LaTeX: move tab:quirke-subtasks to appendix, update main body ref

app.py

@@ -51,47 +51,13 @@ sum-9 boundary (SS), and \texttt{t16}/\texttt{t3} at the trivial positions (SC/S
 At each answer-digit position $n$, the local computation falls into one
 of ten mutually exclusive subtasks determined by the operand digits and
 the carry or borrow state propagating from lower positions
-(Table~\ref{tab:quirke-subtasks}).
+(Table~\ref{tab:quirke-subtasks} in Appendix~\ref{app:arithmetic}).
 A \emph{carry cascade} arises when consecutive digit pairs sum to exactly
 9 (SS positions in addition): whether a carry propagates through such a
 run depends on a single carry entering from the right, requiring the model
 to track state across multiple positions.
 Borrow cascades (UD) are the analogous structure in subtraction.
 
-\begin{table}[h]
-  \centering
-  \small
-  \setlength{\tabcolsep}{6pt}
-  \begin{tabular}{llp{8.2cm}}
-    \toprule
-    & Label & Condition at digit position $n$ \\
-    \midrule
-    \multirow{5}{*}{\rotatebox[origin=c]{90}{Addition\;}}
-      & \textbf{SA} & $d_1{+}d_2 \leq 8$;\; no carry in or out \\
-      & \textbf{SC} & $d_1{+}d_2 \geq 10$;\; generates a carry \\
-      & \textbf{SS} & $d_1{+}d_2 = 9$;\; carry state \emph{uncertain}
-                      (cascade boundary) \\
-      & \textbf{UC} & carry arrives from position $n{-}1$;\;
-                      answer digit depends on it \\
-      & \textbf{US} & carry propagates through a run of SS positions
-                      (sum-of-9 cascade) \\
-    \midrule
-    \multirow{5}{*}{\rotatebox[origin=c]{90}{Subtraction\;}}
-      & \textbf{MD} & $d_1 \geq d_2$;\; no borrow \\
-      & \textbf{MB} & $d_1 < d_2$;\; generates a borrow \\
-      & \textbf{ME} & $d_1 = d_2$;\; borrow state \emph{uncertain} \\
-      & \textbf{UB} & borrow arrives from position $n{-}1$ \\
-      & \textbf{UD} & borrow propagates through a run of ME positions \\
-    \bottomrule
-  \end{tabular}
-  \caption{Per-digit subtask labels for six-digit addition and
-           subtraction~\citep{quirke_2024_addsub_preprint}.
-           Cascades (US, UD) are the hardest: the answer digit cannot
-           be determined locally and requires resolving multi-position
-           carry/borrow propagation.}
-  \label{tab:quirke-subtasks}
-\end{table}
-
 \paragraph{Models and training.}
 We evaluate three undersized architectures:
 \texttt{1L/2H/256d} (1 transformer layer, 2 attention heads, hidden size 256),
@@ -356,6 +322,35 @@ LATEX_APPENDIX = r"""% ═══════════════════
 \section{Arithmetic case study: interpretability analysis}
 \label{app:arithmetic}
 
+\begin{table}[h]
+  \centering\small
+  \setlength{\tabcolsep}{6pt}
+  \begin{tabular}{llp{7.8cm}}
+    \toprule
+    & Label & Condition at digit position $n$ \\
+    \midrule
+    \multirow{5}{*}{\rotatebox[origin=c]{90}{Addition\;}}
+      & \textbf{SA} & $d_1{+}d_2 \leq 8$;\; no carry in or out \\
+      & \textbf{SC} & $d_1{+}d_2 \geq 10$;\; generates a carry \\
+      & \textbf{SS} & $d_1{+}d_2 = 9$;\; carry state \emph{uncertain} (cascade boundary) \\
+      & \textbf{UC} & carry arrives from position $n{-}1$;\; answer digit depends on it \\
+      & \textbf{US} & carry propagates through a run of SS positions (sum-of-9 cascade) \\
+    \midrule
+    \multirow{5}{*}{\rotatebox[origin=c]{90}{Subtraction\;}}
+      & \textbf{MD} & $d_1 \geq d_2$;\; no borrow \\
+      & \textbf{MB} & $d_1 < d_2$;\; generates a borrow \\
+      & \textbf{ME} & $d_1 = d_2$;\; borrow state \emph{uncertain} \\
+      & \textbf{UB} & borrow arrives from position $n{-}1$ \\
+      & \textbf{UD} & borrow propagates through a run of ME positions \\
+    \bottomrule
+  \end{tabular}
+  \caption{Per-digit subtask labels for six-digit addition and
+    subtraction~\citep{quirke_2024_addsub_preprint}.
+    Cascades (US, UD) require tracking carry/borrow state across
+    multiple positions and are the hardest splits.}
+  \label{tab:quirke-subtasks}
+\end{table}
+
 \paragraph{Setup.}
 All interpretability analyses use model
 \texttt{add\_sub\_sorl\_v1\_abs30\_K1\_100K\_2L1H128d}