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 (1.14000,3.95000) {Fine packet vectors};
3 \draw[fill=black!12,draw=black!45,line width=.35pt,] (0.00000,2.83000) rectangle ++(0.57000,0.57000);
4 \node[] at (0.28500,3.11500) {$1$};
5 \draw[fill=black!0,draw=black!45,line width=.35pt,] (0.57000,2.83000) rectangle ++(0.57000,0.57000);
6 \node[] at (0.85500,3.11500) {$0$};
7 \draw[fill=black!0,draw=black!45,line width=.35pt,] (1.14000,2.83000) rectangle ++(0.57000,0.57000);
8 \node[] at (1.42500,3.11500) {$0$};
9 \draw[fill=black!0,draw=black!45,line width=.35pt,] (1.71000,2.83000) rectangle ++(0.57000,0.57000);
10 \node[] at (1.99500,3.11500) {$0$};
11 \draw[fill=black!0,draw=black!45,line width=.35pt,] (0.00000,2.26000) rectangle ++(0.57000,0.57000);
12 \node[] at (0.28500,2.54500) {$0$};
13 \draw[fill=black!12,draw=black!45,line width=.35pt,] (0.57000,2.26000) rectangle ++(0.57000,0.57000);
14 \node[] at (0.85500,2.54500) {$2$};
15 \draw[fill=black!0,draw=black!45,line width=.35pt,] (1.14000,2.26000) rectangle ++(0.57000,0.57000);
16 \node[] at (1.42500,2.54500) {$0$};
17 \draw[fill=black!0,draw=black!45,line width=.35pt,] (1.71000,2.26000) rectangle ++(0.57000,0.57000);
18 \node[] at (1.99500,2.54500) {$0$};
19 \draw[fill=black!0,draw=black!45,line width=.35pt,] (0.00000,1.69000) rectangle ++(0.57000,0.57000);
20 \node[] at (0.28500,1.97500) {$0$};
21 \draw[fill=black!0,draw=black!45,line width=.35pt,] (0.57000,1.69000) rectangle ++(0.57000,0.57000);
22 \node[] at (0.85500,1.97500) {$0$};
23 \draw[fill=black!12,draw=black!45,line width=.35pt,] (1.14000,1.69000) rectangle ++(0.57000,0.57000);
24 \node[] at (1.42500,1.97500) {$3$};
25 \draw[fill=black!0,draw=black!45,line width=.35pt,] (1.71000,1.69000) rectangle ++(0.57000,0.57000);
26 \node[] at (1.99500,1.97500) {$0$};
27 \draw[fill=black!0,draw=black!45,line width=.35pt,] (0.00000,1.12000) rectangle ++(0.57000,0.57000);
28 \node[] at (0.28500,1.40500) {$0$};
29 \draw[fill=black!0,draw=black!45,line width=.35pt,] (0.57000,1.12000) rectangle ++(0.57000,0.57000);
30 \node[] at (0.85500,1.40500) {$0$};
31 \draw[fill=black!0,draw=black!45,line width=.35pt,] (1.14000,1.12000) rectangle ++(0.57000,0.57000);
32 \node[] at (1.42500,1.40500) {$0$};
33 \draw[fill=black!12,draw=black!45,line width=.35pt,] (1.71000,1.12000) rectangle ++(0.57000,0.57000);
34 \node[] at (1.99500,1.40500) {$4$};
35 \node[] at (5.14000,3.95000) {Coarse packet vectors};
36 \draw[fill=black!12,draw=black!45,line width=.35pt,] (4.00000,2.83000) rectangle ++(0.57000,0.57000);
37 \node[] at (4.28500,3.11500) {$1$};
38 \draw[fill=black!0,draw=black!45,line width=.35pt,] (4.57000,2.83000) rectangle ++(0.57000,0.57000);
39 \node[] at (4.85500,3.11500) {$0$};
40 \draw[fill=black!12,draw=black!45,line width=.35pt,] (5.14000,2.83000) rectangle ++(0.57000,0.57000);
41 \node[] at (5.42500,3.11500) {$3$};
42 \draw[fill=black!0,draw=black!45,line width=.35pt,] (5.71000,2.83000) rectangle ++(0.57000,0.57000);
43 \node[] at (5.99500,3.11500) {$0$};
44 \draw[fill=black!0,draw=black!45,line width=.35pt,] (4.00000,2.26000) rectangle ++(0.57000,0.57000);
45 \node[] at (4.28500,2.54500) {$0$};
46 \draw[fill=black!12,draw=black!45,line width=.35pt,] (4.57000,2.26000) rectangle ++(0.57000,0.57000);
47 \node[] at (4.85500,2.54500) {$2$};
48 \draw[fill=black!0,draw=black!45,line width=.35pt,] (5.14000,2.26000) rectangle ++(0.57000,0.57000);
49 \node[] at (5.42500,2.54500) {$0$};
50 \draw[fill=black!12,draw=black!45,line width=.35pt,] (5.71000,2.26000) rectangle ++(0.57000,0.57000);
51 \node[] at (5.99500,2.54500) {$4$};
52 \node[] at (3.15000,2.20000) {$\sum_{\rm children}$};
53 \node[] at (1.14000,0.10000) {$4\times1=4\text{ free coordinates}$};
54 \node[] at (5.14000,0.10000) {$2\times2=4\text{ free coordinates}$};
55 \draw[black!30] (7.35000,-0.35000) -- (7.35000,4.00000);
56 \node[] at (9.74000,3.95000) {Scalar incidence only};
57 \draw[fill=black!12,draw=black!45,line width=.35pt,] (8.60000,2.83000) rectangle ++(0.57000,0.57000);
58 \node[] at (8.88500,3.11500) {$1$};
59 \draw[fill=black!0,draw=black!45,line width=.35pt,] (9.17000,2.83000) rectangle ++(0.57000,0.57000);
60 \node[] at (9.45500,3.11500) {$0$};
61 \draw[fill=black!12,draw=black!45,line width=.35pt,] (9.74000,2.83000) rectangle ++(0.57000,0.57000);
62 \node[] at (10.02500,3.11500) {$1$};
63 \draw[fill=black!0,draw=black!45,line width=.35pt,] (10.31000,2.83000) rectangle ++(0.57000,0.57000);
64 \node[] at (10.59500,3.11500) {$0$};
65 \draw[fill=black!0,draw=black!45,line width=.35pt,] (8.60000,2.26000) rectangle ++(0.57000,0.57000);
66 \node[] at (8.88500,2.54500) {$0$};
67 \draw[fill=black!12,draw=black!45,line width=.35pt,] (9.17000,2.26000) rectangle ++(0.57000,0.57000);
68 \node[] at (9.45500,2.54500) {$1$};
69 \draw[fill=black!0,draw=black!45,line width=.35pt,] (9.74000,2.26000) rectangle ++(0.57000,0.57000);
70 \node[] at (10.02500,2.54500) {$0$};
71 \draw[fill=black!12,draw=black!45,line width=.35pt,] (10.31000,2.26000) rectangle ++(0.57000,0.57000);
72 \node[] at (10.59500,2.54500) {$1$};
73 \node[] at (9.74000,1.55000) {$(x_0+x_2,\ x_1+x_3)$};
74 \node[] at (9.74000,0.10000) {$4\longrightarrow2\text{ scalars: loss}$};
75 \end{tikzpicture}

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