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 (0.68000,4.25000) {$\Ob$};
3 \draw[fill=black!0,draw=black!40,line width=.35pt,] (0.00000,3.02000) rectangle ++(0.68000,0.68000);
4 \node[] at (0.34000,3.36000) {$0$};
5 \draw[fill=black!12,draw=black!40,line width=.35pt,] (0.68000,3.02000) rectangle ++(0.68000,0.68000);
6 \node[] at (1.02000,3.36000) {$1$};
7 \draw[fill=black!0,draw=black!40,line width=.35pt,] (0.00000,2.34000) rectangle ++(0.68000,0.68000);
8 \node[] at (0.34000,2.68000) {$0$};
9 \draw[fill=black!0,draw=black!40,line width=.35pt,] (0.68000,2.34000) rectangle ++(0.68000,0.68000);
10 \node[] at (1.02000,2.68000) {$0$};
11 \node[] at (3.88000,4.25000) {$\sum_iP_i\Ob P_i$};
12 \draw[fill=black!0,draw=black!40,line width=.35pt,] (3.20000,3.02000) rectangle ++(0.68000,0.68000);
13 \node[] at (3.54000,3.36000) {$0$};
14 \draw[fill=black!0,draw=black!40,line width=.35pt,] (3.88000,3.02000) rectangle ++(0.68000,0.68000);
15 \node[] at (4.22000,3.36000) {$0$};
16 \draw[fill=black!0,draw=black!40,line width=.35pt,] (3.20000,2.34000) rectangle ++(0.68000,0.68000);
17 \node[] at (3.54000,2.68000) {$0$};
18 \draw[fill=black!0,draw=black!40,line width=.35pt,] (3.88000,2.34000) rectangle ++(0.68000,0.68000);
19 \node[] at (4.22000,2.68000) {$0$};
20 \node[font=\sffamily\footnotesize] at (0.68000,0.85000) {nonzero};
21 \node[align=center,font=\sffamily\footnotesize] at (3.88000,0.85000) {diagonal test\\misses it};
22 \draw[black!30] (5.80000,0.40000) -- (5.80000,4.40000);
23 \node[] at (7.38000,4.25000) {$Q_0$};
24 \draw[fill=black!12,draw=black!40,line width=.35pt,] (6.70000,3.02000) rectangle ++(0.68000,0.68000);
25 \node[] at (7.04000,3.36000) {$1$};
26 \draw[fill=black!0,draw=black!40,line width=.35pt,] (7.38000,3.02000) rectangle ++(0.68000,0.68000);
27 \node[] at (7.72000,3.36000) {$0$};
28 \draw[fill=black!12,draw=black!40,line width=.35pt,] (6.70000,2.34000) rectangle ++(0.68000,0.68000);
29 \node[] at (7.04000,2.68000) {$1$};
30 \draw[fill=black!0,draw=black!40,line width=.35pt,] (7.38000,2.34000) rectangle ++(0.68000,0.68000);
31 \node[] at (7.72000,2.68000) {$0$};
32 \node[] at (10.68000,4.25000) {$Q_1$};
33 \draw[fill=black!0,draw=black!40,line width=.35pt,] (10.00000,3.02000) rectangle ++(0.68000,0.68000);
34 \node[] at (10.34000,3.36000) {$0$};
35 \draw[fill=black!0,draw=black!40,line width=.35pt,] (10.68000,3.02000) rectangle ++(0.68000,0.68000);
36 \node[] at (11.02000,3.36000) {$0$};
37 \draw[fill=black!12,draw=black!40,line width=.35pt,] (10.00000,2.34000) rectangle ++(0.68000,0.68000);
38 \node[] at (10.34000,2.68000) {$-1$};
39 \draw[fill=black!12,draw=black!40,line width=.35pt,] (10.68000,2.34000) rectangle ++(0.68000,0.68000);
40 \node[] at (11.02000,2.68000) {$1$};
41 \node[] at (9.00000,0.85000) {$Q_0+Q_1=I,\quad Q_i^2=Q_i$};
42 \node[] at (6.00000,-0.10000) {$\sum_{i,j}Q_i\Ob Q_j=\Ob;\qquad Q_0^{\mathsf T}\ne Q_0$};
43 \end{tikzpicture}

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