19_hypotheses.tex

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

19_hypotheses.tex

Download original file

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

Read the typeset paper

Skip source text

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 (2.7,4.65) {$I_5$ over $\mathbb F_5$};
4 \path[draw=black!30,fill=black!8] (1.5,3.47) rectangle (1.98,3.95);
5 \node[font=\small,align=center,font=\small] at (1.74,3.71) {$1$};
6 \path[draw=black!30,fill=white] (1.98,3.47) rectangle (2.46,3.95);
7 \node[font=\small,align=center,font=\small] at (2.22,3.71) {$0$};
8 \path[draw=black!30,fill=white] (2.46,3.47) rectangle (2.94,3.95);
9 \node[font=\small,align=center,font=\small] at (2.7,3.71) {$0$};
10 \path[draw=black!30,fill=white] (2.94,3.47) rectangle (3.42,3.95);
11 \node[font=\small,align=center,font=\small] at (3.18,3.71) {$0$};
12 \path[draw=black!30,fill=white] (3.42,3.47) rectangle (3.9,3.95);
13 \node[font=\small,align=center,font=\small] at (3.66,3.71) {$0$};
14 \path[draw=black!30,fill=white] (1.5,2.99) rectangle (1.98,3.47);
15 \node[font=\small,align=center,font=\small] at (1.74,3.23) {$0$};
16 \path[draw=black!30,fill=black!8] (1.98,2.99) rectangle (2.46,3.47);
17 \node[font=\small,align=center,font=\small] at (2.22,3.23) {$1$};
18 \path[draw=black!30,fill=white] (2.46,2.99) rectangle (2.94,3.47);
19 \node[font=\small,align=center,font=\small] at (2.7,3.23) {$0$};
20 \path[draw=black!30,fill=white] (2.94,2.99) rectangle (3.42,3.47);
21 \node[font=\small,align=center,font=\small] at (3.18,3.23) {$0$};
22 \path[draw=black!30,fill=white] (3.42,2.99) rectangle (3.9,3.47);
23 \node[font=\small,align=center,font=\small] at (3.66,3.23) {$0$};
24 \path[draw=black!30,fill=white] (1.5,2.51) rectangle (1.98,2.99);
25 \node[font=\small,align=center,font=\small] at (1.74,2.75) {$0$};
26 \path[draw=black!30,fill=white] (1.98,2.51) rectangle (2.46,2.99);
27 \node[font=\small,align=center,font=\small] at (2.22,2.75) {$0$};
28 \path[draw=black!30,fill=black!8] (2.46,2.51) rectangle (2.94,2.99);
29 \node[font=\small,align=center,font=\small] at (2.7,2.75) {$1$};
30 \path[draw=black!30,fill=white] (2.94,2.51) rectangle (3.42,2.99);
31 \node[font=\small,align=center,font=\small] at (3.18,2.75) {$0$};
32 \path[draw=black!30,fill=white] (3.42,2.51) rectangle (3.9,2.99);
33 \node[font=\small,align=center,font=\small] at (3.66,2.75) {$0$};
34 \path[draw=black!30,fill=white] (1.5,2.03) rectangle (1.98,2.51);
35 \node[font=\small,align=center,font=\small] at (1.74,2.27) {$0$};
36 \path[draw=black!30,fill=white] (1.98,2.03) rectangle (2.46,2.51);
37 \node[font=\small,align=center,font=\small] at (2.22,2.27) {$0$};
38 \path[draw=black!30,fill=white] (2.46,2.03) rectangle (2.94,2.51);
39 \node[font=\small,align=center,font=\small] at (2.7,2.27) {$0$};
40 \path[draw=black!30,fill=black!8] (2.94,2.03) rectangle (3.42,2.51);
41 \node[font=\small,align=center,font=\small] at (3.18,2.27) {$1$};
42 \path[draw=black!30,fill=white] (3.42,2.03) rectangle (3.9,2.51);
43 \node[font=\small,align=center,font=\small] at (3.66,2.27) {$0$};
44 \path[draw=black!30,fill=white] (1.5,1.55) rectangle (1.98,2.03);
45 \node[font=\small,align=center,font=\small] at (1.74,1.79) {$0$};
46 \path[draw=black!30,fill=white] (1.98,1.55) rectangle (2.46,2.03);
47 \node[font=\small,align=center,font=\small] at (2.22,1.79) {$0$};
48 \path[draw=black!30,fill=white] (2.46,1.55) rectangle (2.94,2.03);
49 \node[font=\small,align=center,font=\small] at (2.7,1.79) {$0$};
50 \path[draw=black!30,fill=white] (2.94,1.55) rectangle (3.42,2.03);
51 \node[font=\small,align=center,font=\small] at (3.18,1.79) {$0$};
52 \path[draw=black!30,fill=black!8] (3.42,1.55) rectangle (3.9,2.03);
53 \node[font=\small,align=center,font=\small] at (3.66,1.79) {$1$};
54 \node[font=\small,align=center] at (2.7,0.8) {rank $5$, trace $0$};
55 \draw[black!25] (6.1,0.1) -- (6.1,4.45);
56 \node[font=\small,align=center,font=\small] at (8.4,4.2) {$N^2=0$};
57 \path[draw=black!30,fill=white] (7.6,2.7) rectangle (8.4,3.5);
58 \node[font=\small,align=center,font=\small] at (8,3.1) {$0$};
59 \path[draw=black!30,fill=black!8] (8.4,2.7) rectangle (9.2,3.5);
60 \node[font=\small,align=center,font=\small] at (8.8,3.1) {$1$};
61 \path[draw=black!30,fill=white] (7.6,1.9) rectangle (8.4,2.7);
62 \node[font=\small,align=center,font=\small] at (8,2.3) {$0$};
63 \path[draw=black!30,fill=white] (8.4,1.9) rectangle (9.2,2.7);
64 \node[font=\small,align=center,font=\small] at (8.8,2.3) {$0$};
65 \node[font=\small,align=center] at (11.6,2.95) {only eigenvalue $0$};
66 \node[font=\small,align=center] at (11.6,2.1) {$\dim\ker N=1$};
67 \node[font=\small,align=center] at (10.4,0.8) {sole-eigenvalue product $=I_2$};
68 \node[font=\small,align=center,font=\footnotesize] at (7,-0.05) {Keep characteristic zero for trace detection, and split semisimplicity for the Lagrange formula.};
69 \end{tikzpicture}

Back to source controls

Other PDFs for this work

Original file and source record

This copy matches the recorded source file. Its publication here does not change the work’s review status.

SHA-256: a6efb01312ef6daec999f9a20dddeb0bc418c969c4b403098a27b8a04d7214fc

Original source on GitHub

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