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 (1.03500,4.65000) {$[e_0\ \ Te_0\ \ T^2e_0]$};
3 \draw[fill=black!12,draw=black!40,line width=.35pt,] (0.00000,3.41000) rectangle ++(0.69000,0.69000);
4 \node[] at (0.34500,3.75500) {$1$};
5 \draw[fill=black!0,draw=black!40,line width=.35pt,] (0.69000,3.41000) rectangle ++(0.69000,0.69000);
6 \node[] at (1.03500,3.75500) {$0$};
7 \draw[fill=black!0,draw=black!40,line width=.35pt,] (1.38000,3.41000) rectangle ++(0.69000,0.69000);
8 \node[] at (1.72500,3.75500) {$0$};
9 \draw[fill=black!0,draw=black!40,line width=.35pt,] (0.00000,2.72000) rectangle ++(0.69000,0.69000);
10 \node[] at (0.34500,3.06500) {$0$};
11 \draw[fill=black!12,draw=black!40,line width=.35pt,] (0.69000,2.72000) rectangle ++(0.69000,0.69000);
12 \node[] at (1.03500,3.06500) {$1$};
13 \draw[fill=black!0,draw=black!40,line width=.35pt,] (1.38000,2.72000) rectangle ++(0.69000,0.69000);
14 \node[] at (1.72500,3.06500) {$0$};
15 \draw[fill=black!0,draw=black!40,line width=.35pt,] (0.00000,2.03000) rectangle ++(0.69000,0.69000);
16 \node[] at (0.34500,2.37500) {$0$};
17 \draw[fill=black!12,draw=black!40,line width=.35pt,] (0.69000,2.03000) rectangle ++(0.69000,0.69000);
18 \node[] at (1.03500,2.37500) {$1$};
19 \draw[fill=black!0,draw=black!40,line width=.35pt,] (1.38000,2.03000) rectangle ++(0.69000,0.69000);
20 \node[] at (1.72500,2.37500) {$0$};
21 \draw[fill=black!0,draw=black!40,line width=.35pt,] (0.00000,1.34000) rectangle ++(0.69000,0.69000);
22 \node[] at (0.34500,1.68500) {$0$};
23 \draw[fill=black!0,draw=black!40,line width=.35pt,] (0.69000,1.34000) rectangle ++(0.69000,0.69000);
24 \node[] at (1.03500,1.68500) {$0$};
25 \draw[fill=black!0,draw=black!40,line width=.35pt,] (1.38000,1.34000) rectangle ++(0.69000,0.69000);
26 \node[] at (1.72500,1.68500) {$0$};
27 \draw[fill=black!0,draw=black!40,line width=.35pt,] (0.00000,0.65000) rectangle ++(0.69000,0.69000);
28 \node[] at (0.34500,0.99500) {$0$};
29 \draw[fill=black!0,draw=black!40,line width=.35pt,] (0.69000,0.65000) rectangle ++(0.69000,0.69000);
30 \node[] at (1.03500,0.99500) {$0$};
31 \draw[fill=black!0,draw=black!40,line width=.35pt,] (1.38000,0.65000) rectangle ++(0.69000,0.69000);
32 \node[] at (1.72500,0.99500) {$0$};
33 \node[] at (-0.30000,3.75500) {$0$};
34 \node[] at (-0.30000,3.06500) {$1$};
35 \node[] at (-0.30000,2.37500) {$2$};
36 \node[] at (-0.30000,1.68500) {$3$};
37 \node[] at (-0.30000,0.99500) {$4$};
38 \node[] at (1.05000,-0.15000) {rank $=2$};
39 \node[] at (4.69000,4.65000) {a basis of the orbit hull};
40 \draw[fill=black!12,draw=black!40,line width=.35pt,] (4.00000,3.41000) rectangle ++(0.69000,0.69000);
41 \node[] at (4.34500,3.75500) {$1$};
42 \draw[fill=black!0,draw=black!40,line width=.35pt,] (4.69000,3.41000) rectangle ++(0.69000,0.69000);
43 \node[] at (5.03500,3.75500) {$0$};
44 \draw[fill=black!0,draw=black!40,line width=.35pt,] (4.00000,2.72000) rectangle ++(0.69000,0.69000);
45 \node[] at (4.34500,3.06500) {$0$};
46 \draw[fill=black!12,draw=black!40,line width=.35pt,] (4.69000,2.72000) rectangle ++(0.69000,0.69000);
47 \node[] at (5.03500,3.06500) {$1$};
48 \draw[fill=black!0,draw=black!40,line width=.35pt,] (4.00000,2.03000) rectangle ++(0.69000,0.69000);
49 \node[] at (4.34500,2.37500) {$0$};
50 \draw[fill=black!12,draw=black!40,line width=.35pt,] (4.69000,2.03000) rectangle ++(0.69000,0.69000);
51 \node[] at (5.03500,2.37500) {$1$};
52 \draw[fill=black!0,draw=black!40,line width=.35pt,] (4.00000,1.34000) rectangle ++(0.69000,0.69000);
53 \node[] at (4.34500,1.68500) {$0$};
54 \draw[fill=black!0,draw=black!40,line width=.35pt,] (4.69000,1.34000) rectangle ++(0.69000,0.69000);
55 \node[] at (5.03500,1.68500) {$0$};
56 \draw[fill=black!0,draw=black!40,line width=.35pt,] (4.00000,0.65000) rectangle ++(0.69000,0.69000);
57 \node[] at (4.34500,0.99500) {$0$};
58 \draw[fill=black!0,draw=black!40,line width=.35pt,] (4.69000,0.65000) rectangle ++(0.69000,0.69000);
59 \node[] at (5.03500,0.99500) {$0$};
60 \node[] at (8.85000,3.80000) {$\operatorname{Reach}(0)=\{0,1,2,3\}$};
61 \node[] at (8.85000,2.75000) {$\operatorname{Hull}_T(e_0)=\{(a,b,b,0,0)\}$};
62 \node[] at (8.85000,1.65000) {$e_3:\ \text{reachable but absent}$};
63 \node[] at (8.85000,0.60000) {$e_4:\ \text{unreachable and absent}$};
64 \end{tikzpicture}

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