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\label{def:combined-ledger}
The \textbf{Combined Gain--Cost Ledger}
across Books~I--II
tallies all mode-classified constructions:

\medskip
\renewcommand{\arraystretch}{1.25}
\begin{center}
\begin{tabular}{@{}clrrl@{}}
\toprule
\textbf{Mode} & \textbf{Name}
  & \textbf{Book~I} & \textbf{Book~II} & \textbf{Assessment} \\
\midrule
A & Same      &  4 &  3 & Identical objects \\
B & Parallel  &  5 &  5 & Same axioms, different carriers \\
C & Refused   &  9 &  7 & Genuine costs \\
D & Gained    & 13 & 10 & Structurally impossible in ZFC \\
E & Earned    &  7 &  6 & Derivation replaces postulation \\
\midrule
\multicolumn{2}{@{}l}{\textbf{Total gains (D+E)}}
  & 20 & 16 & \textbf{36} \\
\multicolumn{2}{@{}l}{\textbf{Total costs (C)}}
  &  9 &  7 & \textbf{16} \\
\multicolumn{2}{@{}l}{\textbf{Neutral (A+B)}}
  &  9 &  8 & \textbf{17} \\
\midrule
\multicolumn{2}{@{}l}{\textbf{Grand total}}
  & 38 & 31 & \textbf{69} \\
\bottomrule
\end{tabular}
\end{center}

\medskip
\noindent
Including Mode~A and~B constructions
that carry additional $\tau$-specific structure,
the gain count rises to approximately 49.
The cost count remains 16.
The ratio is approximately $3{:}1$ gains to costs.

This ratio is \emph{not} evidence
that $\tau$ is ``better.''
It reflects the structural fact
that categoricity, while expensive
(16 refusals),
produces many downstream consequences
(each gain is a theorem that follows
from categoricity + the forced sign).
The costs are concentrated at the foundation;
the gains cascade through the structure.