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

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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 (2.77,4.55) {multiplicity difference $\delta m$};
4 \path[draw=black!30,fill=black!8] (2.4,3.11) rectangle (3.14,3.85);
5 \node[font=\small,align=center,font=\small] at (2.77,3.48) {$4$};
6 \path[draw=black!30,fill=black!8] (2.4,2.37) rectangle (3.14,3.11);
7 \node[font=\small,align=center,font=\small] at (2.77,2.74) {$4$};
8 \path[draw=black!30,fill=white] (2.4,1.63) rectangle (3.14,2.37);
9 \node[font=\small,align=center,font=\small] at (2.77,2) {$0$};
10 \node[font=\small,align=center,font=\small] at (9.37,4.55) {trace difference $C\delta m$};
11 \path[draw=black!30,fill=black!8] (9,3.11) rectangle (9.74,3.85);
12 \node[font=\small,align=center,font=\small] at (9.37,3.48) {$8$};
13 \path[draw=black!30,fill=white] (9,2.37) rectangle (9.74,3.11);
14 \node[font=\small,align=center,font=\small] at (9.37,2.74) {$0$};
15 \path[draw=black!30,fill=black!8] (9,1.63) rectangle (9.74,2.37);
16 \node[font=\small,align=center,font=\small] at (9.37,2) {$8$};
17 \draw[->,line width=.8pt] (4.35,2.8) -- (7.65,2.8);
18 \node[font=\small,align=center] at (6,3.3) {multiply by $C$};
19 \node[font=\small,align=center] at (3.2,1.15) {nonzero modulo $8$};
20 \node[font=\small,align=center] at (10,1.15) {zero modulo $8$};
21 \node[font=\small,align=center,font=\footnotesize] at (7,0.25) {Modulo $16$, the traces separate them. $v_2(\det C)=v_2(6)=1$.};
22 \end{tikzpicture}

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