Paper X: Universal Residual Seeds and Conditional Occupied-System Completion

Download original file

This is the original TeX manuscript source. Use the paper’s PDF for typeset equations.

Read the typeset paper

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] at (2,4.4) {mod $5^{1}$};
4 \path[draw,fill=white] (2,3.3) circle (0.3);
5 \node[font=\small,align=center,font=\scriptsize] at (2,3.3) {$2$};
6 \path[draw,fill=white] (2,1.5) circle (0.3);
7 \node[font=\small,align=center,font=\scriptsize] at (2,1.5) {$3$};
8 \draw[<->] (2,3.05) -- (2,1.75);
9 \node[font=\small,align=center,font=\scriptsize] at (2.45,2.4) {$-x$};
10 \node[font=\small,align=center] at (5.15,4.4) {mod $5^{2}$};
11 \path[draw,fill=white] (5.15,3.3) circle (0.3);
12 \node[font=\small,align=center,font=\scriptsize] at (5.15,3.3) {$7$};
13 \path[draw,fill=white] (5.15,1.5) circle (0.3);
14 \node[font=\small,align=center,font=\scriptsize] at (5.15,1.5) {$18$};
15 \draw[<->] (5.15,3.05) -- (5.15,1.75);
16 \node[font=\small,align=center,font=\scriptsize] at (5.6,2.4) {$-x$};
17 \draw[->] (4.9,3.3) -- (2.25,3.3);
18 \draw[->] (4.9,1.5) -- (2.25,1.5);
19 \node[font=\small,align=center] at (8.3,4.4) {mod $5^{3}$};
20 \path[draw,fill=white] (8.3,3.3) circle (0.3);
21 \node[font=\small,align=center,font=\scriptsize] at (8.3,3.3) {$57$};
22 \path[draw,fill=white] (8.3,1.5) circle (0.3);
23 \node[font=\small,align=center,font=\scriptsize] at (8.3,1.5) {$68$};
24 \draw[<->] (8.3,3.05) -- (8.3,1.75);
25 \node[font=\small,align=center,font=\scriptsize] at (8.75,2.4) {$-x$};
26 \draw[->] (8.05,3.3) -- (5.4,3.3);
27 \draw[->] (8.05,1.5) -- (5.4,1.5);
28 \node[font=\small,align=center] at (11.45,4.4) {mod $5^{4}$};
29 \path[draw,fill=white] (11.45,3.3) circle (0.3);
30 \node[font=\small,align=center,font=\scriptsize] at (11.45,3.3) {$182$};
31 \path[draw,fill=white] (11.45,1.5) circle (0.3);
32 \node[font=\small,align=center,font=\scriptsize] at (11.45,1.5) {$443$};
33 \draw[<->] (11.45,3.05) -- (11.45,1.75);
34 \node[font=\small,align=center,font=\scriptsize] at (11.9,2.4) {$-x$};
35 \draw[->] (11.2,3.3) -- (8.55,3.3);
36 \draw[->] (11.2,1.5) -- (8.55,1.5);
37 \node[font=\small,align=center,font=\footnotesize] at (7,0.3) {Negation commutes with reduction. Translation by $1$ fails already at $2\mapsto3\mapsto4$ mod $5$.};
38 \end{tikzpicture}

Back to source controls

Back to Paper X: Universal Residual Seeds and Conditional Occupied-System Completion