Add labelled sequencing example figure

Embed a worked example of the canonical quadrilateral sequencing into the
paper. The new figure shows the deep embedding of a 9-vertex triangulation
with each quadrilateral filled by type (shallow diamond, deep diamond, S
quad) and annotated with its sequence index and move code. The generator
script renders the figure from a fixed Sage RNG seed for reproducibility.

Co-Authored-By: Claude Opus 4.7 <noreply@anthropic.com>

papers/plane_depth_sequencing/paper.tex

@@ -37,6 +37,7 @@
 \documentclass{amsart}
 
 \usepackage{amssymb}
+\usepackage{graphicx}
 
 \newtheorem{theorem}{Theorem}[section]
 \newtheorem{lemma}[theorem]{Lemma}
@@ -255,6 +256,13 @@ At each step $n \geq 1$, the next quadrilateral $Q_{n+1}$ is chosen by the first
 That is, each move is consulted only when no higher-precedence move applies.
 \end{definition}
 
+\begin{figure}
+\centering
+\includegraphics[width=0.85\textwidth]{example_figure.pdf}
+\caption{The deep embedding $G'$ of a small maximal planar graph (drawn with one outer-cap face as the outer face), with each quadrilateral $Q_n$ of the canonical sequence labelled by its index and the move code (AD = anchor drop, LA = level add, J = join, RC = ring completion) of the move that produced it. Solid edges are non-level; dashed edges are level. Background colour encodes quadrilateral type: amber for shallow diamonds, teal for deep diamonds, pink for S quads. Outer-cycle vertices are blue, the outer-cap vertex $x^{*}$ is red. The move-code string for this example is $01211333$.}
+\label{fig:example-sequence}
+\end{figure}
+
 Let $N$ denote the total number of quadrilaterals in the decomposition of $G'$; equivalently, $N = |F(G')|/2$, where $F(G')$ is the set of triangular faces of $G'$.
 
 \begin{theorem}[Termination and coverage]