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 \draw[->] (0.60000,0.40000) -- (5.80000,0.40000);
3 \draw[->] (0.60000,0.40000) -- (0.60000,4.60000);
4 \draw[line width=1pt] (0.6000,0.4000) -- (0.7050,0.4012) -- (0.8100,0.4046) -- (0.9150,0.4104) -- (1.0200,0.4184) -- (1.1250,0.4288) -- (1.2300,0.4414) -- (1.3350,0.4564) -- (1.4400,0.4736) -- (1.5450,0.4932) -- (1.6500,0.5150) -- (1.7550,0.5392) -- (1.8600,0.5656) -- (1.9650,0.5944) -- (2.0700,0.6254) -- (2.1750,0.6588) -- (2.2800,0.6944) -- (2.3850,0.7324) -- (2.4900,0.7726) -- (2.5950,0.8152) -- (2.7000,0.8600) -- (2.8050,0.9072) -- (2.9100,0.9566) -- (3.0150,1.0084) -- (3.1200,1.0624) -- (3.2250,1.1187) -- (3.3300,1.1774) -- (3.4350,1.2384) -- (3.5400,1.3016) -- (3.6450,1.3672) -- (3.7500,1.4350) -- (3.8550,1.5051) -- (3.9600,1.5776) -- (4.0650,1.6524) -- (4.1700,1.7294) -- (4.2750,1.8088) -- (4.3800,1.8904) -- (4.4850,1.9743) -- (4.5900,2.0606) -- (4.6950,2.1492) -- (4.8000,2.2400);
5 \draw[line width=1pt,dashed] (0.6000,0.4000) -- (0.7050,0.4023) -- (0.8100,0.4092) -- (0.9150,0.4207) -- (1.0200,0.4368) -- (1.1250,0.4575) -- (1.2300,0.4828) -- (1.3350,0.5127) -- (1.4400,0.5472) -- (1.5450,0.5863) -- (1.6500,0.6300) -- (1.7550,0.6783) -- (1.8600,0.7312) -- (1.9650,0.7887) -- (2.0700,0.8508) -- (2.1750,0.9175) -- (2.2800,0.9888) -- (2.3850,1.0647) -- (2.4900,1.1452) -- (2.5950,1.2303) -- (2.7000,1.3200) -- (2.8050,1.4143) -- (2.9100,1.5132) -- (3.0150,1.6167) -- (3.1200,1.7248) -- (3.2250,1.8375) -- (3.3300,1.9548) -- (3.4350,2.0767) -- (3.5400,2.2032) -- (3.6450,2.3343) -- (3.7500,2.4700) -- (3.8550,2.6103) -- (3.9600,2.7552) -- (4.0650,2.9047) -- (4.1700,3.0588) -- (4.2750,3.2175) -- (4.3800,3.3808) -- (4.4850,3.5487) -- (4.5900,3.7212) -- (4.6950,3.8983) -- (4.8000,4.0800);
6 \node[] at (3.80000,2.10000) {$2x^2$};
7 \node[] at (3.80000,4.20000) {$4x^2$};
8 \node[] at (5.50000,0.10000) {$x$};
9 \draw[black!25] (6.20000,0.00000) -- (6.20000,4.75000);
10 \node[anchor=east] at (8.75000,3.94000) {$x$};
11 \draw[fill=black!0,draw=black!40,line width=.35pt,] (9.00000,3.65000) rectangle ++(0.87000,0.58000);
12 \node[] at (9.43500,3.94000) {$0$};
13 \draw[fill=black!0,draw=black!40,line width=.35pt,] (9.87000,3.65000) rectangle ++(0.87000,0.58000);
14 \node[] at (10.30500,3.94000) {$1$};
15 \draw[fill=black!0,draw=black!40,line width=.35pt,] (10.74000,3.65000) rectangle ++(0.87000,0.58000);
16 \node[] at (11.17500,3.94000) {$2$};
17 \node[anchor=east] at (8.75000,3.09000) {$2f(x)$};
18 \draw[fill=black!10,draw=black!40,line width=.35pt,] (9.00000,2.80000) rectangle ++(0.87000,0.58000);
19 \node[] at (9.43500,3.09000) {$0$};
20 \draw[fill=black!10,draw=black!40,line width=.35pt,] (9.87000,2.80000) rectangle ++(0.87000,0.58000);
21 \node[] at (10.30500,3.09000) {$2$};
22 \draw[fill=black!10,draw=black!40,line width=.35pt,] (10.74000,2.80000) rectangle ++(0.87000,0.58000);
23 \node[] at (11.17500,3.09000) {$8$};
24 \node[anchor=east] at (8.75000,2.24000) {$f(2x)$};
25 \draw[fill=black!10,draw=black!40,line width=.35pt,] (9.00000,1.95000) rectangle ++(0.87000,0.58000);
26 \node[] at (9.43500,2.24000) {$0$};
27 \draw[fill=black!10,draw=black!40,line width=.35pt,] (9.87000,1.95000) rectangle ++(0.87000,0.58000);
28 \node[] at (10.30500,2.24000) {$4$};
29 \draw[fill=black!10,draw=black!40,line width=.35pt,] (10.74000,1.95000) rectangle ++(0.87000,0.58000);
30 \node[] at (11.17500,2.24000) {$16$};
31 \node[anchor=east] at (8.75000,1.39000) {$2f(x)-f(2x)$};
32 \draw[fill=black!10,draw=black!40,line width=.35pt,] (9.00000,1.10000) rectangle ++(0.87000,0.58000);
33 \node[] at (9.43500,1.39000) {$0$};
34 \draw[fill=black!10,draw=black!40,line width=.35pt,] (9.87000,1.10000) rectangle ++(0.87000,0.58000);
35 \node[] at (10.30500,1.39000) {$-2$};
36 \draw[fill=black!10,draw=black!40,line width=.35pt,] (10.74000,1.10000) rectangle ++(0.87000,0.58000);
37 \node[] at (11.17500,1.39000) {$-8$};
38 \node[] at (9.65000,-0.05000) {correct chart formula: $f_b(v)=v^2/2$};
39 \end{tikzpicture}

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