From c900ec9a70e0f0c53ea58b0a4a71f3e22790a0d0 Mon Sep 17 00:00:00 2001 From: didericis Date: Tue, 26 May 2026 03:50:12 -0400 Subject: [PATCH] =?UTF-8?q?coloring=5Fnested=5Ftire=5Fgraphs:=20refute=20a?= =?UTF-8?q?ntipodal-chord=20rainbow=20conjecture=20as=20originally=20state?= =?UTF-8?q?d,=20add=20refined=20version=20with=20m=5F1=20=E2=89=A5=20m=20p?= =?UTF-8?q?recondition?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit Counterexample search uncovered: T1 = (m_1=3, chord=(0,3), SP) at γ=6 has |π_D| = 18, but the conjectured rainbow combined orbit has size 36 — only 6 of the 36 elements actually lie in π_D, and the literal generator pattern (1,2,3,2,3,1) is itself missing. Refined conjecture adds m_1 ≥ m precondition (same threshold from step 1 "saturation iff m ≥ k"). Under this precondition all 44 tested strict-Latin pairs are still compatible. Pointer to log path included. Co-Authored-By: Claude Opus 4.7 --- .../notes/orbit_decomposition.aux | 2 +- .../notes/orbit_decomposition.log | 62 ++++++++------- .../notes/orbit_decomposition.pdf | Bin 173654 -> 198450 bytes .../notes/orbit_decomposition.tex | 71 ++++++++++++++---- 4 files changed, 92 insertions(+), 43 deletions(-) diff --git a/papers/coloring_nested_tire_graphs/notes/orbit_decomposition.aux b/papers/coloring_nested_tire_graphs/notes/orbit_decomposition.aux index ba1cbd9..276d5d1 100644 --- a/papers/coloring_nested_tire_graphs/notes/orbit_decomposition.aux +++ b/papers/coloring_nested_tire_graphs/notes/orbit_decomposition.aux @@ -6,4 +6,4 @@ \newlabel{obs:antipodal-rainbow-conjecture}{{}{3}} \@writefile{toc}{\contentsline {paragraph}{Direct test.}{3}{}\protected@file@percent } \@writefile{toc}{\contentsline {paragraph}{Why antipodal?}{3}{}\protected@file@percent } -\gdef \@abspage@last{3} +\gdef \@abspage@last{4} diff --git a/papers/coloring_nested_tire_graphs/notes/orbit_decomposition.log b/papers/coloring_nested_tire_graphs/notes/orbit_decomposition.log index 65e6984..7a156e9 100644 --- a/papers/coloring_nested_tire_graphs/notes/orbit_decomposition.log +++ b/papers/coloring_nested_tire_graphs/notes/orbit_decomposition.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) 26 MAY 2026 03:29 +This is pdfTeX, Version 3.141592653-2.6-1.40.24 (TeX Live 2022) (preloaded format=pdflatex 2022.10.5) 26 MAY 2026 03:50 entering extended mode restricted \write18 enabled. %&-line parsing enabled. @@ -289,38 +289,44 @@ ecomposition[]data.txt\OT1/cmr/m/n/10.95 . [1 {/usr/local/texlive/2022/texmf-var/fonts/map/pdftex/updmap/pdftex.map}] -[2] [3] (./orbit_decomposition.aux) +[2] +Overfull \hbox (39.5773pt too wide) in paragraph at lines 172--176 +\OT1/cmr/m/n/10.95 The orig-i-nal state-ment is false: \OT1/cmr/m/it/10.95 the +counterexample-search log (\OT1/cmtt/m/it/10.95 experiments/counterexample[]sea +rch.log\OT1/cmr/m/it/10.95 ) + [] -LaTeX Warning: Label(s) may have changed. 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