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 (4,4.4) {$d=1$};
4 \node[font=\small,align=center] at (5.5,4.4) {$d=2$};
5 \node[font=\small,align=center] at (7,4.4) {$d=3$};
6 \node[font=\small,align=center] at (8.5,4.4) {$d=4$};
7 \node[font=\small,align=center] at (10,4.4) {$d=5$};
8 \node[font=\small,align=center] at (11.5,4.4) {$d=6$};
9 \node[font=\small,align=center,anchor=east,font=\footnotesize] at (2.8,3.6) {trivial};
10 \path[draw=black!30,fill=white] (3.3,3.3) rectangle (4.7,3.88);
11 \node[font=\small,align=center,font=\scriptsize] at (4,3.6) {no};
12 \path[draw=black!30,fill=white] (4.8,3.3) rectangle (6.2,3.88);
13 \node[font=\small,align=center,font=\scriptsize] at (5.5,3.6) {no};
14 \path[draw=black!30,fill=white] (6.3,3.3) rectangle (7.7,3.88);
15 \node[font=\small,align=center,font=\scriptsize] at (7,3.6) {no};
16 \path[draw=black!30,fill=white] (7.8,3.3) rectangle (9.2,3.88);
17 \node[font=\small,align=center,font=\scriptsize] at (8.5,3.6) {no};
18 \path[draw=black!30,fill=white] (9.3,3.3) rectangle (10.7,3.88);
19 \node[font=\small,align=center,font=\scriptsize] at (10,3.6) {no};
20 \path[draw=black!30,fill=white] (10.8,3.3) rectangle (12.2,3.88);
21 \node[font=\small,align=center,font=\scriptsize] at (11.5,3.6) {no};
22 \node[font=\small,align=center,anchor=east,font=\footnotesize] at (2.8,2.75) {quartic};
23 \path[draw=black!30,fill=black!16] (3.3,2.45) rectangle (4.7,3.03);
24 \node[font=\small,align=center,font=\scriptsize] at (4,2.75) {yes};
25 \path[draw=black!30,fill=black!16] (4.8,2.45) rectangle (6.2,3.03);
26 \node[font=\small,align=center,font=\scriptsize] at (5.5,2.75) {yes};
27 \path[draw=black!30,fill=black!16] (6.3,2.45) rectangle (7.7,3.03);
28 \node[font=\small,align=center,font=\scriptsize] at (7,2.75) {yes};
29 \path[draw=black!30,fill=white] (7.8,2.45) rectangle (9.2,3.03);
30 \node[font=\small,align=center,font=\scriptsize] at (8.5,2.75) {no};
31 \path[draw=black!30,fill=black!16] (9.3,2.45) rectangle (10.7,3.03);
32 \node[font=\small,align=center,font=\scriptsize] at (10,2.75) {yes};
33 \path[draw=black!30,fill=black!16] (10.8,2.45) rectangle (12.2,3.03);
34 \node[font=\small,align=center,font=\scriptsize] at (11.5,2.75) {yes};
35 \node[font=\small,align=center,anchor=east,font=\footnotesize] at (2.8,1.9) {quadratic};
36 \path[draw=black!30,fill=black!16] (3.3,1.6) rectangle (4.7,2.18);
37 \node[font=\small,align=center,font=\scriptsize] at (4,1.9) {yes};
38 \path[draw=black!30,fill=white] (4.8,1.6) rectangle (6.2,2.18);
39 \node[font=\small,align=center,font=\scriptsize] at (5.5,1.9) {no};
40 \path[draw=black!30,fill=black!16] (6.3,1.6) rectangle (7.7,2.18);
41 \node[font=\small,align=center,font=\scriptsize] at (7,1.9) {yes};
42 \path[draw=black!30,fill=white] (7.8,1.6) rectangle (9.2,2.18);
43 \node[font=\small,align=center,font=\scriptsize] at (8.5,1.9) {no};
44 \path[draw=black!30,fill=black!16] (9.3,1.6) rectangle (10.7,2.18);
45 \node[font=\small,align=center,font=\scriptsize] at (10,1.9) {yes};
46 \path[draw=black!30,fill=white] (10.8,1.6) rectangle (12.2,2.18);
47 \node[font=\small,align=center,font=\scriptsize] at (11.5,1.9) {no};
48 \node[font=\small,align=center,anchor=east,font=\footnotesize] at (2.8,1.05) {conjugate quartic};
49 \path[draw=black!30,fill=black!16] (3.3,0.75) rectangle (4.7,1.33);
50 \node[font=\small,align=center,font=\scriptsize] at (4,1.05) {yes};
51 \path[draw=black!30,fill=black!16] (4.8,0.75) rectangle (6.2,1.33);
52 \node[font=\small,align=center,font=\scriptsize] at (5.5,1.05) {yes};
53 \path[draw=black!30,fill=black!16] (6.3,0.75) rectangle (7.7,1.33);
54 \node[font=\small,align=center,font=\scriptsize] at (7,1.05) {yes};
55 \path[draw=black!30,fill=white] (7.8,0.75) rectangle (9.2,1.33);
56 \node[font=\small,align=center,font=\scriptsize] at (8.5,1.05) {no};
57 \path[draw=black!30,fill=black!16] (9.3,0.75) rectangle (10.7,1.33);
58 \node[font=\small,align=center,font=\scriptsize] at (10,1.05) {yes};
59 \path[draw=black!30,fill=black!16] (10.8,0.75) rectangle (12.2,1.33);
60 \node[font=\small,align=center,font=\scriptsize] at (11.5,1.05) {yes};
61 \node[font=\small,align=center,font=\footnotesize] at (7,0.05) {For $\chi_k(2)=i^k$, a witness exists exactly when $kd\not\equiv0\pmod4$.};
62 \end{tikzpicture}

Back to source controls

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