Paper II: Refinement Towers, Weighted Transfer, and Integral Separation of Operator Packets

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1 \begin{tikzpicture}[x=1cm,y=1cm,>=Latex,font=\sffamily\small,line cap=round]
2 \node[circle,draw,minimum size=9mm] at (1.40000,2.00000) {$0$};
3 \node[circle,draw,minimum size=9mm] at (5.00000,2.00000) {$1$};
4 \draw[->] (1.5,2.45) to[out=100,in=170,looseness=6] node[above] {$\ell:1$} (1.05,2.2);
5 \draw[->] (1.85,2.25) to[bend left=25] node[above] {$a:2$} (4.55,2.25);
6 \draw[->] (1.85,1.97) -- node[above] {$b:2$} (4.55,1.97);
7 \draw[->] (4.6,1.7) to[bend left=30] node[below] {$r:1$} (1.8,1.7);
8 \node[] at (3.10000,0.00000) {\shortstack{Edge labels carry\\positive integer weights.}};
9 \draw[black!35] (6.15000,-0.45000) -- (6.15000,4.00000);
10 \node[font=\sffamily\bfseries] at (9.25000,3.60000) {All walks from 0 to 1 of weight 5};
11 \draw[fill=black!10,draw=black!45,line width=.35pt,] (7.10000,2.50000) rectangle ++(1.80000,0.58000);
12 \node[] at (8.00000,2.79000) {$\ell\ell\ell a$};
13 \draw[fill=black!10,draw=black!45,line width=.35pt,] (9.40000,2.50000) rectangle ++(1.80000,0.58000);
14 \node[] at (10.30000,2.79000) {$\ell\ell\ell b$};
15 \draw[fill=black!10,draw=black!45,line width=.35pt,] (7.10000,1.65000) rectangle ++(1.80000,0.58000);
16 \node[] at (8.00000,1.94000) {$ara$};
17 \draw[fill=black!10,draw=black!45,line width=.35pt,] (9.40000,1.65000) rectangle ++(1.80000,0.58000);
18 \node[] at (10.30000,1.94000) {$arb$};
19 \draw[fill=black!10,draw=black!45,line width=.35pt,] (7.10000,0.80000) rectangle ++(1.80000,0.58000);
20 \node[] at (8.00000,1.09000) {$bra$};
21 \draw[fill=black!10,draw=black!45,line width=.35pt,] (9.40000,0.80000) rectangle ++(1.80000,0.58000);
22 \node[] at (10.30000,1.09000) {$brb$};
23 \end{tikzpicture}

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