Paper II: Refinement Towers, Weighted Transfer, and Integral Separation of Operator Packets

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1 \begin{tikzpicture}[x=1cm,y=1cm,>=Latex,font=\sffamily\small,line cap=round]
2 \node[] at (0.70000,3.05000) {$T$};
3 \draw[fill=black!12,draw=black!45,line width=.35pt,] (0.00000,1.80000) rectangle ++(0.70000,0.70000);
4 \node[] at (0.35000,2.15000) {$5$};
5 \draw[fill=black!12,draw=black!45,line width=.35pt,] (0.70000,1.80000) rectangle ++(0.70000,0.70000);
6 \node[] at (1.05000,2.15000) {$3$};
7 \draw[fill=black!12,draw=black!45,line width=.35pt,] (0.00000,1.10000) rectangle ++(0.70000,0.70000);
8 \node[] at (0.35000,1.45000) {$4$};
9 \draw[fill=black!12,draw=black!45,line width=.35pt,] (0.70000,1.10000) rectangle ++(0.70000,0.70000);
10 \node[] at (1.05000,1.45000) {$1$};
11 \node[] at (4.10000,3.05000) {$K$};
12 \draw[fill=black!12,draw=black!45,line width=.35pt,] (3.40000,1.80000) rectangle ++(0.70000,0.70000);
13 \node[] at (3.75000,2.15000) {$9$};
14 \draw[fill=black!12,draw=black!45,line width=.35pt,] (4.10000,1.80000) rectangle ++(0.70000,0.70000);
15 \node[] at (4.45000,2.15000) {$5$};
16 \draw[fill=black!12,draw=black!45,line width=.35pt,] (3.40000,1.10000) rectangle ++(0.70000,0.70000);
17 \node[] at (3.75000,1.45000) {$28$};
18 \draw[fill=black!12,draw=black!45,line width=.35pt,] (4.10000,1.10000) rectangle ++(0.70000,0.70000);
19 \node[] at (4.45000,1.45000) {$13$};
20 \node[] at (7.50000,3.05000) {$TK\pmod{32}$};
21 \draw[fill=black!12,draw=black!45,line width=.35pt,] (6.80000,1.80000) rectangle ++(0.70000,0.70000);
22 \node[] at (7.15000,2.15000) {$1$};
23 \draw[fill=black!0,draw=black!45,line width=.35pt,] (7.50000,1.80000) rectangle ++(0.70000,0.70000);
24 \node[] at (7.85000,2.15000) {$0$};
25 \draw[fill=black!0,draw=black!45,line width=.35pt,] (6.80000,1.10000) rectangle ++(0.70000,0.70000);
26 \node[] at (7.15000,1.45000) {$0$};
27 \draw[fill=black!12,draw=black!45,line width=.35pt,] (7.50000,1.10000) rectangle ++(0.70000,0.70000);
28 \node[] at (7.85000,1.45000) {$1$};
29 \node[] at (10.90000,3.05000) {$KT\pmod{32}$};
30 \draw[fill=black!12,draw=black!45,line width=.35pt,] (10.20000,1.80000) rectangle ++(0.70000,0.70000);
31 \node[] at (10.55000,2.15000) {$1$};
32 \draw[fill=black!0,draw=black!45,line width=.35pt,] (10.90000,1.80000) rectangle ++(0.70000,0.70000);
33 \node[] at (11.25000,2.15000) {$0$};
34 \draw[fill=black!0,draw=black!45,line width=.35pt,] (10.20000,1.10000) rectangle ++(0.70000,0.70000);
35 \node[] at (10.55000,1.45000) {$0$};
36 \draw[fill=black!12,draw=black!45,line width=.35pt,] (10.90000,1.10000) rectangle ++(0.70000,0.70000);
37 \node[] at (11.25000,1.45000) {$1$};
38 \node[] at (6.00000,-0.05000) {$S=\begin{pmatrix}9&-18\\-4&9\end{pmatrix},\qquad K=SD^{-1}\pmod{32}$};
39 \end{tikzpicture}

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