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main.fdb_latexmk
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main.fdb_latexmk
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# Fdb version 4
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["pdflatex"] 1753127848.43771 "main.tex" "main.pdf" "main" 1753127848.89585 0
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"/nix/store/dmm8f43zw2rwzgr1xs03ac1r98m8zp5i-texlive-combined-full-2024-final/share/texmf-var/fonts/map/pdftex/updmap/pdftex.map" 1 5467273 8adf9322fbd4564c966dec2fb8102906 ""
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"/nix/store/dmm8f43zw2rwzgr1xs03ac1r98m8zp5i-texlive-combined-full-2024-final/share/texmf-var/web2c/pdftex/pdflatex.fmt" 1 3353366 6b55f6472b88ee4260a36562e619a9e4 ""
|
||||
"/nix/store/dmm8f43zw2rwzgr1xs03ac1r98m8zp5i-texlive-combined-full-2024-final/share/texmf-var/web2c/texmf.cnf" 1 44167 843349d21bfcf9445e4ce4f7d9a9f0d0 ""
|
||||
"/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/fonts/map/fontname/texfonts.map" 1 3524 cb3e574dea2d1052e39280babc910dc8 ""
|
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"/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/fonts/tfm/public/amsfonts/cmextra/cmex7.tfm" 1 1004 54797486969f23fa377b128694d548df ""
|
||||
"/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/fonts/tfm/public/amsfonts/cmextra/cmex8.tfm" 1 988 bdf658c3bfc2d96d3c8b02cfc1c94c20 ""
|
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"/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/fonts/tfm/public/amsfonts/symbols/msam10.tfm" 1 916 f87d7c45f9c908e672703b83b72241a3 ""
|
||||
"/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/fonts/tfm/public/amsfonts/symbols/msam7.tfm" 1 928 2dc8d444221b7a635bb58038579b861a ""
|
||||
"/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/fonts/tfm/public/amsfonts/symbols/msbm10.tfm" 1 908 2921f8a10601f252058503cc6570e581 ""
|
||||
"/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/fonts/tfm/public/amsfonts/symbols/msbm7.tfm" 1 940 228d6584342e91276bf566bcf9716b83 ""
|
||||
"/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/fonts/tfm/public/cm/cmbx12.tfm" 1 1324 c910af8c371558dc20f2d7822f66fe64 ""
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||||
"/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/fonts/tfm/public/cm/cmex10.tfm" 1 992 662f679a0b3d2d53c1b94050fdaa3f50 ""
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||||
"/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/fonts/tfm/public/cm/cmmi12.tfm" 1 1524 4414a8315f39513458b80dfc63bff03a ""
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"/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/fonts/tfm/public/cm/cmmi6.tfm" 1 1512 f21f83efb36853c0b70002322c1ab3ad ""
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||||
"/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/fonts/tfm/public/cm/cmmi8.tfm" 1 1520 eccf95517727cb11801f4f1aee3a21b4 ""
|
||||
"/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/fonts/tfm/public/cm/cmr12.tfm" 1 1288 655e228510b4c2a1abe905c368440826 ""
|
||||
"/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/fonts/tfm/public/cm/cmr17.tfm" 1 1292 296a67155bdbfc32aa9c636f21e91433 ""
|
||||
"/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/fonts/tfm/public/cm/cmr6.tfm" 1 1300 b62933e007d01cfd073f79b963c01526 ""
|
||||
"/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/fonts/tfm/public/cm/cmr8.tfm" 1 1292 21c1c5bfeaebccffdb478fd231a0997d ""
|
||||
"/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/fonts/tfm/public/cm/cmsy10.tfm" 1 1124 6c73e740cf17375f03eec0ee63599741 ""
|
||||
"/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/fonts/tfm/public/cm/cmsy6.tfm" 1 1116 933a60c408fc0a863a92debe84b2d294 ""
|
||||
"/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/fonts/tfm/public/cm/cmsy8.tfm" 1 1120 8b7d695260f3cff42e636090a8002094 ""
|
||||
"/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/fonts/tfm/public/cm/cmti12.tfm" 1 1484 ed72f8f5cf654cda15ecc8e32bfcbee5 ""
|
||||
"/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/fonts/type1/public/amsfonts/cm/cmbx12.pfb" 1 32080 340ef9bf63678554ee606688e7b5339d ""
|
||||
"/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/fonts/type1/public/amsfonts/cm/cmex10.pfb" 1 30251 6afa5cb1d0204815a708a080681d4674 ""
|
||||
"/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/fonts/type1/public/amsfonts/cm/cmmi12.pfb" 1 36741 fa121aac0049305630cf160b86157ee4 ""
|
||||
"/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/fonts/type1/public/amsfonts/cm/cmmi6.pfb" 1 37166 8ab3487cbe3ab49ebce74c29ea2418db ""
|
||||
"/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/fonts/type1/public/amsfonts/cm/cmmi8.pfb" 1 35469 70d41d2b9ea31d5d813066df7c99281c ""
|
||||
"/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/fonts/type1/public/amsfonts/cm/cmr12.pfb" 1 32722 d7379af29a190c3f453aba36302ff5a9 ""
|
||||
"/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/fonts/type1/public/amsfonts/cm/cmr17.pfb" 1 32362 179c33bbf43f19adbb3825bb4e36e57a ""
|
||||
"/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/fonts/type1/public/amsfonts/cm/cmr6.pfb" 1 32734 69e00a6b65cedb993666e42eedb3d48f ""
|
||||
"/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/fonts/type1/public/amsfonts/cm/cmr8.pfb" 1 32726 0a1aea6fcd6468ee2cf64d891f5c43c8 ""
|
||||
"/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/fonts/type1/public/amsfonts/cm/cmsy10.pfb" 1 32569 5e5ddc8df908dea60932f3c484a54c0d ""
|
||||
"/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/fonts/type1/public/amsfonts/cm/cmsy8.pfb" 1 32626 4f5c1b83753b1dd3a97d1b399a005b4b ""
|
||||
"/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/fonts/type1/public/amsfonts/cm/cmti12.pfb" 1 36118 fad905eba93cff5bce1e185fe980a177 ""
|
||||
"/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/fonts/type1/public/amsfonts/symbols/msam10.pfb" 1 31764 459c573c03a4949a528c2cc7f557e217 ""
|
||||
"/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/tex/context/base/mkii/supp-pdf.mkii" 1 71627 94eb9990bed73c364d7f53f960cc8c5b ""
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||||
"/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/tex/generic/iftex/iftex.sty" 1 7984 7dbb9280f03c0a315425f1b4f35d43ee ""
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||||
"/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/tex/generic/iftex/ifvtex.sty" 1 1057 525c2192b5febbd8c1f662c9468335bb ""
|
||||
"/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/tex/generic/pgf/basiclayer/pgfcore.code.tex" 1 1016 1c2b89187d12a2768764b83b4945667c ""
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||||
"/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/tex/generic/pgf/basiclayer/pgfcorearrows.code.tex" 1 43820 1fef971b75380574ab35a0d37fd92608 ""
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||||
"/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/tex/generic/pgf/basiclayer/pgfcoreexternal.code.tex" 1 19324 f4e4c6403dd0f1605fd20ed22fa79dea ""
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||||
"/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/tex/generic/pgf/basiclayer/pgfcoregraphicstate.code.tex" 1 6038 ccb406740cc3f03bbfb58ad504fe8c27 ""
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"/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/tex/generic/pgf/basiclayer/pgfcoreimage.code.tex" 1 6911 f6d4cf5a3fef5cc879d668b810e82868 ""
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"/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/tex/generic/pgf/basiclayer/pgfcorelayers.code.tex" 1 4883 42daaf41e27c3735286e23e48d2d7af9 ""
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||||
"/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/tex/generic/pgf/basiclayer/pgfcoreobjects.code.tex" 1 2544 8c06d2a7f0f469616ac9e13db6d2f842 ""
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"/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/tex/generic/pgf/basiclayer/pgfcorepathconstruct.code.tex" 1 44195 5e390c414de027626ca5e2df888fa68d ""
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"/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/tex/generic/pgf/basiclayer/pgfcorepathprocessing.code.tex" 1 17311 2ef6b2e29e2fc6a2fc8d6d652176e257 ""
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||||
"/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/tex/generic/pgf/basiclayer/pgfcorepathusage.code.tex" 1 21302 788a79944eb22192a4929e46963a3067 ""
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"/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/tex/generic/pgf/basiclayer/pgfcorepatterns.code.tex" 1 9691 3d42d89522f4650c2f3dc616ca2b925e ""
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"/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/tex/generic/pgf/basiclayer/pgfcorepoints.code.tex" 1 33335 dd1fa4814d4e51f18be97d88bf0da60c ""
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||||
"/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/tex/generic/pgf/basiclayer/pgfcorequick.code.tex" 1 2965 4c2b1f4e0826925746439038172e5d6f ""
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||||
"/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/tex/generic/pgf/basiclayer/pgfcorerdf.code.tex" 1 5196 2cc249e0ee7e03da5f5f6589257b1e5b ""
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||||
"/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/tex/generic/pgf/basiclayer/pgfcorescopes.code.tex" 1 20821 7579108c1e9363e61a0b1584778804aa ""
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||||
"/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/tex/generic/pgf/basiclayer/pgfcoreshade.code.tex" 1 35249 abd4adf948f960299a4b3d27c5dddf46 ""
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||||
"/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/tex/generic/pgf/basiclayer/pgfcoretransformations.code.tex" 1 22012 81b34a0aa8fa1a6158cc6220b00e4f10 ""
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||||
"/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/tex/generic/pgf/basiclayer/pgfcoretransparency.code.tex" 1 8893 e851de2175338fdf7c17f3e091d94618 ""
|
||||
"/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibrarydecorations.code.tex" 1 5628 dc0ee4ba7f3e40acae5600067ce833de ""
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||||
"/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibrarydecorations.pathmorphing.code.tex" 1 321 cdd11262840e01e25374a2d458f15e99 ""
|
||||
"/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibrarydecorations.pathreplacing.code.tex" 1 1319 0b2de5126c6cbc295f0eb77f7344b34d ""
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||||
"/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibraryplotmarks.code.tex" 1 325 36322b0789619b270aec5993d5a9ed08 ""
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||||
"/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibrarytopaths.code.tex" 1 11518 738408f795261b70ce8dd47459171309 ""
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||||
"/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/tex/generic/pgf/frontendlayer/tikz/tikz.code.tex" 1 186782 af500404a9edec4d362912fe762ded92 ""
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||||
"/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/tex/generic/pgf/libraries/decorations/pgflibrarydecorations.pathmorphing.code.tex" 1 8843 5533436db3e30fbad1e0440db6027dac ""
|
||||
"/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/tex/generic/pgf/libraries/decorations/pgflibrarydecorations.pathreplacing.code.tex" 1 7474 f05a7223b140f230922562ac6a9fede5 ""
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||||
"/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/tex/generic/pgf/libraries/pgflibraryfpu.code.tex" 1 85938 8e4ba97c5906e1c0d158aea81fe29af7 ""
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||||
"/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/tex/generic/pgf/libraries/pgflibraryplothandlers.code.tex" 1 32995 ac577023e12c0e4bd8aa420b2e852d1a ""
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||||
"/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/tex/generic/pgf/libraries/pgflibraryplotmarks.code.tex" 1 14526 4bc184b12436aa7f6490b2d2036870ef ""
|
||||
"/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/tex/generic/pgf/math/pgfint.code.tex" 1 3063 8c415c68a0f3394e45cfeca0b65f6ee6 ""
|
||||
"/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/tex/generic/pgf/math/pgfmath.code.tex" 1 949 cea70942e7b7eddabfb3186befada2e6 ""
|
||||
"/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/tex/generic/pgf/math/pgfmathcalc.code.tex" 1 13270 2e54f2ce7622437bf37e013d399743e3 ""
|
||||
"/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/tex/generic/pgf/math/pgfmathfloat.code.tex" 1 104717 9b2393fbf004a0ce7fa688dbce423848 ""
|
||||
"/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/tex/generic/pgf/math/pgfmathfunctions.base.code.tex" 1 10165 cec5fa73d49da442e56efc2d605ef154 ""
|
||||
"/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/tex/generic/pgf/math/pgfmathfunctions.basic.code.tex" 1 28178 41c17713108e0795aac6fef3d275fbca ""
|
||||
"/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/tex/generic/pgf/math/pgfmathfunctions.code.tex" 1 9649 85779d3d8d573bfd2cd4137ba8202e60 ""
|
||||
"/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/tex/generic/pgf/math/pgfmathfunctions.comparison.code.tex" 1 3865 ac538ab80c5cf82b345016e474786549 ""
|
||||
"/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/tex/generic/pgf/math/pgfmathfunctions.integerarithmetics.code.tex" 1 3177 27d85c44fbfe09ff3b2cf2879e3ea434 ""
|
||||
"/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/tex/generic/pgf/math/pgfmathfunctions.misc.code.tex" 1 11024 0179538121bc2dba172013a3ef89519f ""
|
||||
"/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/tex/generic/pgf/math/pgfmathfunctions.random.code.tex" 1 7890 0a86dbf4edfd88d022e0d889ec78cc03 ""
|
||||
"/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/tex/generic/pgf/math/pgfmathfunctions.round.code.tex" 1 3379 781797a101f647bab82741a99944a229 ""
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||||
"/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/tex/generic/pgf/math/pgfmathfunctions.trigonometric.code.tex" 1 92405 f515f31275db273f97b9d8f52e1b0736 ""
|
||||
"/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/tex/generic/pgf/math/pgfmathparser.code.tex" 1 37466 97b0a1ba732e306a1a2034f5a73e239f ""
|
||||
"/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/tex/generic/pgf/math/pgfmathutil.code.tex" 1 8471 c2883569d03f69e8e1cabfef4999cfd7 ""
|
||||
"/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/tex/generic/pgf/modules/pgfmoduledecorations.code.tex" 1 71742 3da44a8be6626eef1c400c68776c7a0f ""
|
||||
"/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/tex/generic/pgf/modules/pgfmodulematrix.code.tex" 1 21211 1e73ec76bd73964d84197cc3d2685b01 ""
|
||||
"/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/tex/generic/pgf/modules/pgfmoduleplot.code.tex" 1 16121 346f9013d34804439f7436ff6786cef7 ""
|
||||
"/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/tex/generic/pgf/modules/pgfmoduleshapes.code.tex" 1 44792 271e2e1934f34c759f4dedb1e14a5015 ""
|
||||
"/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/tex/generic/pgf/pgf.revision.tex" 1 114 e6d443369d0673933b38834bf99e422d ""
|
||||
"/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/tex/generic/pgf/systemlayer/pgf.cfg" 1 926 2963ea0dcf6cc6c0a770b69ec46a477b ""
|
||||
"/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/tex/generic/pgf/systemlayer/pgfsys-common-pdf.def" 1 5542 32f75a31ea6c3a7e1148cd6d5e93dbb7 ""
|
||||
"/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/tex/generic/pgf/systemlayer/pgfsys-luatex.def" 1 13255 83878f3f820beccc0dd1c2683dabc65e ""
|
||||
"/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/tex/generic/pgf/systemlayer/pgfsys-pdftex.def" 1 12612 7774ba67bfd72e593c4436c2de6201e3 ""
|
||||
"/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/tex/generic/pgf/systemlayer/pgfsys.code.tex" 1 61351 bc5f86e0355834391e736e97a61abced ""
|
||||
"/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/tex/generic/pgf/systemlayer/pgfsysprotocol.code.tex" 1 1896 b8e0ca0ac371d74c0ca05583f6313c91 ""
|
||||
"/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/tex/generic/pgf/systemlayer/pgfsyssoftpath.code.tex" 1 7778 53c8b5623d80238f6a20aa1df1868e63 ""
|
||||
"/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/tex/generic/pgf/utilities/pgffor.code.tex" 1 24033 d8893a1ec4d1bfa101b172754743d340 ""
|
||||
"/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/tex/generic/pgf/utilities/pgfkeys.code.tex" 1 39784 414c54e866ebab4b801e2ad81d9b21d8 ""
|
||||
"/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/tex/generic/pgf/utilities/pgfkeyslibraryfiltered.code.tex" 1 37433 940bc6d409f1ffd298adfdcaf125dd86 ""
|
||||
"/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/tex/generic/pgf/utilities/pgfrcs.code.tex" 1 4385 510565c2f07998c8a0e14f0ec07ff23c ""
|
||||
"/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/tex/generic/pgf/utilities/pgfutil-common.tex" 1 29239 22e8c7516012992a49873eff0d868fed ""
|
||||
"/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/tex/generic/pgf/utilities/pgfutil-latex.def" 1 6950 8524a062d82b7afdc4a88a57cb377784 ""
|
||||
"/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/tex/generic/pgfplots/libs/pgflibrarypgfplots.surfshading.code.tex" 1 22701 5fab7b8ebb90b053dc067d1bd37e43c2 ""
|
||||
"/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/tex/generic/pgfplots/libs/pgfplotslibrary.code.tex" 1 3047 aa82404aec57311271f4991c44bd71dc ""
|
||||
"/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/tex/generic/pgfplots/libs/tikzlibrarypgfplots.contourlua.code.tex" 1 2931 5d52092da9e839accd7c9026062fe5c3 ""
|
||||
"/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/tex/generic/pgfplots/liststructure/pgfplotsarray.code.tex" 1 23537 54be8160344d894595f6d145b1311658 ""
|
||||
"/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/tex/generic/pgfplots/liststructure/pgfplotsdeque.code.tex" 1 4288 b8d6247899b21e3bb66bb11b24d30f2c ""
|
||||
"/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/tex/generic/pgfplots/liststructure/pgfplotsliststructure.code.tex" 1 13828 11d1b09335a4a8baa693dd1e6cac3edf ""
|
||||
"/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/tex/generic/pgfplots/liststructure/pgfplotsliststructureext.code.tex" 1 24373 6544c1554e5da33118301011eb03058d ""
|
||||
"/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/tex/generic/pgfplots/liststructure/pgfplotsmatrix.code.tex" 1 18861 7dc35832c8ccea3aa73cdcd75ec0a60b ""
|
||||
"/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/tex/generic/pgfplots/numtable/pgfplotstableshared.code.tex" 1 83469 f77a7d8a23834d4c2472f8dba8e67bff ""
|
||||
"/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/tex/generic/pgfplots/oldpgfcompatib/pgfplotsoldpgfsupp_loader.code.tex" 1 12347 43d867ea29e34d528123d9ef750aa146 ""
|
||||
"/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/tex/generic/pgfplots/oldpgfcompatib/pgfplotsoldpgfsupp_pgfutil-common-lists.tex" 1 8008 3bb2d07671e6afab7dcb90dfaec572a4 ""
|
||||
"/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/tex/generic/pgfplots/pgfplots.code.tex" 1 485274 aafeb7052fbed4c8aba6fcc36c94ea72 ""
|
||||
"/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/tex/generic/pgfplots/pgfplots.errorbars.code.tex" 1 22428 72578a4c9324bc5dfafe23fe64f64024 ""
|
||||
"/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/tex/generic/pgfplots/pgfplots.markers.code.tex" 1 12489 859c23df41fb9067128ef5a64b01c0a4 ""
|
||||
"/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/tex/generic/pgfplots/pgfplots.paths.code.tex" 1 3533 973f376afa5a4526f16b11630b9931b4 ""
|
||||
"/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/tex/generic/pgfplots/pgfplots.revision.tex" 1 520 2a55e10851bbb34fb49a8e1d6b50a09b ""
|
||||
"/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/tex/generic/pgfplots/pgfplots.scaling.code.tex" 1 123680 d33fda4929d7200c3e6f0ec83c006aef ""
|
||||
"/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/tex/generic/pgfplots/pgfplotscoordprocessing.code.tex" 1 367035 be5ad6faf030b5e07b899b712359f9d2 ""
|
||||
"/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/tex/generic/pgfplots/pgfplotscore.code.tex" 1 19944 7957349fbe31c4e8dea9de4cd41cb086 ""
|
||||
"/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/tex/generic/pgfplots/pgfplotsmeshplothandler.code.tex" 1 133871 7247b31742a2240343a6739cb76d6821 ""
|
||||
"/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/tex/generic/pgfplots/pgfplotsmeshplotimage.code.tex" 1 25239 bf1615252744653354985789b73e7404 ""
|
||||
"/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/tex/generic/pgfplots/pgfplotsplothandlers.code.tex" 1 120954 bdf135670013db80411b2fb0f95876ac ""
|
||||
"/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/tex/generic/pgfplots/pgfplotsstackedplots.code.tex" 1 26393 a7d9bbecdd0db20d652c909dac892e25 ""
|
||||
"/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/tex/generic/pgfplots/pgfplotsticks.code.tex" 1 91244 1a0e9e49b7a2d10d1b1a610306ba4f8c ""
|
||||
"/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/tex/generic/pgfplots/sys/pgflibrarypgfplots.surfshading.pgfsys-pdftex.def" 1 5907 9dc460712c23e5b3338820499d47608c ""
|
||||
"/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/tex/generic/pgfplots/sys/pgfplotssysgeneric.code.tex" 1 3095 c82d281b748902a65be2ccca97360b11 ""
|
||||
"/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/tex/generic/pgfplots/util/pgfplotsbinary.code.tex" 1 23050 a369aa910ef860a3621fe0459faa335c ""
|
||||
"/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/tex/generic/pgfplots/util/pgfplotsbinary.data.code.tex" 1 26859 7a4ee9d206fb0a0daa0d3108445afb57 ""
|
||||
"/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/tex/generic/pgfplots/util/pgfplotscolor.code.tex" 1 23958 1b96260863091af1669c3a38b1c4c9af ""
|
||||
"/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/tex/generic/pgfplots/util/pgfplotscolormap.code.tex" 1 88956 018b2512ef27998e97af72e8b1dcdbd5 ""
|
||||
"/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/tex/generic/pgfplots/util/pgfplotsutil.code.tex" 1 71792 dba1b75b15201895eb36f142f13b3238 ""
|
||||
"/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/tex/generic/pgfplots/util/pgfplotsutil.verb.code.tex" 1 3286 c17079ba50483e1ac1721268ea016041 ""
|
||||
"/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/tex/latex/amscls/amsthm.sty" 1 12594 0d51ac3a545aaaa555021326ff22a6cc ""
|
||||
"/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/tex/latex/amsfonts/amsfonts.sty" 1 5949 3f3fd50a8cc94c3d4cbf4fc66cd3df1c ""
|
||||
"/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/tex/latex/amsfonts/amssymb.sty" 1 13829 94730e64147574077f8ecfea9bb69af4 ""
|
||||
"/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/tex/latex/amsfonts/umsa.fd" 1 961 6518c6525a34feb5e8250ffa91731cff ""
|
||||
"/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/tex/latex/amsfonts/umsb.fd" 1 961 d02606146ba5601b5645f987c92e6193 ""
|
||||
"/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/tex/latex/amsmath/amsbsy.sty" 1 2222 2166a1f7827be30ddc30434e5efcee1b ""
|
||||
"/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/tex/latex/amsmath/amsgen.sty" 1 4173 d22509bc0c91281d991b2de7c88720dd ""
|
||||
"/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/tex/latex/amsmath/amsmath.sty" 1 88370 c780f23aea0ece6add91e09b44dca2cd ""
|
||||
"/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/tex/latex/amsmath/amsopn.sty" 1 4474 23ca1d3a79a57b405388059456d0a8df ""
|
||||
"/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/tex/latex/amsmath/amstext.sty" 1 2444 71618ea5f2377e33b04fb97afdd0eac2 ""
|
||||
"/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/tex/latex/base/article.cls" 1 20144 63d8bacaf52e5abf4db3bc322373e1d4 ""
|
||||
"/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/tex/latex/base/inputenc.sty" 1 5048 0270515b828149155424600fd2d58ac5 ""
|
||||
"/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/tex/latex/base/size12.clo" 1 8449 ffe4ba2166a344827c3a832d1d5e0a91 ""
|
||||
"/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/tex/latex/epstopdf-pkg/epstopdf-base.sty" 1 13886 d1306dcf79a944f6988e688c1785f9ce ""
|
||||
"/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/tex/latex/geometry/geometry.sty" 1 41601 9cf6c5257b1bc7af01a58859749dd37a ""
|
||||
"/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/tex/latex/graphics-cfg/color.cfg" 1 1213 620bba36b25224fa9b7e1ccb4ecb76fd ""
|
||||
"/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/tex/latex/graphics-cfg/graphics.cfg" 1 1224 978390e9c2234eab29404bc21b268d1e ""
|
||||
"/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/tex/latex/graphics-def/pdftex.def" 1 19440 9da9dcbb27470349a580fca7372d454b ""
|
||||
"/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/tex/latex/graphics/graphics.sty" 1 18363 dee506cb8d56825d8a4d020f5d5f8704 ""
|
||||
"/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/tex/latex/graphics/graphicx.sty" 1 8010 6f2ad8c2b2ffbd607af6475441c7b5e4 ""
|
||||
"/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/tex/latex/graphics/keyval.sty" 1 2671 70891d50dac933918b827d326687c6e8 ""
|
||||
"/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/tex/latex/graphics/mathcolor.ltx" 1 2885 9c645d672ae17285bba324998918efd8 ""
|
||||
"/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/tex/latex/graphics/trig.sty" 1 4023 2c9f39712cf7b43d3eb93a8bbd5c8f67 ""
|
||||
"/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/tex/latex/l3backend/l3backend-pdftex.def" 1 29785 9f93ab201fe5dd053afcc6c1bcf7d266 ""
|
||||
"/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/tex/latex/latexconfig/epstopdf-sys.cfg" 1 678 4792914a8f45be57bb98413425e4c7af ""
|
||||
"/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/tex/latex/pgf/basiclayer/pgf.sty" 1 1090 bae35ef70b3168089ef166db3e66f5b2 ""
|
||||
"/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/tex/latex/pgf/basiclayer/pgfcore.sty" 1 373 00b204b1d7d095b892ad31a7494b0373 ""
|
||||
"/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/tex/latex/pgf/compatibility/pgfcomp-version-0-65.sty" 1 21013 f4ff83d25bb56552493b030f27c075ae ""
|
||||
"/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/tex/latex/pgf/compatibility/pgfcomp-version-1-18.sty" 1 989 c49c8ae06d96f8b15869da7428047b1e ""
|
||||
"/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/tex/latex/pgf/frontendlayer/tikz.sty" 1 339 c2e180022e3afdb99c7d0ea5ce469b7d ""
|
||||
"/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/tex/latex/pgf/math/pgfmath.sty" 1 306 c56a323ca5bf9242f54474ced10fca71 ""
|
||||
"/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/tex/latex/pgf/systemlayer/pgfsys.sty" 1 443 8c872229db56122037e86bcda49e14f3 ""
|
||||
"/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/tex/latex/pgf/utilities/pgffor.sty" 1 348 ee405e64380c11319f0e249fed57e6c5 ""
|
||||
"/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/tex/latex/pgf/utilities/pgfkeys.sty" 1 274 5ae372b7df79135d240456a1c6f2cf9a ""
|
||||
"/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/tex/latex/pgf/utilities/pgfrcs.sty" 1 325 f9f16d12354225b7dd52a3321f085955 ""
|
||||
"/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/tex/latex/pgfplots/pgfplots.sty" 1 4904 ee78b44e85d6fccf08cd99370557481e ""
|
||||
"/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/tex/latex/xcolor/xcolor.sty" 1 55384 b454dec21c2d9f45ec0b793f0995b992 ""
|
||||
"main.aux" 1753127848.86231 32 044b7f8fc9779af7531264e0c5c84b6d "pdflatex"
|
||||
"main.tex" 1753127846.84123 3197 f45a3479336ca31493b2b995d7bdf3ae ""
|
||||
(generated)
|
||||
"main.aux"
|
||||
"main.log"
|
||||
"main.pdf"
|
||||
(rewritten before read)
|
||||
286
main.fls
Normal file
286
main.fls
Normal file
@@ -0,0 +1,286 @@
|
||||
PWD /home/allen/papers/pi3
|
||||
INPUT /nix/store/dmm8f43zw2rwzgr1xs03ac1r98m8zp5i-texlive-combined-full-2024-final/share/texmf-var/web2c/texmf.cnf
|
||||
INPUT /nix/store/dmm8f43zw2rwzgr1xs03ac1r98m8zp5i-texlive-combined-full-2024-final/share/texmf-var/web2c/pdftex/pdflatex.fmt
|
||||
INPUT main.tex
|
||||
OUTPUT main.log
|
||||
INPUT /nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/tex/latex/base/article.cls
|
||||
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INPUT /nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/fonts/tfm/public/amsfonts/symbols/msbm10.tfm
|
||||
INPUT /nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/fonts/tfm/public/amsfonts/symbols/msbm10.tfm
|
||||
INPUT /nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/fonts/tfm/public/amsfonts/symbols/msbm10.tfm
|
||||
INPUT /nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/fonts/tfm/public/amsfonts/cmextra/cmex7.tfm
|
||||
INPUT /nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/fonts/tfm/public/amsfonts/symbols/msam10.tfm
|
||||
INPUT /nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/fonts/tfm/public/amsfonts/symbols/msam7.tfm
|
||||
INPUT /nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/fonts/tfm/public/amsfonts/symbols/msbm10.tfm
|
||||
INPUT /nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/fonts/tfm/public/amsfonts/symbols/msbm7.tfm
|
||||
INPUT /nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/fonts/tfm/public/cm/cmr17.tfm
|
||||
INPUT /nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/fonts/tfm/public/cm/cmbx12.tfm
|
||||
INPUT /nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/fonts/tfm/public/cm/cmr8.tfm
|
||||
INPUT /nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/fonts/tfm/public/cm/cmr6.tfm
|
||||
INPUT /nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/fonts/tfm/public/cm/cmmi8.tfm
|
||||
INPUT /nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/fonts/tfm/public/cm/cmmi6.tfm
|
||||
INPUT /nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/fonts/tfm/public/cm/cmsy8.tfm
|
||||
INPUT /nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/fonts/tfm/public/cm/cmsy6.tfm
|
||||
INPUT /nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/fonts/tfm/public/amsfonts/cmextra/cmex8.tfm
|
||||
INPUT /nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/fonts/tfm/public/amsfonts/cmextra/cmex7.tfm
|
||||
INPUT /nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/fonts/tfm/public/amsfonts/symbols/msam10.tfm
|
||||
INPUT /nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/fonts/tfm/public/amsfonts/symbols/msam7.tfm
|
||||
INPUT /nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/fonts/tfm/public/amsfonts/symbols/msbm10.tfm
|
||||
INPUT /nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/fonts/tfm/public/amsfonts/symbols/msbm7.tfm
|
||||
INPUT /nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/fonts/tfm/public/cm/cmti12.tfm
|
||||
INPUT /nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/fonts/tfm/public/cm/cmbx12.tfm
|
||||
OUTPUT main.pdf
|
||||
INPUT /nix/store/dmm8f43zw2rwzgr1xs03ac1r98m8zp5i-texlive-combined-full-2024-final/share/texmf-var/fonts/map/pdftex/updmap/pdftex.map
|
||||
INPUT main.aux
|
||||
INPUT /nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/fonts/type1/public/amsfonts/cm/cmbx12.pfb
|
||||
INPUT /nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/fonts/type1/public/amsfonts/cm/cmex10.pfb
|
||||
INPUT /nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/fonts/type1/public/amsfonts/cm/cmmi12.pfb
|
||||
INPUT /nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/fonts/type1/public/amsfonts/cm/cmmi6.pfb
|
||||
INPUT /nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/fonts/type1/public/amsfonts/cm/cmmi8.pfb
|
||||
INPUT /nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/fonts/type1/public/amsfonts/cm/cmr12.pfb
|
||||
INPUT /nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/fonts/type1/public/amsfonts/cm/cmr17.pfb
|
||||
INPUT /nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/fonts/type1/public/amsfonts/cm/cmr6.pfb
|
||||
INPUT /nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/fonts/type1/public/amsfonts/cm/cmr8.pfb
|
||||
INPUT /nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/fonts/type1/public/amsfonts/cm/cmsy10.pfb
|
||||
INPUT /nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/fonts/type1/public/amsfonts/cm/cmsy8.pfb
|
||||
INPUT /nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/fonts/type1/public/amsfonts/cm/cmti12.pfb
|
||||
INPUT /nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/fonts/type1/public/amsfonts/symbols/msam10.pfb
|
||||
510
main.log
Normal file
510
main.log
Normal file
@@ -0,0 +1,510 @@
|
||||
This is pdfTeX, Version 3.141592653-2.6-1.40.26 (TeX Live 2024/nixos.org) (preloaded format=pdflatex 1980.1.1) 22 JUL 2025 04:57
|
||||
entering extended mode
|
||||
restricted \write18 enabled.
|
||||
file:line:error style messages enabled.
|
||||
%&-line parsing enabled.
|
||||
**main.tex
|
||||
(./main.tex
|
||||
LaTeX2e <2024-11-01> patch level 2
|
||||
L3 programming layer <2025-01-18>
|
||||
(/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/tex/latex/base/article.cls
|
||||
Document Class: article 2024/06/29 v1.4n Standard LaTeX document class
|
||||
(/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/tex/latex/base/size12.clo
|
||||
File: size12.clo 2024/06/29 v1.4n Standard LaTeX file (size option)
|
||||
)
|
||||
\c@part=\count196
|
||||
\c@section=\count197
|
||||
\c@subsection=\count198
|
||||
\c@subsubsection=\count199
|
||||
\c@paragraph=\count266
|
||||
\c@subparagraph=\count267
|
||||
\c@figure=\count268
|
||||
\c@table=\count269
|
||||
\abovecaptionskip=\skip49
|
||||
\belowcaptionskip=\skip50
|
||||
\bibindent=\dimen141
|
||||
) (/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/tex/latex/base/inputenc.sty
|
||||
Package: inputenc 2024/02/08 v1.3d Input encoding file
|
||||
\inpenc@prehook=\toks17
|
||||
\inpenc@posthook=\toks18
|
||||
) (/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/tex/latex/amsmath/amsmath.sty
|
||||
Package: amsmath 2024/11/05 v2.17t AMS math features
|
||||
\@mathmargin=\skip51
|
||||
|
||||
For additional information on amsmath, use the `?' option.
|
||||
(/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/tex/latex/amsmath/amstext.sty
|
||||
Package: amstext 2021/08/26 v2.01 AMS text
|
||||
(/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/tex/latex/amsmath/amsgen.sty
|
||||
File: amsgen.sty 1999/11/30 v2.0 generic functions
|
||||
\@emptytoks=\toks19
|
||||
\ex@=\dimen142
|
||||
)) (/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/tex/latex/amsmath/amsbsy.sty
|
||||
Package: amsbsy 1999/11/29 v1.2d Bold Symbols
|
||||
\pmbraise@=\dimen143
|
||||
) (/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/tex/latex/amsmath/amsopn.sty
|
||||
Package: amsopn 2022/04/08 v2.04 operator names
|
||||
)
|
||||
\inf@bad=\count270
|
||||
LaTeX Info: Redefining \frac on input line 233.
|
||||
\uproot@=\count271
|
||||
\leftroot@=\count272
|
||||
LaTeX Info: Redefining \overline on input line 398.
|
||||
LaTeX Info: Redefining \colon on input line 409.
|
||||
\classnum@=\count273
|
||||
\DOTSCASE@=\count274
|
||||
LaTeX Info: Redefining \ldots on input line 495.
|
||||
LaTeX Info: Redefining \dots on input line 498.
|
||||
LaTeX Info: Redefining \cdots on input line 619.
|
||||
\Mathstrutbox@=\box52
|
||||
\strutbox@=\box53
|
||||
LaTeX Info: Redefining \big on input line 721.
|
||||
LaTeX Info: Redefining \Big on input line 722.
|
||||
LaTeX Info: Redefining \bigg on input line 723.
|
||||
LaTeX Info: Redefining \Bigg on input line 724.
|
||||
\big@size=\dimen144
|
||||
LaTeX Font Info: Redeclaring font encoding OML on input line 742.
|
||||
LaTeX Font Info: Redeclaring font encoding OMS on input line 743.
|
||||
\macc@depth=\count275
|
||||
LaTeX Info: Redefining \bmod on input line 904.
|
||||
LaTeX Info: Redefining \pmod on input line 909.
|
||||
LaTeX Info: Redefining \smash on input line 939.
|
||||
LaTeX Info: Redefining \relbar on input line 969.
|
||||
LaTeX Info: Redefining \Relbar on input line 970.
|
||||
\c@MaxMatrixCols=\count276
|
||||
\dotsspace@=\muskip17
|
||||
\c@parentequation=\count277
|
||||
\dspbrk@lvl=\count278
|
||||
\tag@help=\toks20
|
||||
\row@=\count279
|
||||
\column@=\count280
|
||||
\maxfields@=\count281
|
||||
\andhelp@=\toks21
|
||||
\eqnshift@=\dimen145
|
||||
\alignsep@=\dimen146
|
||||
\tagshift@=\dimen147
|
||||
\tagwidth@=\dimen148
|
||||
\totwidth@=\dimen149
|
||||
\lineht@=\dimen150
|
||||
\@envbody=\toks22
|
||||
\multlinegap=\skip52
|
||||
\multlinetaggap=\skip53
|
||||
\mathdisplay@stack=\toks23
|
||||
LaTeX Info: Redefining \[ on input line 2953.
|
||||
LaTeX Info: Redefining \] on input line 2954.
|
||||
) (/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/tex/latex/amsfonts/amssymb.sty
|
||||
Package: amssymb 2013/01/14 v3.01 AMS font symbols
|
||||
(/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/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.
|
||||
)) (/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/tex/latex/amscls/amsthm.sty
|
||||
Package: amsthm 2020/05/29 v2.20.6
|
||||
\thm@style=\toks24
|
||||
\thm@bodyfont=\toks25
|
||||
\thm@headfont=\toks26
|
||||
\thm@notefont=\toks27
|
||||
\thm@headpunct=\toks28
|
||||
\thm@preskip=\skip54
|
||||
\thm@postskip=\skip55
|
||||
\thm@headsep=\skip56
|
||||
\dth@everypar=\toks29
|
||||
) (/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/tex/latex/pgfplots/pgfplots.sty (/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/tex/generic/pgfplots/pgfplots.revision.tex)
|
||||
Package: pgfplots 2021/05/15 v1.18.1 Data Visualization (1.18.1)
|
||||
(/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/tex/latex/graphics/graphicx.sty
|
||||
Package: graphicx 2021/09/16 v1.2d Enhanced LaTeX Graphics (DPC,SPQR)
|
||||
(/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/tex/latex/graphics/keyval.sty
|
||||
Package: keyval 2022/05/29 v1.15 key=value parser (DPC)
|
||||
\KV@toks@=\toks30
|
||||
) (/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/tex/latex/graphics/graphics.sty
|
||||
Package: graphics 2024/08/06 v1.4g Standard LaTeX Graphics (DPC,SPQR)
|
||||
(/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/tex/latex/graphics/trig.sty
|
||||
Package: trig 2023/12/02 v1.11 sin cos tan (DPC)
|
||||
) (/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/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 106.
|
||||
(/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/tex/latex/graphics-def/pdftex.def
|
||||
File: pdftex.def 2024/04/13 v1.2c Graphics/color driver for pdftex
|
||||
))
|
||||
\Gin@req@height=\dimen151
|
||||
\Gin@req@width=\dimen152
|
||||
) (/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/tex/latex/pgf/frontendlayer/tikz.sty
|
||||
(/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/tex/latex/pgf/basiclayer/pgf.sty (/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/tex/latex/pgf/utilities/pgfrcs.sty (/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/tex/generic/pgf/utilities/pgfutil-common.tex
|
||||
\pgfutil@everybye=\toks31
|
||||
\pgfutil@tempdima=\dimen153
|
||||
\pgfutil@tempdimb=\dimen154
|
||||
) (/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/tex/generic/pgf/utilities/pgfutil-latex.def
|
||||
\pgfutil@abb=\box54
|
||||
) (/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/tex/generic/pgf/utilities/pgfrcs.code.tex (/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/tex/generic/pgf/pgf.revision.tex)
|
||||
Package: pgfrcs 2023-01-15 v3.1.10 (3.1.10)
|
||||
))
|
||||
Package: pgf 2023-01-15 v3.1.10 (3.1.10)
|
||||
(/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/tex/latex/pgf/basiclayer/pgfcore.sty (/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/tex/latex/pgf/systemlayer/pgfsys.sty (/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/tex/generic/pgf/systemlayer/pgfsys.code.tex
|
||||
Package: pgfsys 2023-01-15 v3.1.10 (3.1.10)
|
||||
(/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/tex/generic/pgf/utilities/pgfkeys.code.tex
|
||||
\pgfkeys@pathtoks=\toks32
|
||||
\pgfkeys@temptoks=\toks33
|
||||
(/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/tex/generic/pgf/utilities/pgfkeyslibraryfiltered.code.tex
|
||||
\pgfkeys@tmptoks=\toks34
|
||||
))
|
||||
\pgf@x=\dimen155
|
||||
\pgf@y=\dimen156
|
||||
\pgf@xa=\dimen157
|
||||
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|
||||
\pgf@xb=\dimen159
|
||||
\pgf@yb=\dimen160
|
||||
\pgf@xc=\dimen161
|
||||
\pgf@yc=\dimen162
|
||||
\pgf@xd=\dimen163
|
||||
\pgf@yd=\dimen164
|
||||
\w@pgf@writea=\write3
|
||||
\r@pgf@reada=\read2
|
||||
\c@pgf@counta=\count282
|
||||
\c@pgf@countb=\count283
|
||||
\c@pgf@countc=\count284
|
||||
\c@pgf@countd=\count285
|
||||
\t@pgf@toka=\toks35
|
||||
\t@pgf@tokb=\toks36
|
||||
\t@pgf@tokc=\toks37
|
||||
\pgf@sys@id@count=\count286
|
||||
(/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/tex/generic/pgf/systemlayer/pgf.cfg
|
||||
File: pgf.cfg 2023-01-15 v3.1.10 (3.1.10)
|
||||
)
|
||||
Driver file for pgf: pgfsys-pdftex.def
|
||||
(/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/tex/generic/pgf/systemlayer/pgfsys-pdftex.def
|
||||
File: pgfsys-pdftex.def 2023-01-15 v3.1.10 (3.1.10)
|
||||
(/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/tex/generic/pgf/systemlayer/pgfsys-common-pdf.def
|
||||
File: pgfsys-common-pdf.def 2023-01-15 v3.1.10 (3.1.10)
|
||||
))) (/nix/store/z5ws6797p4763ycdkmdpayprws409k1g-texlive-combined-full-2024-final-texmfdist/tex/generic/pgf/systemlayer/pgfsyssoftpath.code.tex
|
||||
File: pgfsyssoftpath.code.tex 2023-01-15 v3.1.10 (3.1.10)
|
||||
\pgfsyssoftpath@smallbuffer@items=\count287
|
||||
\pgfsyssoftpath@bigbuffer@items=\count288
|
||||
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[1
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***********
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LaTeX2e <2024-11-01> patch level 2
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L3 programming layer <2025-01-18>
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\documentclass[12pt]{article}
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\usepackage[utf8]{inputenc}
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\usepackage{amsmath, amssymb, amsthm}
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\usepackage{pgfplots}
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\usepackage{geometry}
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\geometry{margin=1in}
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\newtheorem{theorem}{Theorem}
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\newtheorem{lemma}[theorem]{Lemma}
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\newtheorem{proposition}[theorem]{Proposition}
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\newtheorem{corollary}[theorem]{Corollary}
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\theoremstyle{definition}
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\newtheorem{definition}[theorem]{Definition}
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\newtheorem*{remark}{Remark}
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||||
% Document
|
||||
\begin{document}
|
||||
|
||||
\title{Simple Proof That \( \pi ^ {3} < 3^{\pi} \)}
|
||||
\author{Minco}
|
||||
\date{\today}
|
||||
\maketitle
|
||||
|
||||
\section*{Introduction}
|
||||
This document presents a very simple mathematical proof that $\pi^3 < 3^{\pi}$.
|
||||
The proof illustrates the beauty of pure mathematics, which allows a simple question to be shown in verbose manner.
|
||||
|
||||
\begin{theorem}
|
||||
\[
|
||||
\pi^3 < 3^{\pi}
|
||||
\]
|
||||
\end{theorem}
|
||||
|
||||
\begin{proposition}
|
||||
Since the both bases are over 1, we can exponentiate both sides of the inequality by \(\frac{1}{3 \pi}\).
|
||||
So we have to prove that:
|
||||
\[
|
||||
\pi^{\frac{1}{\pi}} < 3^{\frac{1}{3}}
|
||||
\]
|
||||
\end{proposition}
|
||||
|
||||
\section*{Limit Analysis}
|
||||
Consider the function
|
||||
\[
|
||||
f(x) = x^{\frac{1}{x}}, \quad x > 0.
|
||||
\]
|
||||
|
||||
First, take the logarithm on both sides.
|
||||
|
||||
\[
|
||||
\log {f(x)} = \frac{1}{x} \log{x} \quad (\text{log is a natural logarithm})
|
||||
\]
|
||||
\[
|
||||
\therefore f(x) = e^{\frac{1}{x} \log{x}}
|
||||
\]
|
||||
|
||||
Then analyze the limits at the boundaries of the domain:
|
||||
|
||||
\[
|
||||
\lim_{x \to 0^+} f(x) = \lim_{X \to - \infty} e^{X} = 0
|
||||
\]
|
||||
|
||||
And
|
||||
|
||||
\[
|
||||
\lim_{x \to \infty} f(x) = \lim_{X \to 0^+} e^{X} = 1 .
|
||||
\]
|
||||
|
||||
\section*{Derivative Analysis}
|
||||
|
||||
To find the derivative of \(f(x)\), use logarithmic differentiation as in Limit Analysis:
|
||||
|
||||
\[
|
||||
y = x^{\frac{1}{x}} \implies \log y = \frac{\ln x}{x}.
|
||||
\]
|
||||
|
||||
Differentiating both sides:
|
||||
\[
|
||||
\frac{1}{y} \frac{dy}{dx} = \frac{d}{dx}\left(\frac{\log x}{x}\right) = \frac{1 - \log x}{x^2}.
|
||||
\]
|
||||
|
||||
Since \(x > 0\),
|
||||
|
||||
\[
|
||||
\frac{1- \log x}{x^2} = 0 \quad \rm{iff.} \quad 1 - \log x = 0
|
||||
\]
|
||||
|
||||
\[
|
||||
\therefore x = e \quad \text{where} \quad \frac{d}{dx} f(x) = 0
|
||||
\]
|
||||
|
||||
\section*{Graph}
|
||||
\begin{center}
|
||||
\begin{tikzpicture}
|
||||
\begin{axis}[
|
||||
domain=0.1:5,
|
||||
samples=200,
|
||||
axis lines=middle,
|
||||
xlabel=$x$, ylabel={$f(x)$},
|
||||
ymin=0, ymax=2,
|
||||
]
|
||||
\addplot [black, thick] {x^(1/x)};
|
||||
\addplot[
|
||||
only marks,
|
||||
mark=*,
|
||||
mark size=2pt,
|
||||
black
|
||||
] coordinates {(3, {3^(1/3)})};
|
||||
\draw[dotted] (axis cs:3,0) -- (axis cs:3,{3^(1/3)});
|
||||
\draw[dotted] (axis cs:0,{3^(1/3)}) -- (axis cs:3,{3^(1/3)});
|
||||
\node [anchor=south east] at (axis cs:3,{3^(1/3)}) {$\bigl(3,\,3^{\frac{1}{3}}\bigr)$};
|
||||
|
||||
\addplot[
|
||||
only marks,
|
||||
mark=*,
|
||||
mark size=2pt,
|
||||
black
|
||||
] coordinates {(3.14, {3.14^(1/3.14)})};
|
||||
\draw[dotted] (axis cs:3.14,0) -- (axis cs:3.14,{3.14^(1/3.14)});
|
||||
\draw[dotted] (axis cs:0,{3.14^(1/3.14)}) -- (axis cs:3.14,{3.14^(1/3.14)});
|
||||
\node [anchor=south west] at (axis cs:3.14,{3.14^(1/3.14)}) {$\bigl(\pi,\,\pi^{\frac{1}{\pi}}\bigr)$};
|
||||
\end{axis}
|
||||
\end{tikzpicture}
|
||||
\end{center}
|
||||
|
||||
\begin{proof}
|
||||
As shown in the graph,
|
||||
|
||||
\[
|
||||
\pi^{\frac{1}{\pi}} < 3^{\frac{1}{3}}
|
||||
\]
|
||||
\[
|
||||
\therefore \boxed{\pi^3 < 3^{\pi}}
|
||||
\]
|
||||
\end{proof}
|
||||
\end{document}
|
||||
Reference in New Issue
Block a user