From 5f6a04571c0f68eb159d9866a8a29078f3d03ede Mon Sep 17 00:00:00 2001 From: didericis Date: Fri, 22 May 2026 11:11:25 -0400 Subject: [PATCH] Confirm duals 1,2 are Even Level Graphs outright; archive all six witnesses Tested duals 1 and 2: both are Even Level Graphs directly (dual 1 for source 10, dual 2 for source 9), so bridge-derived with a zero-length switch sequence. All six Holton-McKay duals are confirmed non-intertwining (consistent with the dual-Hamiltonian theorem, since all six HM graphs are non-Hamiltonian) and all six are bridge-derived. Saved witness files dual_1.json, dual_2.json (0 switches) to complete the archive for all six. Updated the n=21 subsection accordingly. Co-Authored-By: Claude Opus 4.7 --- .../experiments/witnesses/dual_1.json | 495 +++++++++++++++ .../experiments/witnesses/dual_2.json | 495 +++++++++++++++ .../paper.fdb_latexmk | 100 +++ papers/even_level_graph_generators/paper.fls | 584 ++++++++++++++++++ papers/even_level_graph_generators/paper.log | 12 +- papers/even_level_graph_generators/paper.pdf | Bin 550765 -> 550793 bytes papers/even_level_graph_generators/paper.tex | 5 +- 7 files changed, 1683 insertions(+), 8 deletions(-) create mode 100644 papers/even_level_graph_generators/experiments/witnesses/dual_1.json create mode 100644 papers/even_level_graph_generators/experiments/witnesses/dual_2.json create mode 100644 papers/even_level_graph_generators/paper.fdb_latexmk create mode 100644 papers/even_level_graph_generators/paper.fls diff --git a/papers/even_level_graph_generators/experiments/witnesses/dual_1.json b/papers/even_level_graph_generators/experiments/witnesses/dual_1.json new file mode 100644 index 0000000..fea82d3 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t#0+_6$lDCHK@k{H->!W6d-&}g@BRZ^j!{RKU}p#*2{SngB_%~qMhbL3QaS(t diff --git a/papers/even_level_graph_generators/paper.tex b/papers/even_level_graph_generators/paper.tex index 62c0bdc..30dffee 100644 --- a/papers/even_level_graph_generators/paper.tex +++ b/papers/even_level_graph_generators/paper.tex @@ -396,8 +396,9 @@ partitions of the same triangulations have orbits exceeding $10^6$; finding one good partition suffices. Each witness is in fact only a \emph{handful} of bridge switches from its dual: the explicit Even Level Graph, parity labelling, and bridge-switch sequence are recorded for all -four, with path lengths $3, 1, 2, 4$ respectively, and each step has been -verified to be a valid bridge switch. +six -- path lengths $3,1,2,4$ for these four and $0$ for the two that are +Even Level Graphs outright -- and each step has been verified to be a +valid bridge switch. \end{itemize} Thus at $n = 21$ the disjunction is confirmed for all six critical iso classes: two are Even Level Graphs outright, and the other four are