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 (1.05000,3.10000) {input pair};
3 \node[] at (3.55000,3.10000) {difference};
4 \node[] at (6.05000,3.10000) {same mod 8?};
5 \node[] at (8.55000,3.10000) {$E_+$ difference};
6 \node[] at (11.05000,3.10000) {same mod 8?};
7 \draw[fill=black!10,draw=black!45,line width=.35pt,] (0.00000,1.95000) rectangle ++(2.10000,0.75000);
8 \node[] at (1.05000,2.32500) {$0,(0,8)$};
9 \draw[fill=black!10,draw=black!45,line width=.35pt,] (2.50000,1.95000) rectangle ++(2.10000,0.75000);
10 \node[] at (3.55000,2.32500) {$(0,8)$};
11 \draw[fill=black!10,draw=black!45,line width=.35pt,] (5.00000,1.95000) rectangle ++(2.10000,0.75000);
12 \node[] at (6.05000,2.32500) {yes};
13 \draw[fill=black!10,draw=black!45,line width=.35pt,] (7.50000,1.95000) rectangle ++(2.10000,0.75000);
14 \node[] at (8.55000,2.32500) {$(4,0)$};
15 \draw[fill=black!10,draw=black!45,line width=.35pt,] (10.00000,1.95000) rectangle ++(2.10000,0.75000);
16 \node[] at (11.05000,2.32500) {no};
17 \draw[fill=black!22,draw=black!45,line width=.35pt,] (0.00000,0.95000) rectangle ++(2.10000,0.75000);
18 \node[] at (1.05000,1.32500) {$0,(0,16)$};
19 \draw[fill=black!22,draw=black!45,line width=.35pt,] (2.50000,0.95000) rectangle ++(2.10000,0.75000);
20 \node[] at (3.55000,1.32500) {$(0,16)$};
21 \draw[fill=black!22,draw=black!45,line width=.35pt,] (5.00000,0.95000) rectangle ++(2.10000,0.75000);
22 \node[] at (6.05000,1.32500) {yes};
23 \draw[fill=black!22,draw=black!45,line width=.35pt,] (7.50000,0.95000) rectangle ++(2.10000,0.75000);
24 \node[] at (8.55000,1.32500) {$(8,0)$};
25 \draw[fill=black!22,draw=black!45,line width=.35pt,] (10.00000,0.95000) rectangle ++(2.10000,0.75000);
26 \node[] at (11.05000,1.32500) {yes};
27 \node[] at (6.00000,-0.05000) {$m=3:\quad 3\text{ input digits fail; }4\text{ input digits suffice.}$};
28 \end{tikzpicture}

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