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Extend Level Switching paper with d>=2 preprocessing analysis

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Add 21-vertex and 24-vertex examples showing recursive lopsidedness
at d=2. Empirically confirm that the iterated algorithm (balanced
switch when available, preprocess otherwise) drives every face to
depth 0 on all tested configurations. Frame the remaining open
question as identifying a strictly-decreasing monovariant under
unbalanced preprocessing switches.

Co-Authored-By: Claude Opus 4.7 <noreply@anthropic.com>
This commit is contained in:
didericis
2026-05-20 23:20:06 -04:00
parent 7183dc1b67
commit 77093cb0b0
12 changed files with 827 additions and 28 deletions
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papers/level_switching/paper.log
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@@ -413,7 +413,7 @@ bal-anced-ness gives $[](\OML/cmm/m/it/10 A[]\OT1/cmr/m/n/10 ) = \OML/cmm/m/it/
/m/n/10 ) \OMS/cmsy/m/n/10 ^^T
[]
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\OT1/cmr/m/n/10 the unique depth-$2$ face $\OML/cmm/m/it/10 F \OT1/cmr/m/n/10 =
(0\OML/cmm/m/it/10 ; \OT1/cmr/m/n/10 7\OML/cmm/m/it/10 ; \OT1/cmr/m/n/10 14)$
has three depth-$1$ neigh-bours $(0\OML/cmm/m/it/10 ; \OT1/cmr/m/n/10 3\OML/cmm
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T1/cmr/m/n/10 0)$,
[]
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\OT1/cmr/m/n/10 each lop-sided: their depth-$1$ "deep side" is a degree-$3$ fac
e $(3\OML/cmm/m/it/10 ; \OT1/cmr/m/n/10 5\OML/cmm/m/it/10 ; \OT1/cmr/m/n/10 7)\
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/m/it/10 ; \OT1/cmr/m/n/10 19\OML/cmm/m/it/10 ; \OT1/cmr/m/n/10 0)$
[]
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Output written on paper.pdf (8 pages, 1034024 bytes).
Output written on paper.pdf (9 pages, 1268281 bytes).
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