nested_level_duals: scaffold paper (shelved for alternative approach)
New paper introducing the dual (inner/weak dual) of a maximal planar graph, dual depth (BFS-derived min level over a face's vertices), and a Tait-based framing of a minimal 4CT counterexample via nested level duals. Includes a dual-depth figure and its generator. Shelved per closing note in favour of an alternative approach. Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>
This commit is contained in:
@@ -0,0 +1,232 @@
|
||||
This is pdfTeX, Version 3.141592653-2.6-1.40.24 (TeX Live 2022) (preloaded format=pdflatex 2022.10.5) 22 MAY 2026 16:46
|
||||
entering extended mode
|
||||
restricted \write18 enabled.
|
||||
%&-line parsing enabled.
|
||||
**paper.tex
|
||||
(./paper.tex
|
||||
LaTeX2e <2021-11-15> patch level 1
|
||||
L3 programming layer <2022-02-24>
|
||||
(/usr/local/texlive/2022/texmf-dist/tex/latex/amscls/amsart.cls
|
||||
Document Class: amsart 2020/05/29 v2.20.6
|
||||
\linespacing=\dimen138
|
||||
\normalparindent=\dimen139
|
||||
\normaltopskip=\skip47
|
||||
(/usr/local/texlive/2022/texmf-dist/tex/latex/amsmath/amsmath.sty
|
||||
Package: amsmath 2021/10/15 v2.17l AMS math features
|
||||
\@mathmargin=\skip48
|
||||
|
||||
For additional information on amsmath, use the `?' option.
|
||||
(/usr/local/texlive/2022/texmf-dist/tex/latex/amsmath/amstext.sty
|
||||
Package: amstext 2021/08/26 v2.01 AMS text
|
||||
|
||||
(/usr/local/texlive/2022/texmf-dist/tex/latex/amsmath/amsgen.sty
|
||||
File: amsgen.sty 1999/11/30 v2.0 generic functions
|
||||
\@emptytoks=\toks16
|
||||
\ex@=\dimen140
|
||||
))
|
||||
(/usr/local/texlive/2022/texmf-dist/tex/latex/amsmath/amsbsy.sty
|
||||
Package: amsbsy 1999/11/29 v1.2d Bold Symbols
|
||||
\pmbraise@=\dimen141
|
||||
)
|
||||
(/usr/local/texlive/2022/texmf-dist/tex/latex/amsmath/amsopn.sty
|
||||
Package: amsopn 2021/08/26 v2.02 operator names
|
||||
)
|
||||
\inf@bad=\count185
|
||||
LaTeX Info: Redefining \frac on input line 234.
|
||||
\uproot@=\count186
|
||||
\leftroot@=\count187
|
||||
LaTeX Info: Redefining \overline on input line 399.
|
||||
\classnum@=\count188
|
||||
\DOTSCASE@=\count189
|
||||
LaTeX Info: Redefining \ldots on input line 496.
|
||||
LaTeX Info: Redefining \dots on input line 499.
|
||||
LaTeX Info: Redefining \cdots on input line 620.
|
||||
\Mathstrutbox@=\box50
|
||||
\strutbox@=\box51
|
||||
\big@size=\dimen142
|
||||
LaTeX Font Info: Redeclaring font encoding OML on input line 743.
|
||||
LaTeX Font Info: Redeclaring font encoding OMS on input line 744.
|
||||
\macc@depth=\count190
|
||||
\c@MaxMatrixCols=\count191
|
||||
\dotsspace@=\muskip16
|
||||
\c@parentequation=\count192
|
||||
\dspbrk@lvl=\count193
|
||||
\tag@help=\toks17
|
||||
\row@=\count194
|
||||
\column@=\count195
|
||||
\maxfields@=\count196
|
||||
\andhelp@=\toks18
|
||||
\eqnshift@=\dimen143
|
||||
\alignsep@=\dimen144
|
||||
\tagshift@=\dimen145
|
||||
\tagwidth@=\dimen146
|
||||
\totwidth@=\dimen147
|
||||
\lineht@=\dimen148
|
||||
\@envbody=\toks19
|
||||
\multlinegap=\skip49
|
||||
\multlinetaggap=\skip50
|
||||
\mathdisplay@stack=\toks20
|
||||
LaTeX Info: Redefining \[ on input line 2938.
|
||||
LaTeX Info: Redefining \] on input line 2939.
|
||||
)
|
||||
LaTeX Font Info: Trying to load font information for U+msa on input line 397
|
||||
.
|
||||
|
||||
(/usr/local/texlive/2022/texmf-dist/tex/latex/amsfonts/umsa.fd
|
||||
File: umsa.fd 2013/01/14 v3.01 AMS symbols A
|
||||
)
|
||||
(/usr/local/texlive/2022/texmf-dist/tex/latex/amsfonts/amsfonts.sty
|
||||
Package: amsfonts 2013/01/14 v3.01 Basic AMSFonts support
|
||||
\symAMSa=\mathgroup4
|
||||
\symAMSb=\mathgroup5
|
||||
LaTeX Font Info: Redeclaring math symbol \hbar on input line 98.
|
||||
LaTeX Font Info: Overwriting math alphabet `\mathfrak' in version `bold'
|
||||
(Font) U/euf/m/n --> U/euf/b/n on input line 106.
|
||||
)
|
||||
\copyins=\insert199
|
||||
\abstractbox=\box52
|
||||
\listisep=\skip51
|
||||
\c@part=\count197
|
||||
\c@section=\count198
|
||||
\c@subsection=\count266
|
||||
\c@subsubsection=\count267
|
||||
\c@paragraph=\count268
|
||||
\c@subparagraph=\count269
|
||||
\c@figure=\count270
|
||||
\c@table=\count271
|
||||
\abovecaptionskip=\skip52
|
||||
\belowcaptionskip=\skip53
|
||||
\captionindent=\dimen149
|
||||
\thm@style=\toks21
|
||||
\thm@bodyfont=\toks22
|
||||
\thm@headfont=\toks23
|
||||
\thm@notefont=\toks24
|
||||
\thm@headpunct=\toks25
|
||||
\thm@preskip=\skip54
|
||||
\thm@postskip=\skip55
|
||||
\thm@headsep=\skip56
|
||||
\dth@everypar=\toks26
|
||||
)
|
||||
(/usr/local/texlive/2022/texmf-dist/tex/latex/amsfonts/amssymb.sty
|
||||
Package: amssymb 2013/01/14 v3.01 AMS font symbols
|
||||
)
|
||||
(/usr/local/texlive/2022/texmf-dist/tex/latex/graphics/graphicx.sty
|
||||
Package: graphicx 2021/09/16 v1.2d Enhanced LaTeX Graphics (DPC,SPQR)
|
||||
|
||||
(/usr/local/texlive/2022/texmf-dist/tex/latex/graphics/keyval.sty
|
||||
Package: keyval 2014/10/28 v1.15 key=value parser (DPC)
|
||||
\KV@toks@=\toks27
|
||||
)
|
||||
(/usr/local/texlive/2022/texmf-dist/tex/latex/graphics/graphics.sty
|
||||
Package: graphics 2021/03/04 v1.4d Standard LaTeX Graphics (DPC,SPQR)
|
||||
|
||||
(/usr/local/texlive/2022/texmf-dist/tex/latex/graphics/trig.sty
|
||||
Package: trig 2021/08/11 v1.11 sin cos tan (DPC)
|
||||
)
|
||||
(/usr/local/texlive/2022/texmf-dist/tex/latex/graphics-cfg/graphics.cfg
|
||||
File: graphics.cfg 2016/06/04 v1.11 sample graphics configuration
|
||||
)
|
||||
Package graphics Info: Driver file: pdftex.def on input line 107.
|
||||
|
||||
(/usr/local/texlive/2022/texmf-dist/tex/latex/graphics-def/pdftex.def
|
||||
File: pdftex.def 2020/10/05 v1.2a Graphics/color driver for pdftex
|
||||
))
|
||||
\Gin@req@height=\dimen150
|
||||
\Gin@req@width=\dimen151
|
||||
)
|
||||
\c@theorem=\count272
|
||||
|
||||
(/usr/local/texlive/2022/texmf-dist/tex/latex/l3backend/l3backend-pdftex.def
|
||||
File: l3backend-pdftex.def 2022-02-07 L3 backend support: PDF output (pdfTeX)
|
||||
\l__color_backend_stack_int=\count273
|
||||
\l__pdf_internal_box=\box53
|
||||
)
|
||||
(./paper.aux)
|
||||
\openout1 = `paper.aux'.
|
||||
|
||||
LaTeX Font Info: Checking defaults for OML/cmm/m/it on input line 26.
|
||||
LaTeX Font Info: ... okay on input line 26.
|
||||
LaTeX Font Info: Checking defaults for OMS/cmsy/m/n on input line 26.
|
||||
LaTeX Font Info: ... okay on input line 26.
|
||||
LaTeX Font Info: Checking defaults for OT1/cmr/m/n on input line 26.
|
||||
LaTeX Font Info: ... okay on input line 26.
|
||||
LaTeX Font Info: Checking defaults for T1/cmr/m/n on input line 26.
|
||||
LaTeX Font Info: ... okay on input line 26.
|
||||
LaTeX Font Info: Checking defaults for TS1/cmr/m/n on input line 26.
|
||||
LaTeX Font Info: ... okay on input line 26.
|
||||
LaTeX Font Info: Checking defaults for OMX/cmex/m/n on input line 26.
|
||||
LaTeX Font Info: ... okay on input line 26.
|
||||
LaTeX Font Info: Checking defaults for U/cmr/m/n on input line 26.
|
||||
LaTeX Font Info: ... okay on input line 26.
|
||||
LaTeX Font Info: Trying to load font information for U+msa on input line 26.
|
||||
|
||||
(/usr/local/texlive/2022/texmf-dist/tex/latex/amsfonts/umsa.fd
|
||||
File: umsa.fd 2013/01/14 v3.01 AMS symbols A
|
||||
)
|
||||
LaTeX Font Info: Trying to load font information for U+msb on input line 26.
|
||||
|
||||
|
||||
(/usr/local/texlive/2022/texmf-dist/tex/latex/amsfonts/umsb.fd
|
||||
File: umsb.fd 2013/01/14 v3.01 AMS symbols B
|
||||
)
|
||||
(/usr/local/texlive/2022/texmf-dist/tex/context/base/mkii/supp-pdf.mkii
|
||||
[Loading MPS to PDF converter (version 2006.09.02).]
|
||||
\scratchcounter=\count274
|
||||
\scratchdimen=\dimen152
|
||||
\scratchbox=\box54
|
||||
\nofMPsegments=\count275
|
||||
\nofMParguments=\count276
|
||||
\everyMPshowfont=\toks28
|
||||
\MPscratchCnt=\count277
|
||||
\MPscratchDim=\dimen153
|
||||
\MPnumerator=\count278
|
||||
\makeMPintoPDFobject=\count279
|
||||
\everyMPtoPDFconversion=\toks29
|
||||
) (/usr/local/texlive/2022/texmf-dist/tex/latex/epstopdf-pkg/epstopdf-base.sty
|
||||
Package: epstopdf-base 2020-01-24 v2.11 Base part for package epstopdf
|
||||
Package epstopdf-base Info: Redefining graphics rule for `.eps' on input line 4
|
||||
85.
|
||||
|
||||
(/usr/local/texlive/2022/texmf-dist/tex/latex/latexconfig/epstopdf-sys.cfg
|
||||
File: epstopdf-sys.cfg 2010/07/13 v1.3 Configuration of (r)epstopdf for TeX Liv
|
||||
e
|
||||
))
|
||||
<fig_dual_depth.png, id=1, 642.8015pt x 606.265pt>
|
||||
File: fig_dual_depth.png Graphic file (type png)
|
||||
<use fig_dual_depth.png>
|
||||
Package pdftex.def Info: fig_dual_depth.png used on input line 106.
|
||||
(pdftex.def) Requested size: 251.9989pt x 237.67276pt.
|
||||
|
||||
|
||||
LaTeX Warning: `h' float specifier changed to `ht'.
|
||||
|
||||
[1{/usr/local/texlive/2022/texmf-var/fonts/map/pdftex/updmap/pdftex.map}]
|
||||
[2 <./fig_dual_depth.png>] (./paper.aux) )
|
||||
Here is how much of TeX's memory you used:
|
||||
2993 strings out of 478268
|
||||
41697 string characters out of 5846347
|
||||
338099 words of memory out of 5000000
|
||||
21041 multiletter control sequences out of 15000+600000
|
||||
475666 words of font info for 53 fonts, out of 8000000 for 9000
|
||||
1302 hyphenation exceptions out of 8191
|
||||
69i,6n,76p,625b,208s stack positions out of 10000i,1000n,20000p,200000b,200000s
|
||||
</usr/local/texlive/2022/texmf-dist/f
|
||||
onts/type1/public/amsfonts/cm/cmbx10.pfb></usr/local/texlive/2022/texmf-dist/fo
|
||||
nts/type1/public/amsfonts/cm/cmcsc10.pfb></usr/local/texlive/2022/texmf-dist/fo
|
||||
nts/type1/public/amsfonts/cm/cmmi10.pfb></usr/local/texlive/2022/texmf-dist/fon
|
||||
ts/type1/public/amsfonts/cm/cmmi7.pfb></usr/local/texlive/2022/texmf-dist/fonts
|
||||
/type1/public/amsfonts/cm/cmr10.pfb></usr/local/texlive/2022/texmf-dist/fonts/t
|
||||
ype1/public/amsfonts/cm/cmr7.pfb></usr/local/texlive/2022/texmf-dist/fonts/type
|
||||
1/public/amsfonts/cm/cmr8.pfb></usr/local/texlive/2022/texmf-dist/fonts/type1/p
|
||||
ublic/amsfonts/cm/cmsy10.pfb></usr/local/texlive/2022/texmf-dist/fonts/type1/pu
|
||||
blic/amsfonts/cm/cmsy5.pfb></usr/local/texlive/2022/texmf-dist/fonts/type1/publ
|
||||
ic/amsfonts/cm/cmsy7.pfb></usr/local/texlive/2022/texmf-dist/fonts/type1/public
|
||||
/amsfonts/cm/cmti10.pfb></usr/local/texlive/2022/texmf-dist/fonts/type1/public/
|
||||
amsfonts/cm/cmti8.pfb>
|
||||
Output written on paper.pdf (2 pages, 331553 bytes).
|
||||
PDF statistics:
|
||||
74 PDF objects out of 1000 (max. 8388607)
|
||||
43 compressed objects within 1 object stream
|
||||
0 named destinations out of 1000 (max. 500000)
|
||||
6 words of extra memory for PDF output out of 10000 (max. 10000000)
|
||||
|
||||
Reference in New Issue
Block a user