cancellation.tex
Paper VIII: Packet Operator Algorithms, Exact Compilation, and GPU Realization
cancellation.tex
This is the original TeX manuscript source. Use the paper’s PDF for typeset equations.
1 \begin{tikzpicture}[x=1cm,y=1cm,>=Stealth,line cap=round,line join=round]
2 \path[use as bounding box] (0,-.6) rectangle (14,4.8);
3 \node[font=\small,align=center,font=\small] at (2.3,4.3) {$K$};
4 \path[draw=black!30,fill=white] (0.7,2.8) rectangle (1.5,3.6);
5 \node[font=\small,align=center,font=\small] at (1.1,3.2) {$0$};
6 \path[draw=black!30,fill=white] (1.5,2.8) rectangle (2.3,3.6);
7 \node[font=\small,align=center,font=\small] at (1.9,3.2) {$0$};
8 \path[draw=black!30,fill=white] (2.3,2.8) rectangle (3.1,3.6);
9 \node[font=\small,align=center,font=\small] at (2.7,3.2) {$0$};
10 \path[draw=black!30,fill=white] (3.1,2.8) rectangle (3.9,3.6);
11 \node[font=\small,align=center,font=\small] at (3.5,3.2) {$0$};
12 \path[draw=black!30,fill=black!8] (0.7,2) rectangle (1.5,2.8);
13 \node[font=\small,align=center,font=\small] at (1.1,2.4) {$1$};
14 \path[draw=black!30,fill=white] (1.5,2) rectangle (2.3,2.8);
15 \node[font=\small,align=center,font=\small] at (1.9,2.4) {$0$};
16 \path[draw=black!30,fill=white] (2.3,2) rectangle (3.1,2.8);
17 \node[font=\small,align=center,font=\small] at (2.7,2.4) {$0$};
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20 \path[draw=black!30,fill=black!8] (0.7,1.2) rectangle (1.5,2);
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23 \node[font=\small,align=center,font=\small] at (1.9,1.6) {$0$};
24 \path[draw=black!30,fill=white] (2.3,1.2) rectangle (3.1,2);
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29 \node[font=\small,align=center,font=\small] at (1.1,0.8) {$0$};
30 \path[draw=black!30,fill=black!8] (1.5,0.4) rectangle (2.3,1.2);
31 \node[font=\small,align=center,font=\small] at (1.9,0.8) {$1$};
32 \path[draw=black!30,fill=black!8] (2.3,0.4) rectangle (3.1,1.2);
33 \node[font=\small,align=center,font=\small] at (2.7,0.8) {$-1$};
34 \path[draw=black!30,fill=white] (3.1,0.4) rectangle (3.9,1.2);
35 \node[font=\small,align=center,font=\small] at (3.5,0.8) {$0$};
36 \node[font=\small,align=center,font=\small] at (7.2,4.3) {path counts at length two};
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41 \path[draw=black!30,fill=white] (7.2,2.8) rectangle (8,3.6);
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43 \path[draw=black!30,fill=white] (8,2.8) rectangle (8.8,3.6);
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51 \path[draw=black!30,fill=white] (8,2) rectangle (8.8,2.8);
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53 \path[draw=black!30,fill=white] (5.6,1.2) rectangle (6.4,2);
54 \node[font=\small,align=center,font=\small] at (6,1.6) {$0$};
55 \path[draw=black!30,fill=white] (6.4,1.2) rectangle (7.2,2);
56 \node[font=\small,align=center,font=\small] at (6.8,1.6) {$0$};
57 \path[draw=black!30,fill=white] (7.2,1.2) rectangle (8,2);
58 \node[font=\small,align=center,font=\small] at (7.6,1.6) {$0$};
59 \path[draw=black!30,fill=white] (8,1.2) rectangle (8.8,2);
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61 \path[draw=black!30,fill=black!8] (5.6,0.4) rectangle (6.4,1.2);
62 \node[font=\small,align=center,font=\small] at (6,0.8) {$2$};
63 \path[draw=black!30,fill=white] (6.4,0.4) rectangle (7.2,1.2);
64 \node[font=\small,align=center,font=\small] at (6.8,0.8) {$0$};
65 \path[draw=black!30,fill=white] (7.2,0.4) rectangle (8,1.2);
66 \node[font=\small,align=center,font=\small] at (7.6,0.8) {$0$};
67 \path[draw=black!30,fill=white] (8,0.4) rectangle (8.8,1.2);
68 \node[font=\small,align=center,font=\small] at (8.4,0.8) {$0$};
69 \node[font=\small,align=center] at (11.85,3) {$1+(-1)=0$};
70 \node[font=\small,align=center] at (11.85,1.65) {$K^2=0$};
71 \node[font=\small,align=center,font=\scriptsize] at (7,0.1) {Structural support is an upper bound. It does not encode destructive cancellation.};
72 \end{tikzpicture}
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