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) {$A$};
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) {$1$};
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) {$1$};
7 \draw[fill=black!0,draw=black!45,line width=.35pt,] (0.00000,1.10000) rectangle ++(0.70000,0.70000);
8 \node[] at (0.35000,1.45000) {$0$};
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 (4.30000,3.05000) {$N=I+A$};
12 \draw[fill=black!12,draw=black!45,line width=.35pt,] (3.60000,1.80000) rectangle ++(0.70000,0.70000);
13 \node[] at (3.95000,2.15000) {$2$};
14 \draw[fill=black!12,draw=black!45,line width=.35pt,] (4.30000,1.80000) rectangle ++(0.70000,0.70000);
15 \node[] at (4.65000,2.15000) {$1$};
16 \draw[fill=black!0,draw=black!45,line width=.35pt,] (3.60000,1.10000) rectangle ++(0.70000,0.70000);
17 \node[] at (3.95000,1.45000) {$0$};
18 \draw[fill=black!0,draw=black!45,line width=.35pt,] (4.30000,1.10000) rectangle ++(0.70000,0.70000);
19 \node[] at (4.65000,1.45000) {$0$};
20 \node[] at (7.90000,3.05000) {$E_+=N/2$};
21 \draw[fill=black!12,draw=black!45,line width=.35pt,] (7.20000,1.80000) rectangle ++(0.70000,0.70000);
22 \node[] at (7.55000,2.15000) {$1$};
23 \draw[fill=black!12,draw=black!45,line width=.35pt,] (7.90000,1.80000) rectangle ++(0.70000,0.70000);
24 \node[] at (8.25000,2.15000) {$\frac{1}{2}$};
25 \draw[fill=black!0,draw=black!45,line width=.35pt,] (7.20000,1.10000) rectangle ++(0.70000,0.70000);
26 \node[] at (7.55000,1.45000) {$0$};
27 \draw[fill=black!0,draw=black!45,line width=.35pt,] (7.90000,1.10000) rectangle ++(0.70000,0.70000);
28 \node[] at (8.25000,1.45000) {$0$};
29 \node[] at (11.00000,2.10000) {$N^2=2N$};
30 \node[] at (11.00000,1.20000) {$E_+^2=E_+$};
31 \node[] at (6.00000,-0.05000) {$E_+(1,0)=(1,0),\qquad E_+(-1,2)=(0,0)$};
32 \end{tikzpicture}

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