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 <noreply@anthropic.com>
The hunt only logged partition indices; the actual witness ELGs were lost.
Re-extract them (deterministic) with full bridge-switch paths and verify
every step independently. Saved as experiments/witnesses/dual_<i>.json
(labels, ELG source, ELG + dual graph6 and edge lists, the explicit
remove/add bridge-switch sequence, verified flag). All four verify:
dual 0: ELG source 18, 3 bridge switches to dual
dual 3: ELG source 16, 1 bridge switch to dual
dual 4: ELG source 20, 2 bridge switches to dual
dual 5: ELG source 1, 4 bridge switches to dual
So each dual is only a handful of bridge switches from an Even Level Graph,
and the witnesses are now reproducible and human-checkable.
Co-Authored-By: Claude Opus 4.7 <noreply@anthropic.com>
didericis