\label{def:five-forbidden-moves}
The following five \emph{forbidden moves} are operations admitted
by ZFC but prohibited by Category~$\T$.
\begin{enumerate}
\item \textbf{Unbounded fan-out.}
      \emph{ZFC}: Power Set.
      \emph{$\T$~block}: $\KAxiom{3}$ (bounded multiplicity).
      \emph{Bridge}: brute-force search over $\mathcal{P}(X)$
      unavailable; the NP-hardness gap.

\item \textbf{Global equality.}
      \emph{ZFC}: Extensionality.
      \emph{$\T$~block}: $\KAxiom{5}$ (diagonal discipline).
      \emph{Bridge}: diagonal arguments (Cantor, Russell)
      have no $\T$-analogue; equality is local and earned.

\item \textbf{Succinct circuits.}
      \emph{ZFC}: Replacement.
      \emph{$\T$~block}: operational closure finiteness.
      \emph{Bridge}: some ZFC-compressible objects have no
      $\T$-short description; the compression gap.

\item \textbf{Exponential quantification.}
      \emph{ZFC}: unrestricted quantification over
      uncountable sets.
      \emph{$\T$~block}: observation finiteness.
      \emph{Bridge}: exponential-witness searches trivially
      resolve in~$\T$; the witness gap.

\item \textbf{Non-local disguise.}
      \emph{ZFC}: Foundation + Replacement (re-encoding).
      \emph{$\T$~block}: NF uniqueness.
      \emph{Bridge}: encoding tricks that shift complexity
      cannot operate in~$\T$; the disguise gap.
\end{enumerate}