Paper VII: Quantum Seed Calculus

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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 \draw[->,line width=.8pt] (0.8,2.3) -- (13,2.3);
4 \path[fill=black] (2.610913,2.3) circle (0.1);
5 \draw[black!50] (2.610913,2.45) -- (2.610913,3.15);
6 \node[font=\small,align=center] at (2.610913,3.4) {$1-\sqrt2$};
7 \path[fill=black] (10.389087,2.3) circle (0.1);
8 \draw[black!50] (10.389087,2.45) -- (10.389087,3.15);
9 \node[font=\small,align=center] at (10.389087,3.4) {$1+\sqrt2$};
10 \path[draw,fill=white] (9.25,2.3) circle (0.1);
11 \draw[black!50] (9.25,2.15) -- (9.25,1.55);
12 \node[font=\small,align=center] at (9.25,1.3) {$2$};
13 \path[draw,fill=white] (12,2.3) circle (0.1);
14 \draw[black!50] (12,2.15) -- (12,1.55);
15 \node[font=\small,align=center] at (12,1.3) {$3$};
16 \node[font=\small,align=center,font=\scriptsize] at (6.9,4.55) {Filled: full resolvent poles. Open at 2: only the eliminated inverse fails.};
17 \node[font=\small,align=center,font=\small] at (6.9,0.12) {At $z=3$: exact retained resolvent $1/2$, bare truncation $1/3$.};
18 \end{tikzpicture}

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