28_frobenius_boundary.tex

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

28_frobenius_boundary.tex

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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=\scriptsize] at (1.25,4) {$3$};
4 \node[font=\small,align=center,font=\scriptsize] at (1.25,3.3) {$0$};
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6 \node[font=\small,align=center,font=\scriptsize] at (1.85,3.3) {$2$};
7 \node[font=\small,align=center,font=\scriptsize] at (2.45,4) {$7$};
8 \node[font=\small,align=center,font=\scriptsize] at (2.45,3.3) {$0$};
9 \node[font=\small,align=center,font=\scriptsize] at (3.05,4) {$11$};
10 \node[font=\small,align=center,font=\scriptsize] at (3.05,3.3) {$0$};
11 \node[font=\small,align=center,font=\scriptsize] at (3.65,4) {$13$};
12 \node[font=\small,align=center,font=\scriptsize] at (3.65,3.3) {$2$};
13 \node[font=\small,align=center,font=\scriptsize] at (4.25,4) {$17$};
14 \node[font=\small,align=center,font=\scriptsize] at (4.25,3.3) {$2$};
15 \node[font=\small,align=center,font=\scriptsize] at (4.85,4) {$19$};
16 \node[font=\small,align=center,font=\scriptsize] at (4.85,3.3) {$0$};
17 \node[font=\small,align=center,font=\scriptsize] at (5.45,4) {$23$};
18 \node[font=\small,align=center,font=\scriptsize] at (5.45,3.3) {$0$};
19 \node[font=\small,align=center] at (3.4,4.65) {odd primes $p$};
20 \node[font=\small,align=center,font=\scriptsize] at (3.4,2.7) {roots of $x^2+1$ in $\mathbb F_p$};
21 \node[font=\small,align=center,font=\footnotesize] at (3.4,1.5) {two factorization types\\already appear in this finite list};
22 \node[font=\small,align=center,font=\small] at (9.155,4.4) {repeat one class};
23 \path[draw=black!30,fill=black!8] (8,2.93) rectangle (8.77,3.7);
24 \node[font=\small,align=center,font=\small] at (8.385,3.315) {$1$};
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40 \node[font=\small,align=center,font=\small] at (9.925,1.775) {$2$};
41 \node[font=\small,align=center] at (10.2,0.8) {three rows, rank one};
42 \node[font=\small,align=center,font=\footnotesize] at (7,-0.1) {Finite character separation needs enough different evaluations, not just more evaluations.};
43 \end{tikzpicture}

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