Paper I: Typed Operator Systems, Seed Rank, and Exact Packet Coordinates

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1 \begin{tikzpicture}[x=1cm,y=1cm,>=Latex,
2  every node/.style={font=\sffamily\small},line cap=round,line join=round]
3 \node[circle,draw,minimum size=8mm,fill=white] at (0.0000,0.0000) {$e_1$};
4 \node[circle,draw,minimum size=8mm,fill=white] at (2.0000,1.2500) {$e_2$};
5 \node[circle,draw,minimum size=8mm,fill=white] at (2.0000,-1.2500) {$e_3$};
6 \node[circle,draw,minimum size=8mm,fill=white] at (4.0000,0.0000) {$e_4$};
7 \draw[->,thick,shorten <=5mm,shorten >=5mm] (0,0) -- node[above,sloped,font=\scriptsize] {$+1$} (2,1.25);
8 \draw[->,thick,shorten <=5mm,shorten >=5mm] (0,0) -- node[above,sloped,font=\scriptsize] {$+1$} (2,-1.25);
9 \draw[->,thick,shorten <=5mm,shorten >=5mm] (2,1.25) -- node[above,sloped,font=\scriptsize] {$+1$} (4,0);
10 \draw[->,thick,shorten <=5mm,shorten >=5mm] (2,-1.25) -- node[above,sloped,font=\scriptsize] {$-1$} (4,0);
11 \filldraw[fill=black!78,draw=white,line width=.8pt] (6.1000,1.6500) rectangle ++(0.6300,-0.6300);
12 \node[text=white,font=\scriptsize] at (6.4150,1.3350) {$1$};
13 \filldraw[fill=black!5,draw=white,line width=.8pt] (6.7300,1.6500) rectangle ++(0.6300,-0.6300);
14 \node[text=black!45,font=\scriptsize] at (7.0450,1.3350) {$0$};
15 \filldraw[fill=black!5,draw=white,line width=.8pt] (7.3600,1.6500) rectangle ++(0.6300,-0.6300);
16 \node[text=black!45,font=\scriptsize] at (7.6750,1.3350) {$0$};
17 \filldraw[fill=black!5,draw=white,line width=.8pt] (6.1000,1.0200) rectangle ++(0.6300,-0.6300);
18 \node[text=black!45,font=\scriptsize] at (6.4150,0.7050) {$0$};
19 \filldraw[fill=black!78,draw=white,line width=.8pt] (6.7300,1.0200) rectangle ++(0.6300,-0.6300);
20 \node[text=white,font=\scriptsize] at (7.0450,0.7050) {$1$};
21 \filldraw[fill=black!5,draw=white,line width=.8pt] (7.3600,1.0200) rectangle ++(0.6300,-0.6300);
22 \node[text=black!45,font=\scriptsize] at (7.6750,0.7050) {$0$};
23 \filldraw[fill=black!5,draw=white,line width=.8pt] (6.1000,0.3900) rectangle ++(0.6300,-0.6300);
24 \node[text=black!45,font=\scriptsize] at (6.4150,0.0750) {$0$};
25 \filldraw[fill=black!78,draw=white,line width=.8pt] (6.7300,0.3900) rectangle ++(0.6300,-0.6300);
26 \node[text=white,font=\scriptsize] at (7.0450,0.0750) {$1$};
27 \filldraw[fill=black!5,draw=white,line width=.8pt] (7.3600,0.3900) rectangle ++(0.6300,-0.6300);
28 \node[text=black!45,font=\scriptsize] at (7.6750,0.0750) {$0$};
29 \filldraw[fill=black!5,draw=white,line width=.8pt] (6.1000,-0.2400) rectangle ++(0.6300,-0.6300);
30 \node[text=black!45,font=\scriptsize] at (6.4150,-0.5550) {$0$};
31 \filldraw[fill=black!5,draw=white,line width=.8pt] (6.7300,-0.2400) rectangle ++(0.6300,-0.6300);
32 \node[text=black!45,font=\scriptsize] at (7.0450,-0.5550) {$0$};
33 \filldraw[fill=black!5,draw=white,line width=.8pt] (7.3600,-0.2400) rectangle ++(0.6300,-0.6300);
34 \node[text=black!45,font=\scriptsize] at (7.6750,-0.5550) {$0$};
35 \draw[black!60,line width=.5pt] (6.1,1.65) rectangle ++(1.8900000000000001,-2.52);
36 \node[font=\sffamily\bfseries\small] at (7.0450,2.1300) {$[e_1,De_1,D^2e_1]$};
37 \node[] at (7.0450,-1.3500) {rank $=2$};
38 \node[] at (2.0000,-2.0500) {$(D^2)_{41}=1-1=0$};
39 \end{tikzpicture}

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