Paper III: Typed Transfer, Nonlinear Packets, and Obstruction Theory

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1 \begin{tikzpicture}[x=1cm,y=1cm,>=Latex,font=\sffamily\small,line cap=round,line join=round]
2 \node[] at (1.08000,4.25000) {$L_e$};
3 \draw[fill=black!0,draw=black!40,line width=.35pt,] (0.00000,2.98000) rectangle ++(0.72000,0.72000);
4 \node[] at (0.36000,3.34000) {$0$};
5 \draw[fill=black!0,draw=black!40,line width=.35pt,] (0.72000,2.98000) rectangle ++(0.72000,0.72000);
6 \node[] at (1.08000,3.34000) {$0$};
7 \draw[fill=black!0,draw=black!40,line width=.35pt,] (1.44000,2.98000) rectangle ++(0.72000,0.72000);
8 \node[] at (1.80000,3.34000) {$0$};
9 \draw[fill=black!12,draw=black!40,line width=.35pt,] (0.00000,2.26000) rectangle ++(0.72000,0.72000);
10 \node[] at (0.36000,2.62000) {$2$};
11 \draw[fill=black!0,draw=black!40,line width=.35pt,] (0.72000,2.26000) rectangle ++(0.72000,0.72000);
12 \node[] at (1.08000,2.62000) {$0$};
13 \draw[fill=black!0,draw=black!40,line width=.35pt,] (1.44000,2.26000) rectangle ++(0.72000,0.72000);
14 \node[] at (1.80000,2.62000) {$0$};
15 \draw[fill=black!0,draw=black!40,line width=.35pt,] (0.00000,1.54000) rectangle ++(0.72000,0.72000);
16 \node[] at (0.36000,1.90000) {$0$};
17 \draw[fill=black!0,draw=black!40,line width=.35pt,] (0.72000,1.54000) rectangle ++(0.72000,0.72000);
18 \node[] at (1.08000,1.90000) {$0$};
19 \draw[fill=black!0,draw=black!40,line width=.35pt,] (1.44000,1.54000) rectangle ++(0.72000,0.72000);
20 \node[] at (1.80000,1.90000) {$0$};
21 \node[font=\sffamily\scriptsize] at (0.36000,3.95000) {$0$};
22 \node[font=\sffamily\scriptsize] at (1.08000,3.95000) {$1$};
23 \node[font=\sffamily\scriptsize] at (1.80000,3.95000) {$2$};
24 \node[font=\sffamily\scriptsize] at (-0.24000,3.34000) {$0$};
25 \node[font=\sffamily\scriptsize] at (-0.24000,2.62000) {$1$};
26 \node[font=\sffamily\scriptsize] at (-0.24000,1.90000) {$2$};
27 \node[] at (5.28000,4.25000) {$L_f$};
28 \draw[fill=black!0,draw=black!40,line width=.35pt,] (4.20000,2.98000) rectangle ++(0.72000,0.72000);
29 \node[] at (4.56000,3.34000) {$0$};
30 \draw[fill=black!0,draw=black!40,line width=.35pt,] (4.92000,2.98000) rectangle ++(0.72000,0.72000);
31 \node[] at (5.28000,3.34000) {$0$};
32 \draw[fill=black!0,draw=black!40,line width=.35pt,] (5.64000,2.98000) rectangle ++(0.72000,0.72000);
33 \node[] at (6.00000,3.34000) {$0$};
34 \draw[fill=black!0,draw=black!40,line width=.35pt,] (4.20000,2.26000) rectangle ++(0.72000,0.72000);
35 \node[] at (4.56000,2.62000) {$0$};
36 \draw[fill=black!0,draw=black!40,line width=.35pt,] (4.92000,2.26000) rectangle ++(0.72000,0.72000);
37 \node[] at (5.28000,2.62000) {$0$};
38 \draw[fill=black!0,draw=black!40,line width=.35pt,] (5.64000,2.26000) rectangle ++(0.72000,0.72000);
39 \node[] at (6.00000,2.62000) {$0$};
40 \draw[fill=black!0,draw=black!40,line width=.35pt,] (4.20000,1.54000) rectangle ++(0.72000,0.72000);
41 \node[] at (4.56000,1.90000) {$0$};
42 \draw[fill=black!12,draw=black!40,line width=.35pt,] (4.92000,1.54000) rectangle ++(0.72000,0.72000);
43 \node[] at (5.28000,1.90000) {$3$};
44 \draw[fill=black!0,draw=black!40,line width=.35pt,] (5.64000,1.54000) rectangle ++(0.72000,0.72000);
45 \node[] at (6.00000,1.90000) {$0$};
46 \node[font=\sffamily\scriptsize] at (4.56000,3.95000) {$0$};
47 \node[font=\sffamily\scriptsize] at (5.28000,3.95000) {$1$};
48 \node[font=\sffamily\scriptsize] at (6.00000,3.95000) {$2$};
49 \node[font=\sffamily\scriptsize] at (3.96000,3.34000) {$0$};
50 \node[font=\sffamily\scriptsize] at (3.96000,2.62000) {$1$};
51 \node[font=\sffamily\scriptsize] at (3.96000,1.90000) {$2$};
52 \node[] at (9.48000,4.25000) {$L_fL_e$};
53 \draw[fill=black!0,draw=black!40,line width=.35pt,] (8.40000,2.98000) rectangle ++(0.72000,0.72000);
54 \node[] at (8.76000,3.34000) {$0$};
55 \draw[fill=black!0,draw=black!40,line width=.35pt,] (9.12000,2.98000) rectangle ++(0.72000,0.72000);
56 \node[] at (9.48000,3.34000) {$0$};
57 \draw[fill=black!0,draw=black!40,line width=.35pt,] (9.84000,2.98000) rectangle ++(0.72000,0.72000);
58 \node[] at (10.20000,3.34000) {$0$};
59 \draw[fill=black!0,draw=black!40,line width=.35pt,] (8.40000,2.26000) rectangle ++(0.72000,0.72000);
60 \node[] at (8.76000,2.62000) {$0$};
61 \draw[fill=black!0,draw=black!40,line width=.35pt,] (9.12000,2.26000) rectangle ++(0.72000,0.72000);
62 \node[] at (9.48000,2.62000) {$0$};
63 \draw[fill=black!0,draw=black!40,line width=.35pt,] (9.84000,2.26000) rectangle ++(0.72000,0.72000);
64 \node[] at (10.20000,2.62000) {$0$};
65 \draw[fill=black!12,draw=black!40,line width=.35pt,] (8.40000,1.54000) rectangle ++(0.72000,0.72000);
66 \node[] at (8.76000,1.90000) {$6$};
67 \draw[fill=black!0,draw=black!40,line width=.35pt,] (9.12000,1.54000) rectangle ++(0.72000,0.72000);
68 \node[] at (9.48000,1.90000) {$0$};
69 \draw[fill=black!0,draw=black!40,line width=.35pt,] (9.84000,1.54000) rectangle ++(0.72000,0.72000);
70 \node[] at (10.20000,1.90000) {$0$};
71 \node[font=\sffamily\scriptsize] at (8.76000,3.95000) {$0$};
72 \node[font=\sffamily\scriptsize] at (9.48000,3.95000) {$1$};
73 \node[font=\sffamily\scriptsize] at (10.20000,3.95000) {$2$};
74 \node[font=\sffamily\scriptsize] at (8.16000,3.34000) {$0$};
75 \node[font=\sffamily\scriptsize] at (8.16000,2.62000) {$1$};
76 \node[font=\sffamily\scriptsize] at (8.16000,1.90000) {$2$};
77 \node[] at (5.30000,0.65000) {row = target / column = source};
78 \node[circle,draw,fill=white,minimum size=7mm,inner sep=1pt,] at (1.10000,-0.30000) {$0$};
79 \node[circle,draw,fill=white,minimum size=7mm,inner sep=1pt,] at (5.30000,-0.30000) {$1$};
80 \node[circle,draw,fill=white,minimum size=7mm,inner sep=1pt,] at (9.50000,-0.30000) {$2$};
81 \draw[->,line width=.85pt,shorten <=4mm,shorten >=4mm,] (1.1,-0.3) -- node[sloped,above,font=\sffamily\footnotesize] {$e:2$} (5.3,-0.3);
82 \draw[->,line width=.85pt,shorten <=4mm,shorten >=4mm,] (5.3,-0.3) -- node[sloped,above,font=\sffamily\footnotesize] {$f:3$} (9.5,-0.3);
83 \node[] at (5.30000,-1.20000) {$e\text{ first},\ f\text{ second};\qquad L_eL_f=0$};
84 \end{tikzpicture}

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