02_extension.tex

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02_extension.tex

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1 \begin{tikzpicture}[x=1cm,y=1cm]
2 \node[box,text width=3.15cm,minimum height=1.3cm] (raw) at (-5,1.6) {raw extension\\$p_U\widetilde s=s$};
3 \node[box,text width=2.8cm,minimum height=1.3cm] (res) at (0,1.6) {measured defect\\$\delta\widetilde s$};
4 \node[box,text width=3.55cm,minimum height=1.3cm] (obs) at (5,1.6) {obstruction class\\$[\delta\widetilde s]\in R/\delta(\ker p_U)$};
5 \node[box,text width=3.15cm,minimum height=1.3cm] (allow) at (-5,-1.5) {permitted change\\$h\in\ker p_U$};
6 \node[box,text width=2.8cm,minimum height=1.3cm] (image) at (0,-1.5) {removable defect\\$\delta h$};
7 \node[box,text width=3.55cm,minimum height=1.3cm] (zero) at (5,-1.5) {zero in the quotient\\$[\delta h]=0$};
8 \draw[arr] (raw) -- node[lab,above] {$\delta$} (res);
9 \draw[arr] (res) -- node[lab,above,font=\footnotesize] {quotient} (obs);
10 \draw[arr] (allow) -- node[lab,above] {$\delta$} (image);
11 \draw[arr] (image) -- node[lab,above,font=\footnotesize] {quotient} (zero);
12 \draw[<->,thick,draw=KomorebiOchre] (res.south)--(image.north);
13 \node[lab,fill=white,inner sep=4pt] at (0,.05) {$\delta\widetilde s=\delta h$};
14 \node[lab,text width=4.0cm] at (-4.8,.05) {This equality is the\\repair equation.};
15 \node[lab,text width=4.1cm] at (5,.05) {Solvable exactly when\\the top class is zero.};
16 \node[lab,text width=13.7cm] at (0,-2.8) {Then $x=\widetilde s-h$ satisfies both $\delta x=0$ and $p_Ux=s$.};
17 \end{tikzpicture}

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