chore: SAVEPOINT
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This is pdfTeX, Version 3.141592653-2.6-1.40.24 (TeX Live 2022) (preloaded format=pdflatex 2022.10.5) 12 APR 2026 22:19
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This is pdfTeX, Version 3.141592653-2.6-1.40.24 (TeX Live 2022) (preloaded format=pdflatex 2022.10.5) 13 APR 2026 00:00
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entering extended mode
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restricted \write18 enabled.
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file:line:error style messages enabled.
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@@ -130,20 +130,30 @@ File: umsa.fd 2013/01/14 v3.01 AMS symbols A
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LaTeX Font Info: Trying to load font information for U+msb on input line 52.
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(/usr/local/texlive/2022/texmf-dist/tex/latex/amsfonts/umsb.fd
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File: umsb.fd 2013/01/14 v3.01 AMS symbols B
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) [1{/usr/local/texlive/2022/texmf-var/fonts/map/pdftex/updmap/pdftex.map}] (./paper.aux) )
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) [1{/usr/local/texlive/2022/texmf-var/fonts/map/pdftex/updmap/pdftex.map}] [2] [3]
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Overfull \hbox (2.17857pt too wide) in paragraph at lines 247--248
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\OT1/cmr/bx/n/10 Lemma 3.2. \OT1/cmr/m/it/10 For each $\OML/cmm/m/it/10 G[] \OMS/cmsy/m/n/10 2 M$\OT1/cmr/m/it/10 , the ex-ten-sions of $\OT1/cmr/m/n/10 ^^H[](\OML/cmm/m/it/10 G[]\OT1/cmr/m/n/10 )$ \OT1/cmr/m/it/10 lie in $\OT1/cmr/m/n/10 ^^H[]$\OT1/cmr/m/it/10 , i.e., $[] \OMS/cmsy/m/n/10 ^^R
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[]
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Overfull \hbox (18.04422pt too wide) detected at line 257
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[]\OT1/cmr/m/n/10 (\OML/cmm/m/it/10 N\OT1/cmr/m/n/10 (\OML/cmm/m/it/10 v[]\OT1/cmr/m/n/10 )) = [](\OMS/cmsy/m/n/10 f\OML/cmm/m/it/10 a[]; a[]\OMS/cmsy/m/n/10 g [ \OT1/cmr/m/n/10 (\OML/cmm/m/it/10 N\OT1/cmr/m/n/10 (\OML/cmm/m/it/10 v[]\OT1/cmr/m/n/10 ) \OMS/cmsy/m/n/10 n f\OML/cmm/m/it/10 a[]; a[]\OMS/cmsy/m/n/10 g\OT1/cmr/m/n/10 )) = \OMS/cmsy/m/n/10 f\OML/cmm/m/it/10 \OT1/cmr/m/n/10 (\OML/cmm/m/it/10 a[]\OT1/cmr/m/n/10 )\OMS/cmsy/m/n/10 g [ \OML/cmm/m/it/10 \OT1/cmr/m/n/10 (\OML/cmm/m/it/10 N\OT1/cmr/m/n/10 (\OML/cmm/m/it/10 v[]\OT1/cmr/m/n/10 ) \OMS/cmsy/m/n/10 n f\OML/cmm/m/it/10 a[]; a[]\OMS/cmsy/m/n/10 g\OT1/cmr/m/n/10 ) = \OML/cmm/m/it/10 \OT1/cmr/m/n/10 (\OML/cmm/m/it/10 N[]\OT1/cmr/m/n/10 (\OML/cmm/m/it/10 v[]\OT1/cmr/m/n/10 ))\OML/cmm/m/it/10 :
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[]
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[4] (./paper.aux) )
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Here is how much of TeX's memory you used:
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1710 strings out of 478268
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23958 string characters out of 5846347
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316202 words of memory out of 5000000
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19795 multiletter control sequences out of 15000+600000
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474133 words of font info for 47 fonts, out of 8000000 for 9000
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1719 strings out of 478268
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24065 string characters out of 5846347
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330202 words of memory out of 5000000
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19803 multiletter control sequences out of 15000+600000
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475834 words of font info for 54 fonts, out of 8000000 for 9000
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1302 hyphenation exceptions out of 8191
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69i,5n,76p,280b,204s stack positions out of 10000i,1000n,20000p,200000b,200000s
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</usr/local/texlive/2022/texmf-dist/fonts/type1/public/amsfonts/cm/cmbx10.pfb></usr/local/texlive/2022/texmf-dist/fonts/type1/public/amsfonts/cm/cmcsc10.pfb></usr/local/texlive/2022/texmf-dist/fonts/type1/public/amsfonts/cm/cmr7.pfb></usr/local/texlive/2022/texmf-dist/fonts/type1/public/amsfonts/cm/cmr8.pfb></usr/local/texlive/2022/texmf-dist/fonts/type1/public/amsfonts/cm/cmti8.pfb></usr/local/texlive/2022/texmf-dist/fonts/type1/public/amsfonts/cm/cmtt8.pfb>
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Output written on paper.pdf (1 page, 64345 bytes).
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69i,9n,76p,727b,280s stack positions out of 10000i,1000n,20000p,200000b,200000s
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</usr/local/texlive/2022/texmf-dist/fonts/type1/public/amsfonts/cm/cmbx10.pfb></usr/local/texlive/2022/texmf-dist/fonts/type1/public/amsfonts/cm/cmcsc10.pfb></usr/local/texlive/2022/texmf-dist/fonts/type1/public/amsfonts/cm/cmex10.pfb></usr/local/texlive/2022/texmf-dist/fonts/type1/public/amsfonts/cm/cmmi10.pfb></usr/local/texlive/2022/texmf-dist/fonts/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/type1/public/amsfonts/cm/cmr5.pfb></usr/local/texlive/2022/texmf-dist/fonts/type1/public/amsfonts/cm/cmr7.pfb></usr/local/texlive/2022/texmf-dist/fonts/type1/public/amsfonts/cm/cmr8.pfb></usr/local/texlive/2022/texmf-dist/fonts/type1/public/amsfonts/cm/cmsy10.pfb></usr/local/texlive/2022/texmf-dist/fonts/type1/public/amsfonts/cm/cmsy5.pfb></usr/local/texlive/2022/texmf-dist/fonts/type1/public/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></usr/local/texlive/2022/texmf-dist/fonts/type1/public/amsfonts/cm/cmtt8.pfb></usr/local/texlive/2022/texmf-dist/fonts/type1/public/amsfonts/symbols/msam10.pfb></usr/local/texlive/2022/texmf-dist/fonts/type1/public/amsfonts/symbols/msbm10.pfb>
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Output written on paper.pdf (4 pages, 213600 bytes).
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PDF statistics:
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38 PDF objects out of 1000 (max. 8388607)
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22 compressed objects within 1 object stream
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102 PDF objects out of 1000 (max. 8388607)
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61 compressed objects within 1 object stream
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0 named destinations out of 1000 (max. 500000)
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1 words of extra memory for PDF output out of 10000 (max. 10000000)
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