From 411ff7f46506b008ea47e1cbfd30f11a138e06cc Mon Sep 17 00:00:00 2001 From: didericis Date: Wed, 17 Jun 2026 20:27:36 -0400 Subject: [PATCH] Add the lower-bound proof programme to the note Section 4: un-stacking lemma (degree-3 removal preserves Phi, proved), ear-peeling base case (k=0 => 2^(n-2)), reduction to the irreducible case, and the irreducible lemma as the sole open conjecture (|Phi| >= 5/4 * 2^(n-2), tight at the degree-4/5 patch; wheel = floor(2^n/3) is not extremal). Records the two dead ends (monotonicity false, universal toggles insufficient) and ties each claim to its experiment. Co-Authored-By: Claude Opus 4.8 --- .../notes/boundary_restriction_structure.aux | 6 +- .../notes/boundary_restriction_structure.log | 83 +++++++++--------- .../notes/boundary_restriction_structure.pdf | Bin 185232 -> 217886 bytes .../notes/boundary_restriction_structure.tex | 82 +++++++++++++++++ 4 files changed, 130 insertions(+), 41 deletions(-) diff --git a/papers/heawood_restrictions_on_nested_tire_graph_duals/notes/boundary_restriction_structure.aux b/papers/heawood_restrictions_on_nested_tire_graph_duals/notes/boundary_restriction_structure.aux index d490c35..9861c5c 100644 --- a/papers/heawood_restrictions_on_nested_tire_graph_duals/notes/boundary_restriction_structure.aux +++ b/papers/heawood_restrictions_on_nested_tire_graph_duals/notes/boundary_restriction_structure.aux @@ -1,2 +1,6 @@ \relax -\gdef \@abspage@last{2} +\newlabel{lem:unstack}{{}{2}} +\newlabel{lem:base}{{}{3}} +\newlabel{prop:reduction}{{}{3}} +\newlabel{conj:irreducible}{{}{3}} +\gdef \@abspage@last{3} diff --git a/papers/heawood_restrictions_on_nested_tire_graph_duals/notes/boundary_restriction_structure.log b/papers/heawood_restrictions_on_nested_tire_graph_duals/notes/boundary_restriction_structure.log index 4ae5f36..3d0fdea 100644 --- a/papers/heawood_restrictions_on_nested_tire_graph_duals/notes/boundary_restriction_structure.log +++ b/papers/heawood_restrictions_on_nested_tire_graph_duals/notes/boundary_restriction_structure.log @@ -1,4 +1,4 @@ -This is pdfTeX, Version 3.141592653-2.6-1.40.24 (TeX Live 2022) (preloaded format=pdflatex 2022.10.5) 17 JUN 2026 02:21 +This is pdfTeX, Version 3.141592653-2.6-1.40.24 (TeX Live 2022) (preloaded format=pdflatex 2022.10.5) 17 JUN 2026 20:27 entering extended mode restricted \write18 enabled. %&-line parsing enabled. @@ -178,20 +178,20 @@ File: l3backend-pdftex.def 2022-02-07 L3 backend support: PDF output (pdfTeX) (./boundary_restriction_structure.aux) \openout1 = `boundary_restriction_structure.aux'. -LaTeX Font Info: Checking defaults for OML/cmm/m/it on input line 18. -LaTeX Font Info: ... okay on input line 18. -LaTeX Font Info: Checking defaults for OMS/cmsy/m/n on input line 18. -LaTeX Font Info: ... okay on input line 18. -LaTeX Font Info: Checking defaults for OT1/cmr/m/n on input line 18. -LaTeX Font Info: ... okay on input line 18. -LaTeX Font Info: Checking defaults for T1/cmr/m/n on input line 18. -LaTeX Font Info: ... okay on input line 18. -LaTeX Font Info: Checking defaults for TS1/cmr/m/n on input line 18. -LaTeX Font Info: ... okay on input line 18. -LaTeX Font Info: Checking defaults for OMX/cmex/m/n on input line 18. -LaTeX Font Info: ... okay on input line 18. -LaTeX Font Info: Checking defaults for U/cmr/m/n on input line 18. -LaTeX Font Info: ... okay on input line 18. +LaTeX Font Info: Checking defaults for OML/cmm/m/it on input line 19. +LaTeX Font Info: ... okay on input line 19. +LaTeX Font Info: Checking defaults for OMS/cmsy/m/n on input line 19. +LaTeX Font Info: ... okay on input line 19. +LaTeX Font Info: Checking defaults for OT1/cmr/m/n on input line 19. +LaTeX Font Info: ... okay on input line 19. +LaTeX Font Info: Checking defaults for T1/cmr/m/n on input line 19. +LaTeX Font Info: ... okay on input line 19. +LaTeX Font Info: Checking defaults for TS1/cmr/m/n on input line 19. +LaTeX Font Info: ... okay on input line 19. +LaTeX Font Info: Checking defaults for OMX/cmex/m/n on input line 19. +LaTeX Font Info: ... okay on input line 19. +LaTeX Font Info: Checking defaults for U/cmr/m/n on input line 19. +LaTeX Font Info: ... okay on input line 19. 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