didericis/math-research
1
0
Fork 0
Code Issues Pull Requests Packages Projects Releases Wiki Activity
Files
20f19f086937c369b83935f5af77f1abb918294f
math-research/papers/dual_decomposition_minimal_counterexamples/paper.fls
T
didericis 1791b68f4a dual_decomposition: reduced-dual definition, verification, and step figures 
Add Definition 2.1 (reduced dual) and a remark on cubicity/planarity, plus an
experiment verifying it on the icosahedron/dodecahedron and four figures, one
per construction step.

reduced_dual.py builds G' = dodecahedron (dual of the icosahedron), applies the
construction, and confirms the result is a cubic, planar, simple graph whose
dual is a simple triangulation. Finding: the construction is an n -> n-2
reduction (12 -> 10 here), not n-1, since the single apex v_n collapses one more
vertex than a standard pentagon re-triangulation; the result also re-introduces
degree-3 and degree-4 vertices (degree seq [7,5,5,5,5,5,5,4,4,3]).

draw_reduced_dual_steps.py renders fig_reduced_dual_step1..4.png, embedded as a
2x2 grid after the definition.

Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>
2026-05-22 18:50:38 -04:00

264 lines
18 KiB
Plaintext
Raw Blame History

PWD /Users/didericis/Code/math-research/papers/dual_decomposition_minimal_counterexamples
INPUT /usr/local/texlive/2022/texmf.cnf
INPUT /usr/local/texlive/2022/texmf-dist/web2c/texmf.cnf
INPUT /usr/local/texlive/2022/texmf-var/web2c/pdftex/pdflatex.fmt
INPUT paper.tex
OUTPUT paper.log
INPUT /usr/local/texlive/2022/texmf-dist/tex/latex/amscls/amsart.cls
INPUT /usr/local/texlive/2022/texmf-dist/tex/latex/amscls/amsart.cls
INPUT /usr/local/texlive/2022/texmf-dist/tex/latex/amscls/amsart.cls
INPUT /usr/local/texlive/2022/texmf-dist/tex/latex/amscls/amsart.cls
INPUT /usr/local/texlive/2022/texmf-dist/tex/latex/amscls/amsart.cls
INPUT /usr/local/texlive/2022/texmf-dist/tex/latex/amscls/amsart.cls
INPUT /usr/local/texlive/2022/texmf-dist/tex/latex/amscls/amsart.cls
INPUT /usr/local/texlive/2022/texmf-dist/tex/latex/amscls/amsart.cls
INPUT /usr/local/texlive/2022/texmf-dist/tex/latex/amscls/amsart.cls
INPUT /usr/local/texlive/2022/texmf-dist/tex/latex/amscls/amsart.cls
INPUT /usr/local/texlive/2022/texmf-dist/tex/latex/amscls/amsart.cls
INPUT /usr/local/texlive/2022/texmf-dist/tex/latex/amsmath/amsmath.sty
INPUT /usr/local/texlive/2022/texmf-dist/tex/latex/amsmath/amsmath.sty
INPUT /usr/local/texlive/2022/texmf-dist/tex/latex/amsmath/amsmath.sty
INPUT /usr/local/texlive/2022/texmf-dist/tex/latex/amsmath/amsmath.sty
INPUT /usr/local/texlive/2022/texmf-dist/tex/latex/amsmath/amsmath.sty
INPUT /usr/local/texlive/2022/texmf-dist/tex/latex/amsmath/amsmath.sty
INPUT /usr/local/texlive/2022/texmf-dist/tex/latex/amsmath/amsmath.sty
INPUT /usr/local/texlive/2022/texmf-dist/tex/latex/amsmath/amsmath.sty
INPUT /usr/local/texlive/2022/texmf-dist/tex/latex/amsmath/amsmath.sty
INPUT /usr/local/texlive/2022/texmf-dist/tex/latex/amsmath/amsmath.sty
INPUT /usr/local/texlive/2022/texmf-dist/tex/latex/amsmath/amsmath.sty
INPUT /usr/local/texlive/2022/texmf-dist/tex/latex/amsmath/amsmath.sty
INPUT /usr/local/texlive/2022/texmf-dist/tex/latex/amsmath/amsmath.sty
INPUT /usr/local/texlive/2022/texmf-dist/tex/latex/amsmath/amsmath.sty
INPUT /usr/local/texlive/2022/texmf-dist/tex/latex/amsmath/amsmath.sty
INPUT /usr/local/texlive/2022/texmf-dist/tex/latex/amsmath/amsopn.sty
INPUT /usr/local/texlive/2022/texmf-dist/tex/latex/amsmath/amsopn.sty
INPUT /usr/local/texlive/2022/texmf-dist/tex/latex/amsmath/amstext.sty
INPUT /usr/local/texlive/2022/texmf-dist/tex/latex/amsmath/amstext.sty
INPUT /usr/local/texlive/2022/texmf-dist/tex/latex/amsmath/amstext.sty
INPUT /usr/local/texlive/2022/texmf-dist/tex/latex/amsmath/amstext.sty
INPUT /usr/local/texlive/2022/texmf-dist/tex/latex/amsmath/amstext.sty
INPUT /usr/local/texlive/2022/texmf-dist/tex/latex/amsmath/amstext.sty
INPUT /usr/local/texlive/2022/texmf-dist/tex/latex/amsmath/amstext.sty
INPUT /usr/local/texlive/2022/texmf-dist/tex/latex/amsmath/amstext.sty
INPUT /usr/local/texlive/2022/texmf-dist/tex/latex/amsmath/amstext.sty
INPUT /usr/local/texlive/2022/texmf-dist/tex/latex/amsmath/amstext.sty
INPUT /usr/local/texlive/2022/texmf-dist/tex/latex/amsmath/amstext.sty
INPUT /usr/local/texlive/2022/texmf-dist/tex/latex/amsmath/amsgen.sty
INPUT /usr/local/texlive/2022/texmf-dist/tex/latex/amsmath/amsgen.sty
INPUT /usr/local/texlive/2022/texmf-dist/tex/latex/amsmath/amsgen.sty
INPUT /usr/local/texlive/2022/texmf-dist/tex/latex/amsmath/amsgen.sty
INPUT /usr/local/texlive/2022/texmf-dist/tex/latex/amsmath/amsgen.sty
INPUT /usr/local/texlive/2022/texmf-dist/tex/latex/amsmath/amsgen.sty
INPUT /usr/local/texlive/2022/texmf-dist/tex/latex/amsmath/amsgen.sty
INPUT /usr/local/texlive/2022/texmf-dist/tex/latex/amsmath/amsgen.sty
INPUT /usr/local/texlive/2022/texmf-dist/tex/latex/amsmath/amsgen.sty
INPUT /usr/local/texlive/2022/texmf-dist/tex/latex/amsmath/amsgen.sty
INPUT /usr/local/texlive/2022/texmf-dist/tex/latex/amsmath/amsgen.sty
INPUT /usr/local/texlive/2022/texmf-dist/tex/latex/amsmath/amsbsy.sty
INPUT /usr/local/texlive/2022/texmf-dist/tex/latex/amsmath/amsbsy.sty
INPUT /usr/local/texlive/2022/texmf-dist/tex/latex/amsmath/amsbsy.sty
INPUT /usr/local/texlive/2022/texmf-dist/tex/latex/amsmath/amsbsy.sty
INPUT /usr/local/texlive/2022/texmf-dist/tex/latex/amsmath/amsbsy.sty
INPUT /usr/local/texlive/2022/texmf-dist/tex/latex/amsmath/amsbsy.sty
INPUT /usr/local/texlive/2022/texmf-dist/tex/latex/amsmath/amsbsy.sty
INPUT /usr/local/texlive/2022/texmf-dist/tex/latex/amsmath/amsbsy.sty
INPUT /usr/local/texlive/2022/texmf-dist/tex/latex/amsmath/amsbsy.sty
INPUT /usr/local/texlive/2022/texmf-dist/tex/latex/amsmath/amsbsy.sty
INPUT /usr/local/texlive/2022/texmf-dist/tex/latex/amsmath/amsbsy.sty
INPUT /usr/local/texlive/2022/texmf-dist/tex/latex/amsmath/amsgen.sty
INPUT /usr/local/texlive/2022/texmf-dist/tex/latex/amsmath/amsopn.sty
INPUT /usr/local/texlive/2022/texmf-dist/tex/latex/amsmath/amsopn.sty
INPUT /usr/local/texlive/2022/texmf-dist/tex/latex/amsmath/amsopn.sty
INPUT /usr/local/texlive/2022/texmf-dist/tex/latex/amsmath/amsopn.sty
INPUT /usr/local/texlive/2022/texmf-dist/tex/latex/amsmath/amsopn.sty
INPUT /usr/local/texlive/2022/texmf-dist/tex/latex/amsmath/amsopn.sty
INPUT /usr/local/texlive/2022/texmf-dist/tex/latex/amsmath/amsopn.sty
INPUT /usr/local/texlive/2022/texmf-dist/tex/latex/amsmath/amsopn.sty
INPUT /usr/local/texlive/2022/texmf-dist/tex/latex/amsmath/amsopn.sty
INPUT /usr/local/texlive/2022/texmf-dist/tex/latex/amsmath/amsopn.sty
INPUT /usr/local/texlive/2022/texmf-dist/tex/latex/amsmath/amsopn.sty
INPUT /usr/local/texlive/2022/texmf-dist/tex/latex/amsmath/amsgen.sty
INPUT /usr/local/texlive/2022/texmf-dist/tex/latex/amsfonts/umsa.fd
INPUT /usr/local/texlive/2022/texmf-dist/tex/latex/amsfonts/umsa.fd
INPUT /usr/local/texlive/2022/texmf-dist/tex/latex/amsfonts/umsa.fd
INPUT /usr/local/texlive/2022/texmf-dist/tex/latex/amsfonts/umsa.fd
INPUT /usr/local/texlive/2022/texmf-dist/tex/latex/amsfonts/amsfonts.sty
INPUT /usr/local/texlive/2022/texmf-dist/tex/latex/amsfonts/amsfonts.sty
INPUT /usr/local/texlive/2022/texmf-dist/tex/latex/amsfonts/amsfonts.sty
INPUT /usr/local/texlive/2022/texmf-dist/tex/latex/amsfonts/amsfonts.sty
INPUT /usr/local/texlive/2022/texmf-dist/tex/latex/amsfonts/amsfonts.sty
INPUT /usr/local/texlive/2022/texmf-dist/tex/latex/amsfonts/amsfonts.sty
INPUT /usr/local/texlive/2022/texmf-dist/tex/latex/amsfonts/amsfonts.sty
INPUT /usr/local/texlive/2022/texmf-dist/tex/latex/amsfonts/amsfonts.sty
INPUT /usr/local/texlive/2022/texmf-dist/tex/latex/amsfonts/amsfonts.sty
INPUT /usr/local/texlive/2022/texmf-dist/tex/latex/amsfonts/amsfonts.sty
INPUT /usr/local/texlive/2022/texmf-dist/tex/latex/amsfonts/amsfonts.sty
INPUT /usr/local/texlive/2022/texmf-dist/tex/latex/amsfonts/amssymb.sty
INPUT /usr/local/texlive/2022/texmf-dist/tex/latex/amsfonts/amssymb.sty
INPUT /usr/local/texlive/2022/texmf-dist/tex/latex/amsfonts/amssymb.sty
INPUT /usr/local/texlive/2022/texmf-dist/tex/latex/amsfonts/amssymb.sty
INPUT /usr/local/texlive/2022/texmf-dist/tex/latex/amsfonts/amssymb.sty
INPUT /usr/local/texlive/2022/texmf-dist/tex/latex/amsfonts/amssymb.sty
INPUT /usr/local/texlive/2022/texmf-dist/tex/latex/amsfonts/amssymb.sty
INPUT /usr/local/texlive/2022/texmf-dist/tex/latex/amsfonts/amssymb.sty
INPUT /usr/local/texlive/2022/texmf-dist/tex/latex/amsfonts/amssymb.sty
INPUT /usr/local/texlive/2022/texmf-dist/tex/latex/amsfonts/amssymb.sty
INPUT /usr/local/texlive/2022/texmf-dist/tex/latex/amsfonts/amssymb.sty
INPUT /usr/local/texlive/2022/texmf-dist/tex/latex/amsfonts/amsfonts.sty
INPUT /usr/local/texlive/2022/texmf-dist/tex/latex/graphics/graphicx.sty
INPUT /usr/local/texlive/2022/texmf-dist/tex/latex/graphics/graphicx.sty
INPUT /usr/local/texlive/2022/texmf-dist/tex/latex/graphics/graphicx.sty
INPUT /usr/local/texlive/2022/texmf-dist/tex/latex/graphics/graphicx.sty
INPUT /usr/local/texlive/2022/texmf-dist/tex/latex/graphics/graphicx.sty
INPUT /usr/local/texlive/2022/texmf-dist/tex/latex/graphics/graphicx.sty
INPUT /usr/local/texlive/2022/texmf-dist/tex/latex/graphics/graphicx.sty
INPUT /usr/local/texlive/2022/texmf-dist/tex/latex/graphics/graphicx.sty
INPUT /usr/local/texlive/2022/texmf-dist/tex/latex/graphics/graphicx.sty
INPUT /usr/local/texlive/2022/texmf-dist/tex/latex/graphics/graphicx.sty
INPUT /usr/local/texlive/2022/texmf-dist/tex/latex/graphics/graphicx.sty
INPUT /usr/local/texlive/2022/texmf-dist/tex/latex/graphics/keyval.sty
INPUT /usr/local/texlive/2022/texmf-dist/tex/latex/graphics/keyval.sty
INPUT /usr/local/texlive/2022/texmf-dist/tex/latex/graphics/keyval.sty
INPUT /usr/local/texlive/2022/texmf-dist/tex/latex/graphics/keyval.sty
INPUT /usr/local/texlive/2022/texmf-dist/tex/latex/graphics/keyval.sty
INPUT /usr/local/texlive/2022/texmf-dist/tex/latex/graphics/keyval.sty
INPUT /usr/local/texlive/2022/texmf-dist/tex/latex/graphics/keyval.sty
INPUT /usr/local/texlive/2022/texmf-dist/tex/latex/graphics/keyval.sty
INPUT /usr/local/texlive/2022/texmf-dist/tex/latex/graphics/keyval.sty
INPUT /usr/local/texlive/2022/texmf-dist/tex/latex/graphics/keyval.sty
INPUT /usr/local/texlive/2022/texmf-dist/tex/latex/graphics/keyval.sty
INPUT /usr/local/texlive/2022/texmf-dist/tex/latex/graphics/graphics.sty
INPUT /usr/local/texlive/2022/texmf-dist/tex/latex/graphics/graphics.sty
INPUT /usr/local/texlive/2022/texmf-dist/tex/latex/graphics/graphics.sty
INPUT /usr/local/texlive/2022/texmf-dist/tex/latex/graphics/graphics.sty
INPUT /usr/local/texlive/2022/texmf-dist/tex/latex/graphics/graphics.sty
INPUT /usr/local/texlive/2022/texmf-dist/tex/latex/graphics/graphics.sty
INPUT /usr/local/texlive/2022/texmf-dist/tex/latex/graphics/graphics.sty
INPUT /usr/local/texlive/2022/texmf-dist/tex/latex/graphics/graphics.sty
INPUT /usr/local/texlive/2022/texmf-dist/tex/latex/graphics/graphics.sty
INPUT /usr/local/texlive/2022/texmf-dist/tex/latex/graphics/graphics.sty
INPUT /usr/local/texlive/2022/texmf-dist/tex/latex/graphics/graphics.sty
INPUT /usr/local/texlive/2022/texmf-dist/tex/latex/graphics/trig.sty
INPUT /usr/local/texlive/2022/texmf-dist/tex/latex/graphics/trig.sty
INPUT /usr/local/texlive/2022/texmf-dist/tex/latex/graphics/trig.sty
INPUT /usr/local/texlive/2022/texmf-dist/tex/latex/graphics/trig.sty
INPUT /usr/local/texlive/2022/texmf-dist/tex/latex/graphics/trig.sty
INPUT /usr/local/texlive/2022/texmf-dist/tex/latex/graphics/trig.sty
INPUT /usr/local/texlive/2022/texmf-dist/tex/latex/graphics/trig.sty
INPUT /usr/local/texlive/2022/texmf-dist/tex/latex/graphics/trig.sty
INPUT /usr/local/texlive/2022/texmf-dist/tex/latex/graphics/trig.sty
INPUT /usr/local/texlive/2022/texmf-dist/tex/latex/graphics/trig.sty
INPUT /usr/local/texlive/2022/texmf-dist/tex/latex/graphics/trig.sty
INPUT /usr/local/texlive/2022/texmf-dist/tex/latex/graphics-cfg/graphics.cfg
INPUT /usr/local/texlive/2022/texmf-dist/tex/latex/graphics-cfg/graphics.cfg
INPUT /usr/local/texlive/2022/texmf-dist/tex/latex/graphics-cfg/graphics.cfg
INPUT /usr/local/texlive/2022/texmf-dist/tex/latex/graphics-cfg/graphics.cfg
INPUT /usr/local/texlive/2022/texmf-dist/tex/latex/graphics-def/pdftex.def
INPUT /usr/local/texlive/2022/texmf-dist/tex/latex/graphics-def/pdftex.def
INPUT /usr/local/texlive/2022/texmf-dist/tex/latex/graphics-def/pdftex.def
INPUT /usr/local/texlive/2022/texmf-dist/tex/latex/graphics-def/pdftex.def
INPUT /usr/local/texlive/2022/texmf-dist/tex/latex/l3backend/l3backend-pdftex.def
INPUT /usr/local/texlive/2022/texmf-dist/tex/latex/l3backend/l3backend-pdftex.def
INPUT /usr/local/texlive/2022/texmf-dist/tex/latex/l3backend/l3backend-pdftex.def
INPUT /usr/local/texlive/2022/texmf-dist/tex/latex/l3backend/l3backend-pdftex.def
INPUT /usr/local/texlive/2022/texmf-dist/tex/latex/l3backend/l3backend-pdftex.def
INPUT /usr/local/texlive/2022/texmf-dist/tex/latex/l3backend/l3backend-pdftex.def
INPUT /usr/local/texlive/2022/texmf-dist/tex/latex/l3backend/l3backend-pdftex.def
INPUT /usr/local/texlive/2022/texmf-dist/tex/latex/l3backend/l3backend-pdftex.def
INPUT /usr/local/texlive/2022/texmf-dist/tex/latex/l3backend/l3backend-pdftex.def
INPUT /usr/local/texlive/2022/texmf-dist/tex/latex/l3backend/l3backend-pdftex.def
INPUT /usr/local/texlive/2022/texmf-dist/tex/latex/l3backend/l3backend-pdftex.def
INPUT ./paper.aux
INPUT paper.aux
INPUT paper.aux
OUTPUT paper.aux
INPUT /usr/local/texlive/2022/texmf-dist/fonts/map/fontname/texfonts.map
INPUT /usr/local/texlive/2022/texmf-dist/fonts/tfm/public/cm/cmr8.tfm
INPUT /usr/local/texlive/2022/texmf-dist/fonts/tfm/public/cm/cmr6.tfm
INPUT /usr/local/texlive/2022/texmf-dist/fonts/tfm/public/cm/cmmi8.tfm
INPUT /usr/local/texlive/2022/texmf-dist/fonts/tfm/public/cm/cmmi6.tfm
INPUT /usr/local/texlive/2022/texmf-dist/fonts/tfm/public/cm/cmsy8.tfm
INPUT /usr/local/texlive/2022/texmf-dist/fonts/tfm/public/cm/cmsy6.tfm
INPUT /usr/local/texlive/2022/texmf-dist/fonts/tfm/public/amsfonts/cmextra/cmex8.tfm
INPUT /usr/local/texlive/2022/texmf-dist/fonts/tfm/public/amsfonts/cmextra/cmex7.tfm
INPUT /usr/local/texlive/2022/texmf-dist/fonts/tfm/public/amsfonts/cmextra/cmex7.tfm
INPUT /usr/local/texlive/2022/texmf-dist/tex/latex/amsfonts/umsa.fd
INPUT /usr/local/texlive/2022/texmf-dist/tex/latex/amsfonts/umsa.fd
INPUT /usr/local/texlive/2022/texmf-dist/tex/latex/amsfonts/umsa.fd
INPUT /usr/local/texlive/2022/texmf-dist/tex/latex/amsfonts/umsa.fd
INPUT /usr/local/texlive/2022/texmf-dist/fonts/tfm/public/amsfonts/symbols/msam10.tfm
INPUT /usr/local/texlive/2022/texmf-dist/fonts/tfm/public/amsfonts/symbols/msam7.tfm
INPUT /usr/local/texlive/2022/texmf-dist/fonts/tfm/public/amsfonts/symbols/msam5.tfm
INPUT /usr/local/texlive/2022/texmf-dist/tex/latex/amsfonts/umsb.fd
INPUT /usr/local/texlive/2022/texmf-dist/tex/latex/amsfonts/umsb.fd
INPUT /usr/local/texlive/2022/texmf-dist/tex/latex/amsfonts/umsb.fd
INPUT /usr/local/texlive/2022/texmf-dist/tex/latex/amsfonts/umsb.fd
INPUT /usr/local/texlive/2022/texmf-dist/fonts/tfm/public/amsfonts/symbols/msbm10.tfm
INPUT /usr/local/texlive/2022/texmf-dist/fonts/tfm/public/amsfonts/symbols/msbm7.tfm
INPUT /usr/local/texlive/2022/texmf-dist/fonts/tfm/public/amsfonts/symbols/msbm5.tfm
INPUT /usr/local/texlive/2022/texmf-dist/tex/context/base/mkii/supp-pdf.mkii
INPUT /usr/local/texlive/2022/texmf-dist/tex/context/base/mkii/supp-pdf.mkii
INPUT /usr/local/texlive/2022/texmf-dist/tex/context/base/mkii/supp-pdf.mkii
INPUT /usr/local/texlive/2022/texmf-dist/tex/context/base/mkii/supp-pdf.mkii
INPUT /usr/local/texlive/2022/texmf-dist/tex/latex/epstopdf-pkg/epstopdf-base.sty
INPUT /usr/local/texlive/2022/texmf-dist/tex/latex/epstopdf-pkg/epstopdf-base.sty
INPUT /usr/local/texlive/2022/texmf-dist/tex/latex/epstopdf-pkg/epstopdf-base.sty
INPUT /usr/local/texlive/2022/texmf-dist/tex/latex/epstopdf-pkg/epstopdf-base.sty
INPUT /usr/local/texlive/2022/texmf-dist/tex/latex/epstopdf-pkg/epstopdf-base.sty
INPUT /usr/local/texlive/2022/texmf-dist/tex/latex/epstopdf-pkg/epstopdf-base.sty
INPUT /usr/local/texlive/2022/texmf-dist/tex/latex/epstopdf-pkg/epstopdf-base.sty
INPUT /usr/local/texlive/2022/texmf-dist/tex/latex/epstopdf-pkg/epstopdf-base.sty
INPUT /usr/local/texlive/2022/texmf-dist/tex/latex/epstopdf-pkg/epstopdf-base.sty
INPUT /usr/local/texlive/2022/texmf-dist/tex/latex/epstopdf-pkg/epstopdf-base.sty
INPUT /usr/local/texlive/2022/texmf-dist/tex/latex/epstopdf-pkg/epstopdf-base.sty
INPUT /usr/local/texlive/2022/texmf-dist/tex/latex/latexconfig/epstopdf-sys.cfg
INPUT /usr/local/texlive/2022/texmf-dist/tex/latex/latexconfig/epstopdf-sys.cfg
INPUT /usr/local/texlive/2022/texmf-dist/tex/latex/latexconfig/epstopdf-sys.cfg
INPUT /usr/local/texlive/2022/texmf-dist/tex/latex/latexconfig/epstopdf-sys.cfg
INPUT /usr/local/texlive/2022/texmf-dist/fonts/tfm/public/cm/cmcsc10.tfm
INPUT /usr/local/texlive/2022/texmf-dist/fonts/tfm/public/cm/cmti8.tfm
INPUT /usr/local/texlive/2022/texmf-dist/fonts/tfm/public/cm/cmbx10.tfm
INPUT /usr/local/texlive/2022/texmf-dist/fonts/tfm/public/cm/cmcsc10.tfm
INPUT /usr/local/texlive/2022/texmf-dist/fonts/tfm/public/cm/cmti10.tfm
INPUT /usr/local/texlive/2022/texmf-dist/fonts/tfm/public/amsfonts/cmextra/cmex7.tfm
INPUT /usr/local/texlive/2022/texmf-dist/fonts/tfm/public/amsfonts/symbols/msam10.tfm
INPUT /usr/local/texlive/2022/texmf-dist/fonts/tfm/public/amsfonts/symbols/msam7.tfm
INPUT /usr/local/texlive/2022/texmf-dist/fonts/tfm/public/amsfonts/symbols/msbm10.tfm
INPUT /usr/local/texlive/2022/texmf-dist/fonts/tfm/public/amsfonts/symbols/msbm7.tfm
OUTPUT paper.pdf
INPUT /usr/local/texlive/2022/texmf-var/fonts/map/pdftex/updmap/pdftex.map
INPUT ./fig_reduced_dual_step1.png
INPUT ./fig_reduced_dual_step1.png
INPUT fig_reduced_dual_step1.png
INPUT ./fig_reduced_dual_step1.png
INPUT ./fig_reduced_dual_step1.png
INPUT ./fig_reduced_dual_step2.png
INPUT ./fig_reduced_dual_step2.png
INPUT fig_reduced_dual_step2.png
INPUT ./fig_reduced_dual_step2.png
INPUT ./fig_reduced_dual_step2.png
INPUT ./fig_reduced_dual_step3.png
INPUT ./fig_reduced_dual_step3.png
INPUT fig_reduced_dual_step3.png
INPUT ./fig_reduced_dual_step3.png
INPUT ./fig_reduced_dual_step3.png
INPUT ./fig_reduced_dual_step4.png
INPUT ./fig_reduced_dual_step4.png
INPUT fig_reduced_dual_step4.png
INPUT ./fig_reduced_dual_step4.png
INPUT ./fig_reduced_dual_step4.png
INPUT paper.aux
INPUT /usr/local/texlive/2022/texmf-dist/fonts/type1/public/amsfonts/cm/cmbx10.pfb
INPUT /usr/local/texlive/2022/texmf-dist/fonts/type1/public/amsfonts/cm/cmcsc10.pfb
INPUT /usr/local/texlive/2022/texmf-dist/fonts/type1/public/amsfonts/cm/cmex10.pfb
INPUT /usr/local/texlive/2022/texmf-dist/fonts/type1/public/amsfonts/cm/cmmi10.pfb
INPUT /usr/local/texlive/2022/texmf-dist/fonts/type1/public/amsfonts/cm/cmmi7.pfb
INPUT /usr/local/texlive/2022/texmf-dist/fonts/type1/public/amsfonts/cm/cmr10.pfb
INPUT /usr/local/texlive/2022/texmf-dist/fonts/type1/public/amsfonts/cm/cmr7.pfb
INPUT /usr/local/texlive/2022/texmf-dist/fonts/type1/public/amsfonts/cm/cmr8.pfb
INPUT /usr/local/texlive/2022/texmf-dist/fonts/type1/public/amsfonts/cm/cmsy10.pfb
INPUT /usr/local/texlive/2022/texmf-dist/fonts/type1/public/amsfonts/cm/cmsy7.pfb
INPUT /usr/local/texlive/2022/texmf-dist/fonts/type1/public/amsfonts/cm/cmti10.pfb
INPUT /usr/local/texlive/2022/texmf-dist/fonts/type1/public/amsfonts/cm/cmti8.pfb
INPUT /usr/local/texlive/2022/texmf-dist/fonts/type1/public/amsfonts/symbols/msam10.pfb
Reference in New Issue View Git Blame Copy Permalink