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

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43 \draw[fill=white,draw=black!65] (1.950,1.950) circle (.045);
44 \draw[->] (-2.20000,0.00000) -- (2.50000,0.00000);
45 \draw[->] (0.00000,-1.50000) -- (0.00000,2.45000);
46 \draw[->,line width=1.1pt] (0.00000,0.00000) -- (0.65000,0.00000);
47 \node[] at (1.15000,0.30000) {$(1,0)$};
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49 \node[] at (-1.22000,1.48000) {$(-1,2)$};
50 \draw[fill=white,line width=1.2pt] (.325,0) circle (.095);
51 \node[] at (0.00000,-2.03000) {$E_+(0,1)=(\frac12,0)$};
52 \node[] at (6.45000,1.60000) {$B=\begin{pmatrix}1&-1\\0&2\end{pmatrix},\quad\det B=2$};
53 \node[] at (6.45000,0.60000) {Filled: $B\mathbb Z^2=\{(x,y):y\text{ is even}\}$};
54 \node[] at (6.45000,-0.35000) {Unfilled: the other lattice coset.};
55 \node[] at (6.45000,-1.25000) {$B^{-1}$ is integral at odd primes, not at $2$.};
56 \end{tikzpicture}

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