup{hypcap=false}
\captionof{table}{Parameters and their roles. References lead to the explanations in the text.}
\label{tab:parameters}
\small
\setlength{\tabcolsep}{4pt}
\renewcommand{\arraystretch}{1.4}
\begin{tabular}{@{}p{.07\linewidth}p{.21\linewidth}p{.37\linewidth}p{.12\linewidth}p{.12\linewidth}@{}}
\toprule
Symbol & Value & Role & Introduced & Choice\\
\midrule
$k$ & Integer, $k\ge64$ & Repair a vertex that reaches this degree after an answer. & \S\ref{sec:comparison} & \S\ref{sec:potential}\\
$H$ & $2^k$ & Number of vertices refined in a selected directed path. & \S\ref{sec:repairs} & \S\ref{sec:repairs}\\
$B$ & $(k+1)^{2H+1}$ & Bounds the number of other vertices comparable with one vertex in its node graph. & App.~\ref{app:certificates} & App.~\ref{app:certificates}\\
$w_*$ & $2^{-2kB}$ & Calibrates the finite calculations: a coordinate of at least this width guarantees certification. & App.~\ref{app:certificates} & App.~\ref{app:certificates}\\
$\eta$ & $1/(100k)$ & Error in the retained fraction, abbreviated in the comparison-count proof. & \S\ref{sec:rare-refinements} & \S\ref{sec:selection}\\
$Q(n)$ & $n\ceil{\log n}$ & Number of answers before switching to a fixed consistent order. & \S\ref{sec:operation-properties} & \S\ref{sec:comparison}\\
\bottomrule
\end{tabular}
\end{minipage}
\end{center}