\relax 
\@writefile{lof}{\contentsline {figure}{\numberline {1}{\ignorespaces (A) A representative closed PDS chain on a triangulated disk: source $L_0$, level cycles $L_1, L_2, L_3, L_4$ with sizes $5, 6, 5, 3$. Tires $T_1, T_2, T_3, T_4$ are the annular regions between consecutive levels. (B) The outer triangle's contribution in $G'$: the outer face of $G$ becomes a single $G'$-vertex of degree $3$. Proper edge $3$-colouring requires its three incident $G'$-edges (the duals of the three outer-triangle edges) to be distinct. So $\sigma |_{L_n}$ must be a permutation of $\{1,2,3\}$. (C) State trajectory for the chain $(6, 1) | (8, 6) | (10, 8) | (10, 10) | (8, 10) | (5, 8) | (3, 5)$: state grows where cycles are widest and \emph  {collapses to exactly $6$ at the outer triangle}.\relax }}{2}{}\protected@file@percent }
\providecommand*\caption@xref[2]{\@setref\relax\@undefined{#1}}
\newlabel{fig:absorption}{{1}{2}}
\newlabel{conj:absorption-local}{{}{3}}
\gdef \@abspage@last{4}
