Add per-dual summary table for the six Holton-McKay duals at n=21
Table tab:n21 records, for each of the six duals: not an intertwining tree; Even Level Graph source (duals 1,2 only); and bridge-switch path length to an ELG (0,0 for the two ELG-outright cases; 3,1,2,4 for the rest). All six are bridge-derived; all witnesses step-verified. Co-Authored-By: Claude Opus 4.7 <noreply@anthropic.com>
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@@ -405,7 +405,26 @@ classes: two are Even Level Graphs outright, and the other four are
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bridge-derived level graphs. The bridge-switch restriction is what made
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bridge-derived level graphs. The bridge-switch restriction is what made
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the search tractable -- it both shrinks the orbit and guarantees
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the search tractable -- it both shrinks the orbit and guarantees
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validity, so any Even Level Graph located in a backward orbit is an
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validity, so any Even Level Graph located in a backward orbit is an
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immediate witness.
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immediate witness. Table~\ref{tab:n21} records the outcome for each dual.
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\begin{table}[ht]
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\centering
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\begin{tabular}{cccc}
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dual & intertwining tree & Even Level Graph source & bridge switches to ELG \\\hline
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$0$ & no & -- & $3$ \\
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$1$ & no & $10$ & $0$ \\
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$2$ & no & $9$ & $0$ \\
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$3$ & no & -- & $1$ \\
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$4$ & no & -- & $2$ \\
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$5$ & no & -- & $4$ \\
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\end{tabular}
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\caption{The six Holton--McKay duals at $n = 21$, the first triangulations
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that are not intertwining trees. Each is a bridge-derived level graph:
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duals $1$ and $2$ are Even Level Graphs outright (zero switches), and the
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remaining four reach an Even Level Graph in $1$--$4$ bridge switches. All
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witnesses are step-verified.}
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\label{tab:n21}
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\end{table}
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\begin{thebibliography}{9}
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\begin{thebibliography}{9}
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