Add preprints files (part 15)

.gitattributes

@@ -765,3 +765,28 @@ preprints/Uniform-Permanence-in-Weakly-Reversible-Mass-Action-Systems-October-5-
 preprints/Uniform-Pluricanonical-Iitaka-Fibrations-October-3-2026/paper.pdf filter=lfs diff=lfs merge=lfs -text
 preprints/Uniform-quasipolynomial-time-trace-reconstruction-October-5-2026/uniform-trace-reconstruction.pdf filter=lfs diff=lfs merge=lfs -text
 preprints/Uniform-real-Lipschitz-surfaces-on-the-triangular-lattice-September-25-2026/paper.pdf filter=lfs diff=lfs merge=lfs -text
+preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/uniform-stability-spherical-laughlin-gap.pdf filter=lfs diff=lfs merge=lfs -text
+preprints/Uniformization-of-complete-Kahler-manifolds-with-positive-bisectional-curvature-September-23-2026/paper.pdf filter=lfs diff=lfs merge=lfs -text
+preprints/Unitarizability-Implies-Amenability-for-Countable-Groups-September-23-2026/paper.pdf filter=lfs diff=lfs merge=lfs -text
+preprints/Universal-Computation-with-Eventually-Stationary-Navier-Stokes-Forcing-September-27-2026/manuscript.pdf filter=lfs diff=lfs merge=lfs -text
+preprints/Universal-cover-splitting-for-compact-Kahler-manifolds-September-23-2026/paper.pdf filter=lfs diff=lfs merge=lfs -text
+preprints/Universal-optimality-of-the-triangular-lattice-September-23-2026/paper.pdf filter=lfs diff=lfs merge=lfs -text
+preprints/Universal-strong-Kadison-Kastler-stability-September-23-2026/paper.pdf filter=lfs diff=lfs merge=lfs -text
+preprints/Universal-Tensor-Squares-for-Symmetric-Groups-September-24-2026/main.pdf filter=lfs diff=lfs merge=lfs -text
+preprints/Universality-of-critical-quench-autocorrelations-in-the-Sherrington-Kirkpatrick-model-October-5-2026/main.pdf filter=lfs diff=lfs merge=lfs -text
+preprints/Unrestricted-pro-modularity-at-the-prime-two-October-4-2026/two-adic-promodularity.pdf filter=lfs diff=lfs merge=lfs -text
+preprints/Vanishing-of-higher-bounded-Hochschild-cohomology-September-23-2026/paper.pdf filter=lfs diff=lfs merge=lfs -text
+preprints/Variable-dimension-Weisfeiler-Leman-equivalence-on-general-and-subcubic-graphs-September-25-2026/paper.pdf filter=lfs diff=lfs merge=lfs -text
+preprints/Variance-of-the-Random-k-SAT-Hitting-Time-September-27-2026/article.pdf filter=lfs diff=lfs merge=lfs -text
+preprints/Velocity-Field-Detection-of-Computation-in-Forced-Navier-Stokes-Flows-September-27-2026/manuscript.pdf filter=lfs diff=lfs merge=lfs -text
+preprints/Virasoro-Constraints-for-Projective-Complete-Intersections-September-24-2026/article.pdf filter=lfs diff=lfs merge=lfs -text
+preprints/Virasoro-Constraints-under-Projectivization-October-5-2026/virasoro-constraints-under-projectivization.pdf filter=lfs diff=lfs merge=lfs -text
+preprints/Virtual-compact-specialness-of-hyperbolic-one-relator-groups-September-25-2026/paper.pdf filter=lfs diff=lfs merge=lfs -text
+preprints/Weak-and-strong-normalization-in-pure-type-systems-September-25-2026/paper.pdf filter=lfs diff=lfs merge=lfs -text
+preprints/Weak-Hessian-bounds-along-every-geodesic-in-RCD-spaces-September-24-2026/weak-hessian-geodesics.pdf filter=lfs diff=lfs merge=lfs -text
+preprints/Weak-mixing-of-triangular-billiards-with-an-irrational-angle-October-5-2026/weak-mixing-triangular-billiards.pdf filter=lfs diff=lfs merge=lfs -text
+preprints/Weak-pure-infiniteness-and-O-infinity-absorption-September-25-2026/paper.pdf filter=lfs diff=lfs merge=lfs -text
+preprints/Weighted-Dilation-Graphs-Smooth-Shifted-Primes-and-Totient-Fibers-September-24-2026/paper.pdf filter=lfs diff=lfs merge=lfs -text
+preprints/Weil-classes-and-Hodge-classes-on-abelian-powers-September-30-2026/paper.pdf filter=lfs diff=lfs merge=lfs -text
+preprints/Witnessed-symmetric-choice-is-strictly-stronger-than-choiceless-polynomial-time-with-counting-September-24-2026/paper.pdf filter=lfs diff=lfs merge=lfs -text
+preprints/Zero-Plane-Rigidity-for-Einstein-Four-Manifolds-October-4-2026/einstein-boundary.pdf filter=lfs diff=lfs merge=lfs -text

preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/README.md

@@ -0,0 +1,17 @@
+# [Uniform Stability of the Spherical Laughlin Gap](uniform-stability-spherical-laughlin-gap.pdf)
+
+**Author:** OpenAI
+
+**Date:** October 5, 2026
+
+## Citation
+
+```bibtex
+@misc{OAI:Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026,
+  author = {{OpenAI}},
+  title = {{Uniform Stability of the Spherical Laughlin Gap}},
+  howpublished = {OpenAI Math Release preprint
+                  \href{https://github.com/openai/math/blob/main/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/uniform-stability-spherical-laughlin-gap.pdf}{OAI:Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026}},
+  year = {2026}
+}
+```

preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/basiclayer/pgfcoreexternal.code.tex

@@ -0,0 +1,357 @@
+
+\ProvidesFileRCS{pgfcoreexternal.code.tex}
+
+
+
+\newif\ifpgfexternal@aux@in@dpth
+\newif\ifpgfexternal@info
+
+\pgfkeys{
+    /pgf/images/include external/.code={\pgfimage{#1}},
+    /pgf/images/aux in dpth/.is if=pgfexternal@aux@in@dpth,
+    /pgf/images/aux in dpth/.default=true,
+    /pgf/images/trim external/.code n args={4}{%
+        \def\pgf@external@kern@left{#1}%
+        \def\pgf@external@kern@bottom{#2}%
+        \def\pgf@external@kern@right{#3}%
+        \def\pgf@external@kern@top{#4}%
+        \ifx\pgf@external@kern@left\pgfutil@empty\def\pgf@external@kern@left{0sp}\fi%
+        \ifx\pgf@external@kern@bottom\pgfutil@empty\def\pgf@external@kern@bottom{0sp}\fi%
+        \ifx\pgf@external@kern@right\pgfutil@empty\def\pgf@external@kern@right{0sp}\fi%
+        \ifx\pgf@external@kern@top\pgfutil@empty\def\pgf@external@kern@top{0sp}\fi%
+    },
+    /pgf/images/trim external={1truein}{1truein}{1truein}{1truein},
+    /pgf/images/external info/.is if=pgfexternal@info,
+    /pgf/images/external info/.default=true,
+}
+
+
+
+\newif\ifpgfexternalreadmainaux
+\pgfexternalreadmainauxtrue
+
+
+\def\pgfrealjobname#1{%
+  \global\let\pgfactualjobname=\jobname
+  \edef\pgf@tempa{\expandafter\string\csname #1\endcsname}%
+  \edef\pgf@tempb{\expandafter\string\csname\jobname\endcsname}%
+  \ifx\pgf@tempa\pgf@tempb%
+  \else%
+    \pgf@external@grabshipouttrue%
+    \pgfexternal@nofiles%
+    \ifpgfexternalreadmainaux
+        \gdef\jobname{#1}%
+    \fi
+    \ifpgfexternal@aux@in@dpth
+        \csname newwrite\endcsname\w@pgfexternal@auxout
+    \fi
+    \pgfexternal@geometry@compatibility
+  \fi%
+  \gdef\pgfrealjobname##1{}%
+}
+
+\def\pgfexternal@geometry@compatibility{%
+    \pgfutil@ifundefined{geometry}{%
+    }{%
+        \pgf@typeout{Package TikZ externalization: calling \string\geometry{driver=none} during externalization.^^J}%
+        \geometry{driver=none}%
+    }%
+}%
+
+\def\pgfexternal@nofiles{%
+    \let\pgfexternal@nofiles@=\relax
+    \def\relax{\relax}%
+    \csname nofiles\endcsname
+    \let\relax=\pgfexternal@nofiles@
+}%
+
+\newif\ifpgf@external@grabshipout
+\newbox\pgfexternal@startupbox
+
+\pgfutil@ifundefined{AtBeginDocument}{}{%
+    \AtBeginDocument{%
+      \ifpgf@external@grabshipout%
+        \global\let\pgfexternal@originalshipout=\shipout%
+        \global\def\shipout{\setbox\pgfpic=}%
+        \maxdeadcycles=10000%
+        {%
+          \output{\global\setbox\pgfexternal@startupbox=\vbox{\csname @begindvi\endcsname\unvbox255}}%
+          \hbox{}\eject%
+        }%
+      \fi%
+    }
+}%
+
+\pgfutil@ifundefined{AtEndDocument}{}{%
+    \AtEndDocument{%
+      \ifpgf@external@grabshipout
+        \pgfutil@ifundefined{pgfexternal@did@a@shipout}{%
+          \pgfexternal@error@no@shipout
+        }{}%
+      \fi
+    }%
+}
+
+\def\pgfexternal@error@no@shipout{%
+    \pgferror{Sorry, image externalization failed: the resulting image was EMPTY. I tried to externalize '\pgfactualjobname'. Perhaps there was a typo somewhere? Please check that your document contains '\string\beginpgfgraphicnamed{\pgfactualjobname} ... \string\endpgfgraphicnamed'}%
+}%
+
+
+
+\def\pgf@externalbegin#1{%
+  \let\pgf@next=\pgf@external@normal%
+  \ifpgf@external@grabshipout%
+    \edef\pgf@tempa{\expandafter\string\csname #1\endcsname}%
+    \edef\pgf@tempb{\expandafter\string\csname\pgfactualjobname\endcsname}%
+    \ifx\pgf@tempa\pgf@tempb%
+      \let\pgf@next=\pgf@external@grab%
+    \fi%
+  \fi%
+  \pgf@next{#1}%
+}
+
+
+\AtBeginDocument{
+  \let\beginpgfgraphicnamed=\pgf@externalbegin%
+  \let\endpgfgraphicnamed=\unskip
+}
+
+
+\def\pgf@external@normal#1{%
+  \let\pgf@filename=\pgfutil@empty%
+  \expandafter\pgf@findfile\pgfsys@imagesuffixlist:+{#1}%
+  \ifx\pgf@filename\pgfutil@empty%
+    \let\pgf@next=\relax%
+  \else%
+    \let\pgf@next=\pgf@replacepicturebygraphic%
+  \fi%
+  \pgf@next%
+}
+
+\long\def\pgf@replacepicturebygraphic#1\endpgfgraphicnamed{%
+    \expandafter\pgfincludeexternalgraphics\expandafter{\pgf@filename}\unskip
+}
+
+\def\pgfincludeexternalgraphics#1{%
+    \begingroup
+    \pgfexternalreaddpth{#1}%
+    \pgfkeysifdefined{/pgf/images/include external/#1/.@cmd}{%
+        \pgfkeysgetvalue{/pgf/images/include external/#1/.@cmd}\pgf@tempa
+        \pgfkeyslet{/pgf/images/include external/.@cmd}\pgf@tempa
+    }{}%
+    \setbox1=\hbox{\pgfkeysvalueof{/pgf/images/include external/.@cmd}{#1}\pgfeov}%
+    \ifdim\pgfexternaltrimleft=0sp \else \kern\pgfexternaltrimleft\relax \fi
+    \ifdim\pgfexternaldepth=0pt
+        \box1
+    \else
+        \dimen0=\pgfexternaldepth\relax
+        \hbox{\lower\dimen0 \box1 }%
+    \fi
+    \ifdim\pgfexternaltrimright=0sp \else \kern\pgfexternaltrimright\relax \fi
+    \endgroup
+}
+
+\def\pgfexternalreaddpth#1{%
+    \edef\pgfexternalreaddpth@restore{%
+        \noexpand\endlinechar=\the\endlinechar\space
+        \noexpand\catcode`\noexpand\@=\the\catcode`\@\space
+    }%
+    \def\pgfexternaldepth{0sp}%
+    \def\pgfexternaltrimleft{0sp}%
+    \def\pgfexternaltrimright{0sp}%
+    \endlinechar=-1 %
+    \catcode`\@=11
+    \openin\r@pgf@reada=#1.dpth
+    \pgfincludeexternalgraphics@read@dpth
+    \pgfexternalreaddpth@restore
+}%
+\def\pgfincludeexternalgraphics@read@dpth{%
+    \ifeof\r@pgf@reada
+        \closein\r@pgf@reada
+    \else
+        \read\r@pgf@reada to\pgfincludeexternalgraphics@auxline
+        \ifx\pgfincludeexternalgraphics@auxline\pgfutil@empty
+        \else
+            \expandafter\pgfincludeexternalgraphics@read@dpth@line\pgfincludeexternalgraphics@auxline\pgfincludeexternalgraphics@read@dpth@line@EOI
+        \fi
+        \expandafter\pgfincludeexternalgraphics@read@dpth
+    \fi
+}%
+
+\def\pgfexternal@restore#1{#1}%
+
+\long\def\pgfincludeexternalgraphics@read@dpth@line@getfirst#1#2\pgfincludeexternalgraphics@read@dpth@line@EOI{%
+    \def\pgf@first{#1}%
+}%
+\long\def\pgfincludeexternalgraphics@read@dpth@line#1\pgfincludeexternalgraphics@read@dpth@line@EOI{%
+    \pgfincludeexternalgraphics@read@dpth@line@getfirst#1\pgfincludeexternalgraphics@read@dpth@line@EOI
+    \expandafter\ifcat\expandafter\noexpand\pgf@first\relax
+        \expandafter\ifx\pgf@first\pgfexternal@restore
+            #1%
+        \else
+            \pgfutil@ifundefined{if@filesw}{%
+            }{%
+                \if@filesw
+                    {%
+                    \toks0={#1}%
+                    \immediate\write\@auxout{%
+                        \noexpand\def\noexpand\dpthimport{\the\toks0}\noexpand\dpthimport}%
+                    }%
+                \fi
+            }%
+        \fi
+    \else%
+        \def\pgfexternaldepth{#1}%
+    \fi
+}%
+
+\def\pgfexternalstorecommand#1{%
+}%
+\def\pgfexternalstorecommand@isexporting#1{%
+    \immediate\write\w@pgfexternal@auxout{\noexpand\pgfexternal@restore{#1}}%
+}%
+
+
+
+\def\pgf@external@grab#1{%
+  \def\pgf@filename{#1}%
+  \ifpgfexternal@aux@in@dpth
+    \begingroup
+    \pgf@external@init@aux@in@dpth
+    \let\G@refundefinedtrue=\pgf@external@grab@refundefinedtrue
+  \fi
+  \gdef\pgf@trimleft@final{0sp}%
+  \gdef\pgf@trimright@final{0sp}%
+  \setbox\pgfpic=\hbox\bgroup\bgroup%
+    \let\endpgfgraphicnamed=\pgf@externalend%
+}
+
+{\catcode`\^=12 \gdef\pgfexternal@hat{^}}
+
+\expandafter\let\expandafter\pgf@external@grab@refundefinedtrue@orig\csname G@refundefinedtrue\endcsname
+
+\def\pgf@external@grab@refundefinedtrue{%
+    \pgf@external@grab@refundefinedtrue@orig
+    \begingroup
+    \def\n{\pgfexternal@hat\pgfexternal@hat J}%
+    \pgfexternalstorecommand{%
+      \pgf@external@grab@refundefinedtrue@code
+      \noexpand\immediate\noexpand\write16{\pgf@external@grab@refundefinedtrue@warning}%
+      \noexpand\G@refundefinedtrue
+    }%
+    \endgroup
+}%
+
+\def\pgf@external@grab@refundefinedtrue@code{}
+
+\def\pgf@external@grab@refundefinedtrue@warning{%
+    LaTeX Warning: External picture `\pgfactualjobname' contains undefined references\noexpand\on@line.\n
+}%
+
+\let\pgf@external@@protected@write@orig=\protected@write
+\long\def\pgf@external@@protected@write@immediate#1#2#3{%
+  \begingroup
+    \let\pgf@write@=\write
+    \def\write{\noexpand\immediate\pgf@write@}%
+    \pgf@external@@protected@write@orig{#1}{#2}{#3}%
+  \endgroup
+}%
+
+\def\pgf@external@init@aux@in@dpth{%
+  \let\pgfexternalstorecommand=\pgfexternalstorecommand@isexporting
+  \csname @fileswtrue\endcsname
+  \immediate\openout\w@pgfexternal@auxout=\pgf@filename.dpth
+  \let\@auxout=\w@pgfexternal@auxout
+  \let\protected@write=\pgf@external@@protected@write@immediate
+}%
+
+\def\pgf@externalend@storeshifts#1{%
+  \immediate\write#1{\the\dp\pgfpic}%
+  \ifx\pgf@trimleft@final\pgfutil@empty\else
+    \immediate\write#1{\noexpand\pgfexternal@restore{\noexpand\def\noexpand\pgfexternaltrimleft{\pgf@trimleft@final}}}%
+  \fi
+  \ifx\pgf@trimright@final\pgfutil@empty\else
+    \immediate\write#1{\noexpand\pgfexternal@restore{\noexpand\def\noexpand\pgfexternaltrimright{\pgf@trimright@final}}}%
+  \fi
+  \ifpgfexternal@info
+    \immediate\write#1{\noexpand\pgfexternal@restore{\noexpand\def\noexpand\pgfexternalwidth{\the\wd\pgfpic}}}%
+    \immediate\write#1{\noexpand\pgfexternal@restore{\noexpand\def\noexpand\pgfexternalheight{\the\dimen0}}}%
+  \fi
+}
+\def\pgf@externalend{%
+  \unskip\egroup\egroup%
+  {%
+    \def\pgf@external@trim{0}%
+    \def\pgf@external@store@dpth{0}%
+    \ifpgf@trim@lowlevel
+      \gdef\pgf@trimleft@final{}%
+      \gdef\pgf@trimright@final{}%
+    \else
+      \ifdim\pgf@trimleft@final=0sp  \gdef\pgf@trimleft@final{}  \else\def\pgf@external@trim{1}\fi
+      \ifdim\pgf@trimright@final=0sp \gdef\pgf@trimright@final{} \else\def\pgf@external@trim{1}\fi
+      \if1\pgf@external@trim
+          \setbox\pgfpic=\hbox{%
+              \ifx\pgf@trimleft@final\pgfutil@empty\else\kern-\pgf@trimleft@final\fi
+              \box\pgfpic
+              \ifx\pgf@trimright@final\pgfutil@empty\else\kern-\pgf@trimright@final\fi
+          }%
+          \def\pgf@external@store@dpth{1}%
+      \fi
+    \fi
+    \parindent0pt %
+    \hoffset=0pt %
+    \voffset=0pt
+    \dimen0\ht\pgfpic%
+    \advance\dimen0\dp\pgfpic%
+    \ifdim\dp\pgfpic=0pt\relax
+    \else%
+      \def\pgf@external@store@dpth{1}%
+    \fi
+    \ifpgfexternal@info
+      \def\pgf@external@store@dpth{1}%
+    \fi
+    \if1\pgf@external@store@dpth
+      \ifpgfexternal@aux@in@dpth
+        \pgf@externalend@storeshifts\@auxout
+        \immediate\closeout\@auxout
+      \else
+        \immediate\openout\pgf@plotwrite=\pgf@filename.dpth
+        \pgf@externalend@storeshifts\pgf@plotwrite
+        \immediate\closeout\pgf@plotwrite
+      \fi
+    \fi
+    \pgfsys@prepare@papersize{\the\wd\pgfpic}{\the\dimen0}%
+    \setbox0=\vbox{%
+      \kern -\pgf@external@kern@top\relax%
+      \hbox{%
+        \kern -\pgf@external@kern@left\relax%
+        \hbox to0pt{%
+          \wd\pgfexternal@startupbox=0pt %
+          \ht\pgfexternal@startupbox=0pt %
+          \dp\pgfexternal@startupbox=0pt %
+          \box\pgfexternal@startupbox%
+          \pgfsys@atbegindocument\hss}%
+        \box\pgfpic%
+        \kern\pgf@external@kern@right\relax%
+      }%
+      \kern\pgf@external@kern@bottom\relax%
+    }%
+    \let\pgfexternal@nointerlineskip@orig=\nointerlineskip
+    \let\nointerlineskip=\pgfexternal@nointerlineskip
+    \pgfexternal@originalshipout\box0 %
+    \gdef\pgfexternal@did@a@shipout{1}%
+  }%
+  \ifpgfexternal@aux@in@dpth
+    \endgroup
+  \fi
+}
+
+\def\pgfexternal@nointerlineskip{%
+    \ifvmode
+      \pgfexternal@nointerlineskip@orig
+    \else
+      \relax%
+    \fi
+}%
+
+\endinput

preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/basiclayer/pgfcoregraphicstate.code.tex

@@ -0,0 +1,162 @@
+
+\ProvidesFileRCS{pgfcoregraphicstate.code.tex}
+
+
+\newdimen\pgflinewidth
+
+
+
+\def\pgfsetlinewidth#1{%
+  \pgfmathsetlength\pgflinewidth{#1}%
+  \global\pgflinewidth=\pgflinewidth%
+  \pgfsys@setlinewidth{\the\pgflinewidth}%
+  \ignorespaces}
+
+
+
+\def\pgfsetinnerlinewidth#1{%
+  \pgfmathsetlength\pgf@x{#1}%
+  \edef\pgfinnerlinewidth{\the\pgf@x}%
+}
+\def\pgfinnerlinewidth{0pt}
+
+
+
+\def\pgfsetinnerstrokecolor#1{\def\pgfinnerstrokecolor{#1}}
+\def\pgfinnerstrokecolor{white}
+
+
+
+\def\pgfsetmiterlimit#1{%
+  \ifdim#1pt<1pt\pgferror{miter limit cannot be less than 1}\fi%
+  \pgfsys@setmiterlimit{#1}%
+  \ignorespaces}
+
+
+
+\def\pgfsetdash#1#2{%
+  \def\pgf@temp{}%
+  \def\pgf@next{\pgf@strip}%
+  \pgf@strip#1{pgf@stop}%
+  \pgfmathsetlength\pgf@x{#2}%
+  \pgfsys@setdash{\pgf@temp}{\the\pgf@x}%
+  \ignorespaces}
+
+\def\pgf@strip#1{%
+  \def\pgf@@temp{#1}%
+  \ifx\pgf@@temp\pgf@stop%
+    \let\pgf@next=\relax%
+  \else%
+    \pgfmathsetlength\pgf@x{#1}%
+    \ifx\pgf@temp\pgfutil@empty%
+      \edef\pgf@temp{\the\pgf@x}%
+    \else%
+      \edef\pgf@temp{\pgf@temp,\the\pgf@x}%
+    \fi%
+  \fi\pgf@next}
+
+\def\pgf@stop{pgf@stop}
+
+
+
+\def\pgfsetstrokecolor#1{%
+  \pgfutil@colorlet{pgfstrokecolor}{#1}%
+  \pgfutil@ifundefined{applycolormixins}{}{\applycolormixins{pgfstrokecolor}}%
+  \expandafter\let\expandafter\pgf@temp\csname\string\color@pgfstrokecolor\endcsname
+  \global\let\pgf@strokecolor@global=\pgf@temp
+  \expandafter\pgf@setstrokecolor\pgf@temp%
+}
+\def\pgf@setstrokecolor#1#2#3#4#5{%
+  \expandafter\ifx\csname pgfsys@color@#4@stroke\endcsname\relax%
+    \pgferror{Unsupported color model `#4'. Sorry}%
+  \else%
+    \edef\pgf@colmarshal{\expandafter\noexpand\csname pgfsys@color@#4@stroke\endcsname}%
+    \pgf@uncomma#5,,%
+    \pgf@colmarshal%
+  \fi}
+
+\def\pgf@uncomma#1,{%
+  \def\pgf@coltest{#1}%
+  \ifx\pgf@coltest\pgfutil@empty%
+    \let\pgf@colnext=\relax%
+  \else%
+    \expandafter\def\expandafter\pgf@colmarshal\expandafter{\pgf@colmarshal{#1}}%
+    \let\pgf@colnext=\pgf@uncomma%
+  \fi%
+  \pgf@colnext%
+}
+
+
+
+\def\pgfsetfillcolor#1{%
+  \pgfutil@colorlet{pgffillcolor}{#1}%
+  \pgfutil@ifundefined{applycolormixins}{}{\applycolormixins{pgffillcolor}}%
+  \expandafter\let\expandafter\pgf@temp\csname\string\color@pgffillcolor\endcsname
+  \global\let\pgf@fillcolor@global=\pgf@temp
+  \expandafter\pgf@setfillcolor\pgf@temp
+}
+\def\pgf@setfillcolor#1#2#3#4#5{%
+  \expandafter\ifx\csname pgfsys@color@#4@fill\endcsname\relax%
+    \pgferror{Unsupported color model `#4'. Sorry}%
+  \else%
+    \edef\pgf@colmarshal{\expandafter\noexpand\csname pgfsys@color@#4@fill\endcsname}%
+    \pgf@uncomma#5,,%
+    \pgf@colmarshal%
+  \fi}
+
+
+
+
+\def\pgfsetcolor#1{%
+  \pgfutil@colorlet{pgfstrokecolor}{#1}%
+  \pgfutil@ifundefined{applycolormixins}{}{\applycolormixins{pgfstrokecolor}}%
+  \expandafter\let\expandafter\pgf@temp\csname\string\color@pgfstrokecolor\endcsname
+  \global\let\pgf@strokecolor@global=\pgf@temp
+  \global\let\pgf@fillcolor@global=\pgf@temp
+  \expandafter\pgf@setcolor\pgf@temp%
+}
+\def\pgf@setcolor#1#2#3#4#5{%
+  \expandafter\ifx\csname pgfsys@color@#4\endcsname\relax%
+    \pgferror{Unsupported color model `#4'. Sorry}%
+  \else%
+    \edef\pgf@colmarshal{\expandafter\noexpand\csname pgfsys@color@#4\endcsname}%
+    \pgf@uncomma#5,,%
+    \pgf@colmarshal%
+  \fi}
+
+\def\XC@bcolor{\pgfsys@color@reset}
+
+
+\def\pgfsetbuttcap{\pgfsys@buttcap\ignorespaces}
+
+
+
+\def\pgfsetroundcap{\pgfsys@roundcap\ignorespaces}
+
+
+
+\def\pgfsetrectcap{\pgfsys@rectcap\ignorespaces}
+
+
+
+\def\pgfsetmiterjoin{\pgfsys@miterjoin\ignorespaces}
+
+
+
+\def\pgfsetbeveljoin{\pgfsys@beveljoin\ignorespaces}
+
+
+
+\def\pgfsetroundjoin{\pgfsys@roundjoin\ignorespaces}
+
+
+
+\def\pgfseteorule{\pgfsys@eoruletrue\ignorespaces}
+
+
+
+\def\pgfsetnonzerorule{\pgfsys@eorulefalse\ignorespaces}
+
+
+
+\endinput

preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/basiclayer/pgfcoreimage.code.tex

@@ -0,0 +1,150 @@
+
+\ProvidesFileRCS{pgfcoreimage.code.tex}
+
+
+
+
+\def\pgfdeclareimage{\pgfutil@ifnextchar[{\pgf@declareimage}{\pgf@declareimage[]}}
+\def\pgf@declareimage[#1]#2#3{%
+  \pgfqkeys{/pgf/images}{height=,width=,page=,interpolate=false,mask=,#1}%
+  \gdef\pgf@filename{}%
+  \ifx\pgf@imagepage\pgfutil@empty%
+  \else%
+  \expandafter\pgf@findfile\pgfsys@imagesuffixlist:+{#3.page\pgf@imagepage}%
+  \fi%
+  \ifx\pgf@filename\pgfutil@empty%
+    \expandafter\pgf@findfile\pgfsys@imagesuffixlist:+{#3}%
+  \else%
+    \pgfkeys{/pgf/images/page=}%
+  \fi%
+  \ifx\pgf@filename\pgfutil@empty%
+    \pgfwarning%
+    {File "#3" not found when defining image "#2".
+      Tried all extensions in "\pgfsys@imagesuffixlist"}%
+    \pgf@declaredraftimage{#2}{#3}%
+  \else%
+    \ifpgf@draftmode%
+      \pgf@declaredraftimage{#2}{#3}%
+    \else%
+      \pgfsys@defineimage%
+    \fi%
+  \fi%
+  \expandafter\global\expandafter\let\csname pgf@image@#2!\endcsname=\pgf@image%
+}
+
+
+\pgfkeys{
+    /pgf/images/draft/.is if=pgf@draftmode,
+    /pgf/images/draft/.default=true}
+\pgfkeys{/pgf/images/width/.estore in=\pgf@imagewidth}
+\pgfkeys{/pgf/images/height/.estore in=\pgf@imageheight}
+\pgfkeys{/pgf/images/page/.estore in=\pgf@imagepage}
+\pgfkeys{/pgf/images/interpolate/.cd,.code=\edef\pgf@imageinterpolate{#1},.default=true}
+\let\pgf@imageinterpolate\pgfutil@empty
+\pgfkeys{/pgf/images/mask/.code=%
+  {%
+    \edef\pgf@imagemask{#1}%
+    \ifx\pgf@imagemask\pgfutil@empty%
+    \else%
+      \pgfutil@ifundefined{pgf@mask@#1}%
+      {\pgferror{Undefined mask "#1".}%
+        \edef\pgf@imagemask{}}%
+      {\edef\pgf@imagemask{\csname pgf@mask@#1\endcsname}%
+      }%
+    \fi%
+  }}
+
+
+\def\pgf@findfile#1:#2+#3{%
+  \pgfutil@IfFileExists{#3#1}%
+  {\xdef\pgf@filename{#3#1}}%
+  {\def\pgf@mightbeempty{#2}%
+    \ifx\pgf@mightbeempty\pgfutil@empty\else%
+    \pgf@findfile#2+{#3}%
+    \fi}}
+
+\def\pgf@declaredraftimage#1#2{%
+  \ifx\pgf@imagewidth\pgfutil@empty%
+    \pgfwarning{Missing width for image "#1" ("#2") in draft mode. Using 1cm instead}%
+    \edef\pgf@imagewidth{1cm}%
+  \fi%
+  \ifx\pgf@imageheight\pgfutil@empty%
+    \pgfwarning{Missing height for image "#1" ("#2") in draft mode. Using 1cm instead}%
+    \edef\pgf@imageheight{1cm}%
+  \fi%
+  \ifx\pgf@imagepage\pgfutil@empty\else\edef\pgf@imagepagetext{ page \pgf@imagepage}\fi%
+  \edef\pgf@image{%
+    \hbox to \pgf@imagewidth{%
+      \vrule\kern-0.4pt%
+      \vbox to \pgf@imageheight{%
+        \hrule\vfil%
+        \hbox to \pgf@imagewidth{\hskip-10cm\hfil\noexpand\pgfutil@font@tiny#2\pgf@imagepage\hfil\hskip-10cm}%
+        \vfil\hrule}%
+      \kern-0.4pt\vrule}%
+  }%
+}
+
+
+
+
+\def\pgfdeclaremask{\pgfutil@ifnextchar[\pgf@declaremask{\pgf@declaremask[]}}
+\def\pgf@declaremask[#1]#2#3{%
+  \pgfqkeys{/pgf/images/mask}{matte={1 1 1},#1}%
+  \def\pgf@mask{}%
+  \gdef\pgf@filename{}%
+  \expandafter\pgf@findfile\pgfsys@imagesuffixlist:+{#3}%
+  \ifx\pgf@filename\pgfutil@empty%
+    \pgfwarning%
+    {File "#3" not found when defining mask "#2".
+      Tried all extensions in "\pgfsys@imagesuffixlist"}%
+  \else%
+    \pgfsys@definemask%
+  \fi%
+  \expandafter\global\expandafter\let\csname pgf@mask@#2\endcsname=\pgf@mask%
+}
+
+\pgfkeys{/pgf/images/mask/matte/.cd,.estore in=\pgf@maskmatte,.value required}
+
+
+
+
+\def\pgfaliasimage#1#2{%
+  \expandafter\global\expandafter\let\expandafter\pgf@temp\expandafter=\csname pgf@image@#2!\endcsname%
+  \expandafter\global\expandafter\let\csname pgf@image@#1!\endcsname=\pgf@temp%
+  }
+
+
+
+\def\pgfuseimage#1{%
+  \def\pgf@imagename{pgf@image@#1}%
+  \pgf@tryextensions{\pgf@imagename}{\pgfalternateextension}%
+  \expandafter\pgfutil@ifundefined\expandafter{\pgf@imagename}%
+  {\pgferror{Undefined image "#1"}}%
+  {{\leavevmode\csname\pgf@imagename\endcsname}}}
+
+\def\pgf@tryextensions#1#2{%
+  \edef\pgf@args{[#2!]}\expandafter\pgf@@tryextensions\pgf@args{#1}}
+\def\pgf@@tryextensions[#1!#2]#3{%
+  \expandafter\pgfutil@ifundefined\expandafter{#3#1!#2}%
+  {\def\pgf@temp{#2}%
+    \ifx\pgf@temp\pgfutil@empty%
+    \edef#3{#3!}%
+    \else%
+    \pgf@@tryextensions[#2]{#3}%
+    \fi}%
+  {\edef#3{#3#1!#2}}}
+
+
+
+\def\pgfalternateextension{}
+
+
+
+
+\def\pgfimage{\pgfutil@ifnextchar[\pgf@imagecom{\pgf@imagecom[]}}
+\def\pgf@imagecom[#1]#2{%
+  \pgfdeclareimage[#1]{pgflastimage}{#2}%
+  \pgfuseimage{pgflastimage}}
+
+
+\endinput

preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/basiclayer/pgfcorelayers.code.tex

@@ -0,0 +1,161 @@
+
+\ProvidesFileRCS{pgfcorelayers.code.tex}
+
+
+
+\def\pgfdeclarelayer#1{%
+  \pgfutil@ifundefined{pgf@layerbox@#1}{%
+    \expandafter\expandafter\csname pgf@newbox\endcsname\csname pgf@layerbox@#1\endcsname%
+    \expandafter\expandafter\csname pgf@newbox\endcsname\csname pgf@layerboxsaved@#1\endcsname%
+  }{}%
+}
+\let\pgf@newbox=\newbox %
+
+
+\def\pgfsetlayers#1{%
+  \let\pgf@layerlist\pgfutil@empty%
+  \pgf@dosetlayer#1,,\relax%
+}
+
+\def\pgf@dosetlayer#1,#2,\relax{%
+  \ifx\pgf@layerlist\pgfutil@empty%
+    \edef\pgf@layerlist{\pgfutil@trimspaces{#1}}%
+  \else
+    \edef\pgf@layerlist{\pgf@layerlist,\pgfutil@trimspaces{#1}}%
+  \fi
+  \def\pgf@test{#2}%
+  \ifx\pgf@test\pgfutil@empty%
+  \else%
+    \pgf@dosetlayer#2,\relax%
+  \fi%
+}
+
+\pgfsetlayers{main}
+
+
+\def\pgfonlayer@name{main}
+
+\def\pgfonlayer#1{%
+  \pgfutil@ifundefined{pgf@layerbox@#1}{%
+     \pgferror{Sorry, the requested layer '#1' could not be found. Maybe you misspelled it?}%
+   \bgroup
+     \begingroup
+  }{%
+      \begingroup
+        \edef\pgf@temp{#1}%
+        \ifx\pgf@temp\pgfonlayer@name
+          \def\pgf@temp{%
+            \bgroup
+            \begingroup
+          }%
+      \else
+        \let\pgfonlayer@name=\pgf@temp
+        \pgfonlayer@assert@is@active
+        \def\pgf@temp{%
+          \expandafter\global\expandafter%
+          \setbox\csname pgf@layerbox@#1\endcsname=\hbox to 0pt%
+            \bgroup%
+              \expandafter\box\csname pgf@layerbox@#1\endcsname%
+              \begingroup%
+        }%
+      \fi
+   \pgfsetlinewidth{0.4pt}%
+   \pgf@temp
+  }%
+}
+\def\endpgfonlayer{%
+      \endgroup%
+      \hss
+    \egroup%
+  \endgroup
+}
+
+\let\startpgfonlayer=\pgfonlayer
+\let\stoppgfonlayer=\endpgfonlayer
+
+\def\pgfdiscardlayername{discard}
+
+\def\pgfonlayer@assert@is@active{%
+  \ifx\pgfonlayer@name\pgfdiscardlayername
+  \else
+    \begingroup
+    \def\pgfonlayer@isactive{0}%
+    \expandafter\pgf@assert@layer@is@active@loop\pgf@layerlist,,\relax%
+    \if0\pgfonlayer@isactive
+       \pgfonlayer@assert@fail
+    \fi
+    \endgroup
+  \fi
+}%
+\def\pgfonlayer@assert@fail{%
+  \pgferror{Sorry, the requested layer '\pgfonlayer@name' is not 
+   part of the layer list. Please verify that you provided 
+   \string\pgfsetlayers\space and that '\pgfonlayer@name' is part of this list}%
+}%
+\def\pgf@assert@layer@is@active@loop#1,#2,\relax{%
+  \edef\pgf@test{#1}%
+  \ifx\pgf@test\pgfonlayer@name
+     \def\pgfonlayer@isactive{1}%
+  \else
+    \def\pgf@test{#2}%
+    \ifx\pgf@test\pgfutil@empty%
+    \else%
+    \pgf@assert@layer@is@active@loop#2,\relax%
+    \fi%
+  \fi
+}
+
+
+\def\pgf@insertlayers{%
+  \expandafter\pgf@dolayer\pgf@layerlist,,\relax%
+}
+\def\pgf@maintext{main}%
+\def\pgf@dolayer#1,#2,\relax{%
+  \def\pgf@test{#1}%
+  \ifx\pgf@test\pgf@maintext%
+    \box\pgf@layerbox@main%
+  \else%
+    \pgfsys@beginscope%
+      \expandafter\box\csname pgf@layerbox@#1\endcsname%
+    \pgfsys@endscope%
+  \fi%
+  \def\pgf@test{#2}%
+  \ifx\pgf@test\pgfutil@empty%
+  \else%
+    \pgf@dolayer#2,\relax%
+  \fi%
+}
+
+\def\pgf@savelayers{%
+  \expandafter\pgf@dosavelayer\pgf@layerlist,,\relax%
+}
+\def\pgf@dosavelayer#1,#2,\relax{%
+  \def\pgf@test{#1}%
+  \ifx\pgf@test\pgf@maintext%
+  \else%
+    \setbox\csname pgf@layerboxsaved@#1\endcsname=\box\csname pgf@layerbox@#1\endcsname%
+  \fi%
+  \def\pgf@test{#2}%
+  \ifx\pgf@test\pgfutil@empty%
+  \else%
+    \pgf@dosavelayer#2,\relax%
+  \fi%
+}
+
+\def\pgf@restorelayers{%
+  \expandafter\pgf@dorestorelayer\pgf@layerlist,,\relax%
+}
+\def\pgf@dorestorelayer#1,#2,\relax{%
+  \def\pgf@test{#1}%
+  \ifx\pgf@test\pgf@maintext%
+  \else%
+    \global\setbox\csname pgf@layerbox@#1\endcsname=\box\csname pgf@layerboxsaved@#1\endcsname%
+  \fi%
+  \def\pgf@test{#2}%
+  \ifx\pgf@test\pgfutil@empty%
+  \else%
+    \pgf@dorestorelayer#2,\relax%
+  \fi%
+}
+
+\endinput

preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/basiclayer/pgfcoreobjects.code.tex

@@ -0,0 +1,29 @@
+
+\ProvidesFileRCS{pgfcoreobjects.code.tex}
+
+
+
+
+
+\def\pgfdefobject#1#2#3#4{%
+  \pgfinterruptpath%
+    \pgf@relevantforpicturesizefalse%
+    \pgfsys@defobject{#1}{#2}{#3}{#4}%
+  \endpgfinterruptpath%
+  \ignorespaces%
+}
+
+
+
+\def\pgfuseobject#1{\pgfsys@beginscope\pgfsys@useobject{#1}{}\pgfsys@endscope}
+
+
+
+\def\pgfuseobjectmagnify#1{%
+  \pgfsys@beginscope%
+  \pgfsys@useobject{#1}{\pgfsys@transformxyscale{\pgf@sys@tonumber{\pgf@x}}{\pgf@sys@tonumber{\pgf@y}}}%
+  \pgfsys@endscope%
+}
+
+
+\endinput

preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/basiclayer/pgfcorepathconstruct.code.tex

@@ -0,0 +1,997 @@
+
+\ProvidesFileRCS{pgfcorepathconstruct.code.tex}
+
+
+\newdimen\pgf@path@lastx
+\newdimen\pgf@path@lasty
+
+\let\pgfgetpath=\pgfsyssoftpath@getcurrentpath
+\let\pgfsetpath=\pgfsyssoftpath@setcurrentpath
+
+
+
+
+\newif\ifpgf@arccorners
+
+\def\pgfsetcornersarced#1{%
+  \pgf@process{#1}%
+  \edef\pgf@corner@arc{{\the\pgf@x}{\the\pgf@y}}%
+  \pgf@arccornerstrue%
+  \ifdim\pgf@x=0pt%
+    \ifdim\pgf@y=0pt\relax%
+      \pgf@arccornersfalse%
+    \fi%
+  \fi%
+}
+
+\def\pgf@roundcornerifneeded{%
+  \ifpgf@arccorners\expandafter\pgfsyssoftpath@specialround\pgf@corner@arc\fi%
+}
+
+
+
+
+\def\pgf@lt@moveto#1#2{%
+  \pgf@protocolsizes{#1}{#2}%
+  \pgfsyssoftpath@moveto{\the#1}{\the#2}%
+}
+\def\pgf@lt@lineto#1#2{%
+  \pgf@protocolsizes{#1}{#2}%
+  \pgfsyssoftpath@lineto{\the#1}{\the#2}%
+}
+\def\pgf@lt@curveto#1#2#3#4#5#6{%
+  \pgf@protocolsizes{#1}{#2}%
+  \pgf@protocolsizes{#3}{#4}%
+  \pgf@protocolsizes{#5}{#6}%
+  \pgfsyssoftpath@curveto{\the#1}{\the#2}{\the#3}{\the#4}{\the#5}{\the#6}%
+}
+
+\let\pgf@lt@closepath\pgfsyssoftpath@closepath
+
+\let\pgf@nlt@moveto\pgf@lt@moveto
+\let\pgf@nlt@lineto\pgf@lt@lineto
+\let\pgf@nlt@curveto\pgf@lt@curveto
+\let\pgf@nlt@closepath\pgf@lt@closepath
+
+\let\pgf@nlt@list\pgfutil@empty %
+
+
+
+\def\pgfpathmoveto#1{%
+  \pgfpointtransformed{#1}%
+  \pgf@nlt@moveto{\pgf@x}{\pgf@y}%
+  \global\pgf@path@lastx=\pgf@x%
+  \global\pgf@path@lasty=\pgf@y%
+}
+
+\def\pgf@protocolsizes#1#2{%
+  \ifpgf@relevantforpicturesize%
+    \ifdim#1<\pgf@picminx\global\pgf@picminx#1\fi%
+    \ifdim#1>\pgf@picmaxx\global\pgf@picmaxx#1\fi%
+    \ifdim#2<\pgf@picminy\global\pgf@picminy#2\fi%
+    \ifdim#2>\pgf@picmaxy\global\pgf@picmaxy#2\fi%
+    \ifpgf@size@hooked%
+      \let\pgf@size@hook@x#1\let\pgf@size@hook@y#2\pgf@path@size@hook%
+    \fi%
+  \fi%
+  \ifdim#1<\pgf@pathminx\global\pgf@pathminx#1\fi%
+  \ifdim#1>\pgf@pathmaxx\global\pgf@pathmaxx#1\fi%
+  \ifdim#2<\pgf@pathminy\global\pgf@pathminy#2\fi%
+  \ifdim#2>\pgf@pathmaxy\global\pgf@pathmaxy#2\fi%
+}
+\newif\ifpgf@size@hooked
+\let\pgf@path@size@hook=\pgfutil@empty%
+
+\def\pgf@resetpathsizes{%
+  \global\pgf@pathmaxx=-16000pt\relax%
+  \global\pgf@pathminx=16000pt\relax%
+  \global\pgf@pathmaxy=-16000pt\relax%
+  \global\pgf@pathminy=16000pt\relax%
+}
+
+\def\pgf@getpathsizes#1{%
+  \edef#1{{\the\pgf@pathmaxx}{\the\pgf@pathminx}{\the\pgf@pathmaxy}{\the\pgf@pathminy}}%
+}
+\def\pgf@setpathsizes#1{%
+  \expandafter\pgf@@setpathsizes#1%
+}
+\def\pgf@@setpathsizes#1#2#3#4{%
+  \global\pgf@pathmaxx=#1\relax%
+  \global\pgf@pathminx=#2\relax%
+  \global\pgf@pathmaxy=#3\relax%
+  \global\pgf@pathminy=#4\relax%
+}
+
+
+
+
+
+
+\def\pgfpathlineto#1{%
+  \pgfpointtransformed{#1}%
+  \pgf@roundcornerifneeded%
+  \pgf@nlt@lineto{\pgf@x}{\pgf@y}%
+  \global\pgf@path@lastx=\pgf@x%
+  \global\pgf@path@lasty=\pgf@y%
+}
+
+
+
+
+\def\pgfpathclose{%
+  \pgf@roundcornerifneeded%
+  \pgf@nlt@closepath%
+}
+
+
+
+\def\pgfpathcurveto#1#2#3{%
+  \pgfpointtransformed{#3}%
+  \pgf@xb=\pgf@x%
+  \pgf@yb=\pgf@y%
+  \pgfpointtransformed{#2}%
+  \pgf@xa=\pgf@x%
+  \pgf@ya=\pgf@y%
+  \pgfpointtransformed{#1}%
+  \pgf@roundcornerifneeded%
+  \pgf@nlt@curveto{\pgf@x}{\pgf@y}{\pgf@xa}{\pgf@ya}{\pgf@xb}{\pgf@yb}%
+  \global\pgf@path@lastx=\pgf@xb%
+  \global\pgf@path@lasty=\pgf@yb%
+}
+
+
+
+
+\def\pgfpathquadraticcurveto#1#2{%
+  \pgfpointtransformed{#2}%
+  \pgf@xb=\pgf@x%
+  \pgf@yb=\pgf@y%
+  \pgfpointtransformed{#1}%
+  \pgf@xc=.6666666\pgf@x%
+  \pgf@yc=.6666666\pgf@y%
+  \pgf@xa=.33333333\pgf@xb%
+  \pgf@ya=.33333333\pgf@yb%
+  \advance\pgf@xa by\pgf@xc%
+  \advance\pgf@ya by\pgf@yc%
+  \advance\pgf@xc by.3333333\pgf@path@lastx%
+  \advance\pgf@yc by.3333333\pgf@path@lasty%
+  \pgf@roundcornerifneeded%
+  \pgf@nlt@curveto{\pgf@xc}{\pgf@yc}{\pgf@xa}{\pgf@ya}{\pgf@xb}{\pgf@yb}%
+  \global\pgf@path@lastx=\pgf@xb%
+  \global\pgf@path@lasty=\pgf@yb%
+}
+
+
+
+
+
+\def\pgfpatharc#1#2#3{%
+  {%
+    \pgfmathparse{#1}\let\pgf@temp@a=\pgfmathresult%
+    \pgfmathparse{#2}\let\pgf@temp@b=\pgfmathresult%
+    \pgfutil@in@{and }{#3}%
+    \ifpgfutil@in@%
+      \pgf@arc@get@radii#3\pgf@arc@stop%
+    \else
+      \pgf@arc@get@radii#3and #3\pgf@arc@stop%
+    \fi%
+    \pgf@arc@local@angle@a=\pgf@temp@a pt%
+    \pgf@arc@local@angle@b=\pgf@temp@b pt%
+    \loop%
+      \pgfutil@tempdima=\pgf@arc@local@angle@a%
+      \advance\pgfutil@tempdima by-\pgf@arc@local@angle@b\relax%
+      \ifdim\pgfutil@tempdima<0pt\relax%
+        \pgfutil@tempdima=-\pgfutil@tempdima\relax%
+      \fi%
+    \ifdim\pgfutil@tempdima>90pt\relax%
+      \ifdim\pgfutil@tempdima>115pt\relax%
+        \pgf@arc@temp=90pt%
+      \else%
+        \pgf@arc@temp=60pt%
+      \fi%
+      \ifdim\pgf@arc@local@angle@b>\pgf@arc@local@angle@a\relax%
+        {%
+          \pgf@arc@local@angle@b=\pgf@arc@local@angle@a\relax%
+          \advance\pgf@arc@local@angle@b by\pgf@arc@temp\relax%
+          \pgf@arc%
+        }
+        \advance\pgf@arc@local@angle@a by\pgf@arc@temp\relax%
+      \else
+        {%
+          \pgf@arc@local@angle@b=\pgf@arc@local@angle@a\relax%
+          \advance\pgf@arc@local@angle@b by-\pgf@arc@temp\relax%
+          \pgf@arc%
+        }%
+        \advance\pgf@arc@local@angle@a by-\pgf@arc@temp\relax%
+      \fi%
+    \repeat%
+    \pgf@roundcornerifneeded%
+    \pgf@arc%
+  }%
+}
+\dimendef\pgf@arc@local@angle@a=0
+\dimendef\pgf@arc@local@angle@b=1
+\dimendef\pgf@arc@temp=2
+
+\def\pgf@arc@get@radii#1and #2\pgf@arc@stop{%
+  \pgfmathparse{#1}\let\pgf@arc@radius@a=\pgfmathresult%
+  \pgfmathparse{#2}\let\pgf@arc@radius@b=\pgfmathresult%
+}
+
+
+\def\pgf@arc{%
+  {%
+  \pgfutil@tempdima=\pgf@arc@radius@a pt%
+  \pgfutil@tempdimb=\pgf@arc@radius@b pt%
+  \pgf@xa=\pgf@arc@local@angle@a\relax%
+  \pgf@xb=\pgf@arc@local@angle@b\relax%
+  \advance\pgf@xb by-\pgf@xa\relax%
+  \ifdim\pgf@xb<0pt\relax%
+    \pgf@xb=-\pgf@xb\relax%
+  \fi%
+  \ifdim\pgf@xb=90.0pt%
+    \def\pgfmathresult{0.55228475}%
+  \else%
+    \pgfmathparse{1.333333333*tan(.25*\pgf@sys@tonumber{\pgf@xb})}%
+  \fi%
+  \pgfutil@tempdima=\pgfmathresult\pgfutil@tempdima%
+  \pgfutil@tempdimb=\pgfmathresult\pgfutil@tempdimb%
+  \pgf@xa=\pgf@arc@local@angle@a\relax%
+  \ifdim\pgf@arc@local@angle@b>\pgf@arc@local@angle@a\relax%
+    \advance\pgf@xa by 90pt\relax%
+  \else%
+    \advance\pgf@xa by -90pt\relax%
+  \fi%
+  \edef\pgf@arc@angle{\pgf@sys@tonumber{\pgf@xa}}%
+  \pgfpointtransformed{\pgfpointpolar{\pgf@arc@angle}{\pgfutil@tempdima and \pgfutil@tempdimb}}%
+  \advance\pgf@x by-\pgf@pt@x%
+  \advance\pgf@y by-\pgf@pt@y%
+  \pgf@xa=\pgf@path@lastx%
+  \pgf@ya=\pgf@path@lasty%
+  \advance\pgf@xa by \pgf@x%
+  \advance\pgf@ya by \pgf@y%
+  \pgfpointtransformed{\pgfpointpolar{\pgf@sys@tonumber{\pgf@arc@local@angle@a}}{\pgf@arc@radius@a pt and \pgf@arc@radius@b pt}}%
+  \pgf@xb=\pgf@path@lastx%
+  \pgf@yb=\pgf@path@lasty%
+  \advance\pgf@xb by -\pgf@x%
+  \advance\pgf@yb by -\pgf@y%
+  \pgfpointtransformed{\pgfpointpolar{\pgf@sys@tonumber{\pgf@arc@local@angle@b}}{\pgf@arc@radius@a pt and \pgf@arc@radius@b pt}}%
+  \advance\pgf@xb by \pgf@x%
+  \advance\pgf@yb by \pgf@y%
+  \ifdim\pgf@arc@local@angle@b>\pgf@arc@local@angle@a\relax%
+    \advance\pgf@arc@local@angle@b by -90pt\relax%
+  \else%
+    \advance\pgf@arc@local@angle@b by 90pt\relax%
+  \fi%
+  \pgfpointtransformed{\pgfpointpolar{\pgf@sys@tonumber{\pgf@arc@local@angle@b}}{\pgfutil@tempdima and \pgfutil@tempdimb}}%
+  \advance\pgf@x by-\pgf@pt@x%
+  \advance\pgf@y by-\pgf@pt@y%
+  \pgf@xc=\pgf@xb\relax%
+  \pgf@yc=\pgf@yb\relax%
+  \advance \pgf@xc by \pgf@x\relax%
+  \advance \pgf@yc by \pgf@y\relax%
+  \pgf@nlt@curveto{\pgf@xa}{\pgf@ya}{\pgf@xc}{\pgf@yc}{\pgf@xb}{\pgf@yb}%
+  \global\pgf@path@lastx=\pgf@xb%
+  \global\pgf@path@lasty=\pgf@yb%
+  }%
+}
+
+
+
+\def\pgfpatharcaxes#1#2#3#4{%
+  {%
+    \pgftransformtriangle{\pgfpointorigin}{#3}{#4}%
+    \pgfpatharc{#1}{#2}{1pt}%
+  }%
+}
+
+
+
+
+\def\pgfpatharcto#1#2#3#4#5#6{%
+  {%
+    \pgfmathsetmacro\pgf@arcto@rx{abs(#1)}%
+    \pgfmathsetmacro\pgf@arcto@ry{abs(#2)}%
+    \ifdim\pgf@arcto@rx pt=0pt%
+      \gdef\pgf@marshal{\pgfpathlineto{#6}}%
+    \else
+    \ifdim\pgf@arcto@ry pt=0pt%
+      \gdef\pgf@marshal{\pgfpathlineto{#6}}%
+    \else
+    \pgfmathsetmacro\pgf@arcto@phi{#3}%
+    \pgfmathsetmacro\pgf@arcto@fA{#4}%
+    \ifdim\pgf@arcto@fA pt=0pt
+    \else
+      \pgfmathsetmacro\pgf@arcto@fA{1.0} %
+    \fi
+    \pgfmathsetmacro\pgf@arcto@fS{#5}%
+    \ifdim\pgf@arcto@fS pt=0pt
+    \else
+      \pgfmathsetmacro\pgf@arcto@fS{1.0} %
+    \fi
+    \pgf@process{#6}
+    \edef\pgf@arcto@xb{\the\pgf@x}%
+    \edef\pgf@arcto@yb{\the\pgf@y}%
+    \pgftransforminvert%
+    \pgf@process{\pgfpointtransformed{\pgfqpoint{\pgf@path@lastx}{\pgf@path@lasty}}}
+    \edef\pgf@arcto@xa{\the\pgf@x}
+    \edef\pgf@arcto@ya{\the\pgf@y}
+    \edef\pgf@temp@a{\pgf@arcto@xa,\pgf@arcto@ya}
+    \edef\pgf@temp@b{\pgf@arcto@xb,\pgf@arcto@yb}
+    \ifx\pgf@temp@a\pgf@temp@b%
+      \global\let\pgf@marshal\pgfutil@empty
+    \else
+    \pgftransformreset
+    \pgftransformrotate{-\pgf@arcto@phi}
+    \pgf@process{
+      \pgfpointtransformed{\pgfpointscale{.5}{\pgfpointdiff
+          {\pgfqpoint{\pgf@arcto@xb}{\pgf@arcto@yb}}
+          {\pgfqpoint{\pgf@arcto@xa}{\pgf@arcto@ya}}
+        }
+      }
+    }
+    \edef\pgf@arcto@xaprime{\pgf@sys@tonumber\pgf@x}
+    \edef\pgf@arcto@yaprime{\pgf@sys@tonumber\pgf@y}
+    \pgfmathsetmacro\pgf@arcto@frac@x{\pgf@arcto@xaprime/\pgf@arcto@rx}
+    \pgfmathsetmacro\pgf@arcto@frac@y{\pgf@arcto@yaprime/\pgf@arcto@ry}
+    \pgfmathsetmacro\pgf@arcto@lambda{
+      \pgf@arcto@frac@x*\pgf@arcto@frac@x+\pgf@arcto@frac@y*\pgf@arcto@frac@y
+    }
+    \ifdim\pgf@arcto@lambda pt>1pt%
+      \pgfmathsetmacro\pgf@arcto@sqrt@lambda{sqrt(\pgf@arcto@lambda)}
+      \pgfmathsetmacro\pgf@arcto@rx{\pgf@arcto@sqrt@lambda*\pgf@arcto@rx}
+      \pgfmathsetmacro\pgf@arcto@ry{\pgf@arcto@sqrt@lambda*\pgf@arcto@ry}
+    \fi
+    \pgfmathsetmacro\pgf@arcto@xaprime@abs{abs(\pgf@arcto@xaprime)}
+    \pgfmathsetmacro\pgf@arcto@yaprime@abs{abs(\pgf@arcto@yaprime)}
+    \pgfmathmax@{\pgf@arcto@rx,\pgf@arcto@ry,\pgf@arcto@xaprime@abs,\pgf@arcto@yaprime@abs}
+    \pgfmathsetmacro\pgf@arcto@scaling{20/\pgfmathresult}
+    \pgfmathsetmacro\pgf@arcto@rx@scaled{\pgf@arcto@scaling*\pgf@arcto@rx}
+    \pgfmathsetmacro\pgf@arcto@ry@scaled{\pgf@arcto@scaling*\pgf@arcto@ry}
+    \pgfmathsetmacro\pgf@arcto@xaprime@scaled{\pgf@arcto@scaling*\pgf@arcto@xaprime}
+    \pgfmathsetmacro\pgf@arcto@yaprime@scaled{\pgf@arcto@scaling*\pgf@arcto@yaprime}
+    \ifdim\pgf@arcto@rx pt>\pgf@arcto@ry pt%
+      \pgfmathsetmacro\pgf@arcto@rx@over@ry{\pgf@arcto@rx/\pgf@arcto@ry}
+      \pgfmathsetmacro\pgf@arcto@ry@over@rx{\pgf@arcto@ry/\pgf@arcto@rx}
+      \pgfmathsetmacro\pgf@arcto@temp{\pgf@arcto@ry@over@rx*\pgf@arcto@xaprime@scaled}
+      \pgfmathsetmacro\pgf@arcto@numerator{
+        \pgf@arcto@ry@scaled*\pgf@arcto@ry@scaled-
+        \pgf@arcto@yaprime@scaled*\pgf@arcto@yaprime@scaled-
+        \pgf@arcto@temp*\pgf@arcto@temp
+      }
+      \pgfmathsetmacro\pgf@arcto@denominator{
+        \pgf@arcto@yaprime@scaled*\pgf@arcto@yaprime@scaled+
+        \pgf@arcto@temp*\pgf@arcto@temp
+      }
+    \else
+      \pgfmathsetmacro\pgf@arcto@rx@over@ry{\pgf@arcto@rx/\pgf@arcto@ry}
+      \pgfmathsetmacro\pgf@arcto@ry@over@rx{\pgf@arcto@ry/\pgf@arcto@rx}
+      \pgfmathsetmacro\pgf@arcto@temp{\pgf@arcto@rx@over@ry*\pgf@arcto@yaprime@scaled}
+      \pgfmathsetmacro\pgf@arcto@numerator{
+        \pgf@arcto@rx@scaled*\pgf@arcto@rx@scaled-
+        \pgf@arcto@xaprime@scaled*\pgf@arcto@xaprime@scaled-
+        \pgf@arcto@temp*\pgf@arcto@temp
+      }
+      \pgfmathsetmacro\pgf@arcto@denominator{
+        \pgf@arcto@xaprime@scaled*\pgf@arcto@xaprime@scaled+
+        \pgf@arcto@temp*\pgf@arcto@temp
+      }
+    \fi
+    \pgfmathsetmacro\pgf@arcto@frac{
+      \pgf@arcto@numerator/\pgf@arcto@denominator
+    }
+    \ifdim\pgf@arcto@frac pt<0pt
+      \pgfmathsetmacro\pgf@arcto@factor{0}
+    \else
+      \pgfmathsetmacro\pgf@arcto@factor{sqrt(\pgf@arcto@frac)}
+    \fi
+    \ifx\pgf@arcto@fA\pgf@arcto@fS
+      \pgfmathsetmacro\pgf@arcto@factor{-\pgf@arcto@factor}
+    \fi
+    \pgfmathsetmacro\pgf@arcto@cxprime{
+      \pgf@arcto@factor*\pgf@arcto@rx@over@ry*\pgf@arcto@yaprime
+    }
+    \pgfmathsetmacro\pgf@arcto@cyprime{
+      -\pgf@arcto@factor*\pgf@arcto@ry@over@rx*\pgf@arcto@xaprime
+    }
+    \pgftransformreset
+    \pgftransformrotate{\pgf@arcto@phi}
+    \pgf@process{
+      \pgfpointtransformed{\pgfqpoint{\pgf@arcto@cxprime pt}{\pgf@arcto@cyprime pt}}
+    }
+    \edef\pgf@arcto@temp{\noexpand\pgfqpoint{\the\pgf@x}{\the\pgf@y}}
+    \pgf@process{\pgfpointadd{\pgf@arcto@temp}{
+        \pgfpointscale{.5}{
+          \pgfpointadd
+          {\pgfqpoint{\pgf@arcto@xa}{\pgf@arcto@ya}}
+          {\pgfqpoint{\pgf@arcto@xb}{\pgf@arcto@yb}}        }
+      }
+    }
+    \edef\pgf@arcto@cx{\the\pgf@x}
+    \edef\pgf@arcto@cy{\the\pgf@y}
+    \pgfmathsetmacro\pgf@arcto@vec@x{(\pgf@arcto@xaprime-\pgf@arcto@cxprime)/\pgf@arcto@rx}
+    \pgfmathsetmacro\pgf@arcto@vec@y{(\pgf@arcto@yaprime-\pgf@arcto@cyprime)/\pgf@arcto@ry}
+    \pgfmathsetmacro\pgf@arcto@denominator{veclen(\pgf@arcto@vec@x,\pgf@arcto@vec@y)}
+    \pgfmathsetmacro\pgf@arcto@frac{\pgf@arcto@vec@x/\pgf@arcto@denominator}
+    \pgfmathsetmacro\pgf@arcto@theta@start{acos(\pgf@arcto@frac)}
+    \ifdim\pgf@arcto@vec@y pt<0pt
+      \pgfmathsetmacro\pgf@arcto@theta@start{-\pgf@arcto@theta@start}
+    \fi
+    \pgfmathsetmacro\pgf@arcto@vec@x{(-\pgf@arcto@xaprime-\pgf@arcto@cxprime)/\pgf@arcto@rx}
+    \pgfmathsetmacro\pgf@arcto@vec@y{(-\pgf@arcto@yaprime-\pgf@arcto@cyprime)/\pgf@arcto@ry}
+    \pgfmathsetmacro\pgf@arcto@denominator{veclen(\pgf@arcto@vec@x,\pgf@arcto@vec@y)}
+    \pgfmathsetmacro\pgf@arcto@frac{\pgf@arcto@vec@x/\pgf@arcto@denominator}
+    \pgfmathsetmacro\pgf@arcto@theta@end{acos(\pgf@arcto@frac)}
+    \ifdim\pgf@arcto@vec@y pt<0pt
+      \pgfmathsetmacro\pgf@arcto@theta@end{-\pgf@arcto@theta@end}
+    \fi
+    \pgfmathsetmacro\pgf@arcto@delta@theta{abs(\pgf@arcto@theta@start-\pgf@arcto@theta@end)}
+    \ifdim\pgf@arcto@fA pt=0pt%
+      \ifdim\pgf@arcto@delta@theta pt>180pt%
+        \ifdim\pgf@arcto@theta@end pt>\pgf@arcto@theta@start pt
+          \pgfmathsetmacro\pgf@arcto@theta@end{\pgf@arcto@theta@end-360}
+        \else
+          \pgfmathsetmacro\pgf@arcto@theta@end{\pgf@arcto@theta@end+360}
+        \fi
+      \fi
+    \else
+      \ifdim\pgf@arcto@delta@theta pt<180pt%
+        \ifdim\pgf@arcto@theta@end pt>\pgf@arcto@theta@start pt
+          \pgfmathsetmacro\pgf@arcto@theta@end{\pgf@arcto@theta@end-360}
+        \else
+          \pgfmathsetmacro\pgf@arcto@theta@end{\pgf@arcto@theta@end+360}
+        \fi
+      \fi
+    \fi
+    \xdef\pgf@marshal{\noexpand
+      \pgfpatharcaxes{\pgf@arcto@theta@start}{\pgf@arcto@theta@end}
+      {\noexpand\pgfpointpolar{\pgf@arcto@phi}{\pgf@arcto@rx}}
+      {\noexpand\pgfpointpolar{\pgf@arcto@phi+90}{\pgf@arcto@ry}}
+    }
+    \fi\fi\fi
+  }
+  \pgf@marshal
+}
+
+
+
+\def\pgfpatharctomaxstepsize{45}
+
+\def\pgfpatharctoprecomputed#1#2#3#4#5#6#7#8{%
+    \begingroup
+    \pgf@process{#1}%
+    \edef\pgfpath@center@x{\the\pgf@x}%
+    \edef\pgfpath@center@y{\the\pgf@y}%
+    \def\pgfpath@completearcend{#4}%
+    \pgf@xa=#2pt
+    \pgf@xb=#3pt
+    \edef\pgfpath@startangle{#2pt}%
+    \edef\pgfpath@endangle{\pgf@sys@tonumber\pgf@xb}%
+    \pgf@ya=\pgf@xb
+    \advance\pgf@ya by-\pgf@xa
+    \ifx\pgfpatharctomaxstepsize\pgfutil@empty
+        \def\pgfpath@N{1}%
+        \pgf@xc=\pgf@ya
+    \else
+        \pgf@xc=\pgf@ya%
+        \ifdim\pgf@xc<0pt
+            \multiply\pgf@xc by-1
+        \fi
+        \divide\pgf@xc by\pgfpatharctomaxstepsize\relax
+        \afterassignment\pgfutil@gobble@until@relax
+        \c@pgf@counta=\the\pgf@xc\relax
+        \advance\c@pgf@counta by1
+        \edef\pgfpath@N{\the\c@pgf@counta}%
+        \pgf@xc=\pgf@ya
+        \divide\pgf@xc by\c@pgf@counta
+    \fi
+    \edef\pgfpath@h{\pgf@sys@tonumber\pgf@xc}%
+    \pgf@xc=0.116355283466289\pgf@xc %
+    \divide\pgf@xc by20
+    \pgf@xa=#7\pgf@xc
+    \edef\pgfpath@scale@A{\pgf@sys@tonumber\pgf@xa}%
+    \pgf@xa=#8\pgf@xc
+    \edef\pgfpath@scale@B{\pgf@sys@tonumber\pgf@xa}%
+    \c@pgf@countd=1
+    \pgfutil@loop
+    \ifnum\c@pgf@countd<\pgfpath@N\relax
+        \pgf@xa=\pgfpath@startangle %
+        \pgf@xb=\pgfpath@h pt
+        \multiply\pgf@xb by\c@pgf@countd
+        \advance\pgf@xa by\pgf@xb
+        \edef\pgfpath@angle@i{\pgf@sys@tonumber\pgf@xa}%
+        \pgfpatharcofellipse@{%
+            \pgfpoint
+                {\pgfpath@center@x + #5*cos(\pgfpath@angle@i)}
+                {\pgfpath@center@y + #6*sin(\pgfpath@angle@i)}%
+        }%
+        \advance\c@pgf@countd by1
+    \pgfutil@repeat
+    \pgfpatharcofellipse@{\pgfpath@completearcend}%
+    \endgroup
+}%
+\def\pgfpatharcofellipse@#1{%
+    \begingroup
+    \pgf@process{#1}%
+    \edef\pgfpath@endpt{\global\pgf@x=\the\pgf@x\space\global\pgf@y=\the\pgf@y\space}%
+    \pgfpathcurveto{
+        \begingroup
+        \global\pgf@x=\pgf@path@lastx
+        \global\pgf@y=\pgf@path@lasty
+        \pgf@xa=\pgf@x \advance\pgf@xa by-\pgfpath@center@x
+        \pgf@ya=\pgf@y \advance\pgf@ya by-\pgfpath@center@y
+        \global\advance\pgf@x by-\pgfpath@scale@A\pgf@ya
+        \global\advance\pgf@y by \pgfpath@scale@B\pgf@xa
+        \endgroup
+    }{%
+        \begingroup
+        \pgfpath@endpt
+        \pgf@xa=\pgf@x \advance\pgf@xa by-\pgfpath@center@x
+        \pgf@ya=\pgf@y \advance\pgf@ya by-\pgfpath@center@y
+        \global\advance\pgf@x by \pgfpath@scale@A\pgf@ya
+        \global\advance\pgf@y by-\pgfpath@scale@B\pgf@xa
+        \endgroup
+    }{%
+        \pgfpath@endpt
+    }%
+    \endgroup
+}
+
+
+
+
+
+
+
+
+
+
+\def\pgfpathellipse#1#2#3{%
+  \pgfpointtransformed{#1}%
+  \pgf@xc=\pgf@x%
+  \pgf@yc=\pgf@y%
+  \pgfpointtransformed{#2}%
+  \pgf@xa=\pgf@x%
+  \pgf@ya=\pgf@y%
+  \advance\pgf@xa by-\pgf@pt@x%
+  \advance\pgf@ya by-\pgf@pt@y%
+  \pgfpointtransformed{#3}%
+  \pgf@xb=\pgf@x%
+  \pgf@yb=\pgf@y%
+  \advance\pgf@xb by-\pgf@pt@x%
+  \advance\pgf@yb by-\pgf@pt@y%
+  {%
+    \advance\pgf@xa by\pgf@xc%
+    \advance\pgf@ya by\pgf@yc%
+    \pgf@nlt@moveto{\pgf@xa}{\pgf@ya}%
+  }%
+  \pgf@x=0.55228475\pgf@xb%
+  \pgf@y=0.55228475\pgf@yb%
+  \advance\pgf@x by\pgf@xa%
+  \advance\pgf@y by\pgf@ya%
+  \advance\pgf@x by\pgf@xc%
+  \advance\pgf@y by\pgf@yc%
+  \edef\pgf@temp{\pgf@xc\the\pgf@x\pgf@yc\the\pgf@y}%
+  \pgf@x=0.55228475\pgf@xa%
+  \pgf@y=0.55228475\pgf@ya%
+  \advance\pgf@x by\pgf@xb%
+  \advance\pgf@y by\pgf@yb%
+  {%
+    \advance\pgf@x by\pgf@xc%
+    \advance\pgf@y by\pgf@yc%
+    \advance\pgf@xb by\pgf@xc%
+    \advance\pgf@yb by\pgf@yc%
+    \pgf@temp%
+    \pgf@nlt@curveto{\pgf@xc}{\pgf@yc}{\pgf@x}{\pgf@y}{\pgf@xb}{\pgf@yb}%
+  }%
+  \pgf@xa=-\pgf@xa%
+  \pgf@ya=-\pgf@ya%
+  \pgf@x=0.55228475\pgf@xa%
+  \pgf@y=0.55228475\pgf@ya%
+  \advance\pgf@x by\pgf@xb%
+  \advance\pgf@y by\pgf@yb%
+  \advance\pgf@x by\pgf@xc%
+  \advance\pgf@y by\pgf@yc%
+  \edef\pgf@temp{\pgf@xc\the\pgf@x\pgf@yc\the\pgf@y}%
+  \pgf@x=0.55228475\pgf@xb%
+  \pgf@y=0.55228475\pgf@yb%
+  \advance\pgf@x by\pgf@xa%
+  \advance\pgf@y by\pgf@ya%
+  {%
+    \advance\pgf@x by\pgf@xc%
+    \advance\pgf@y by\pgf@yc%
+    \advance\pgf@xa by\pgf@xc%
+    \advance\pgf@ya by\pgf@yc%
+    \pgf@temp%
+    \pgf@nlt@curveto{\pgf@xc}{\pgf@yc}{\pgf@x}{\pgf@y}{\pgf@xa}{\pgf@ya}%
+  }%
+  \pgf@xb=-\pgf@xb%
+  \pgf@yb=-\pgf@yb%
+  \pgf@x=0.55228475\pgf@xb%
+  \pgf@y=0.55228475\pgf@yb%
+  \advance\pgf@x by\pgf@xa%
+  \advance\pgf@y by\pgf@ya%
+  \advance\pgf@x by\pgf@xc%
+  \advance\pgf@y by\pgf@yc%
+  \edef\pgf@temp{\pgf@xc\the\pgf@x\pgf@yc\the\pgf@y}%
+  \pgf@x=0.55228475\pgf@xa%
+  \pgf@y=0.55228475\pgf@ya%
+  \advance\pgf@x by\pgf@xb%
+  \advance\pgf@y by\pgf@yb%
+  {%
+    \advance\pgf@x by\pgf@xc%
+    \advance\pgf@y by\pgf@yc%
+    \advance\pgf@xb by\pgf@xc%
+    \advance\pgf@yb by\pgf@yc%
+    \pgf@temp%
+    \pgf@nlt@curveto{\pgf@xc}{\pgf@yc}{\pgf@x}{\pgf@y}{\pgf@xb}{\pgf@yb}%
+  }%
+  \pgf@xa=-\pgf@xa%
+  \pgf@ya=-\pgf@ya%
+  \pgf@x=0.55228475\pgf@xa%
+  \pgf@y=0.55228475\pgf@ya%
+  \advance\pgf@x by\pgf@xb%
+  \advance\pgf@y by\pgf@yb%
+  \advance\pgf@x by\pgf@xc%
+  \advance\pgf@y by\pgf@yc%
+  \edef\pgf@temp{\pgf@xc\the\pgf@x\pgf@yc\the\pgf@y}%
+  \pgf@x=0.55228475\pgf@xb%
+  \pgf@y=0.55228475\pgf@yb%
+  \advance\pgf@x by\pgf@xa%
+  \advance\pgf@y by\pgf@ya%
+  {%
+    \advance\pgf@x by\pgf@xc%
+    \advance\pgf@y by\pgf@yc%
+    \advance\pgf@xa by\pgf@xc%
+    \advance\pgf@ya by\pgf@yc%
+    \pgf@temp%
+    \pgf@nlt@curveto{\pgf@xc}{\pgf@yc}{\pgf@x}{\pgf@y}{\pgf@xa}{\pgf@ya}%
+  }%
+  \pgf@nlt@closepath%
+  \pgf@nlt@moveto{\pgf@xc}{\pgf@yc}%
+}
+
+
+
+
+\def\pgfpathcircle#1#2{\pgfpathellipse{#1}{\pgfpoint{#2}{0pt}}{\pgfpoint{0pt}{#2}}}
+
+
+
+
+
+\def\pgfpathrectangle{%
+  \let\pgfrect@next=\pgf@specialrect%
+  \ifpgf@pt@identity%
+    \ifpgf@arccorners%
+    \else%
+      \ifx\pgf@nlt@list\pgfutil@empty%
+        \let\pgfrect@next=\pgf@normalrect%
+      \fi%
+    \fi%
+  \fi%
+  \pgfrect@next%
+}
+
+\def\pgf@normalrect#1#2{%
+  \pgf@process{#2}%
+  \pgf@xa=\pgf@x%
+  \pgf@ya=\pgf@y%
+  \pgfpointtransformed{#1}%
+  \pgfsyssoftpath@rect{\the\pgf@x}{\the\pgf@y}{\the\pgf@xa}{\the\pgf@ya}%
+  \pgf@protocolsizes{\pgf@x}{\pgf@y}%
+  \advance\pgf@x by\pgf@xa\relax%
+  \advance\pgf@y by\pgf@ya\relax%
+  \pgf@protocolsizes{\pgf@x}{\pgf@y}%
+}
+
+\def\pgf@specialrect#1#2{%
+  \pgf@process{#2}%
+  \pgf@xa=\pgf@x%
+  \pgf@ya=\pgf@y%
+  \pgf@process{#1}%
+  \pgf@xb=\pgf@x%
+  \pgf@yb=\pgf@y%
+  \advance\pgf@xa by\pgf@xb%
+  \advance\pgf@ya by\pgf@yb%
+  \pgfpathmoveto{\pgfqpoint{\pgf@xa}{\pgf@ya}}%
+  \pgfpathlineto{\pgfqpoint{\pgf@xb}{\pgf@ya}}%
+  \pgfpathlineto{\pgfqpoint{\pgf@xb}{\pgf@yb}}%
+  \pgfpathlineto{\pgfqpoint{\pgf@xa}{\pgf@yb}}%
+  \pgfpathclose%
+  \pgfpathmoveto{\pgfqpoint{\pgf@xb}{\pgf@yb}}%
+}
+
+
+\def\pgfpathrectanglecorners#1#2{%
+  \pgf@process{#2}%
+  \pgf@xc=\pgf@x%
+  \pgf@yc=\pgf@y%
+  \pgf@process{#1}%
+  \advance\pgf@xc by-\pgf@x%
+  \advance\pgf@yc by-\pgf@y%
+  \pgfpathrectangle{#1}{\pgfqpoint{\pgf@xc}{\pgf@yc}}%
+}
+
+
+
+\pgfkeys{
+  /pgf/stepx/.initial=1cm,
+  /pgf/stepy/.initial=1cm,
+  /pgf/step/.code={\pgf@process{#1}\pgfkeysalso{/pgf/stepx/.expanded=\the\pgf@x,/pgf/stepy/.expanded=\the\pgf@y}},
+  /pgf/step/.value required
+}
+
+\def\pgfpathgrid{\pgfutil@ifnextchar[{\pgf@pathgrid}{\pgf@pathgrid[]}}
+\def\pgf@pathgrid[#1]#2#3{%
+  \pgfset{#1}%
+  \pgfmathsetlength\pgf@xc{\pgfkeysvalueof{/pgf/stepx}}%
+  \pgfmathsetlength\pgf@yc{\pgfkeysvalueof{/pgf/stepy}}%
+  \pgf@process{#3}%
+  \pgf@xb=\pgf@x%
+  \pgf@yb=\pgf@y%
+  \pgf@process{#2}%
+  \pgf@xa=\pgf@x%
+  \pgf@ya=\pgf@y%
+  \ifdim\pgf@xa>\pgf@xb%
+    \pgf@x=\pgf@xb%
+    \pgf@xb=\pgf@xa%
+    \pgf@xa=\pgf@x%
+  \fi%
+  \ifdim\pgf@ya>\pgf@yb%
+    \pgf@y=\pgf@yb%
+    \pgf@yb=\pgf@ya%
+    \pgf@ya=\pgf@y%
+  \fi%
+  \ifdim \pgf@yc > .01pt\relax%
+    \c@pgf@counta=\pgf@ya\relax%
+    \c@pgf@countb=\pgf@yc\relax%
+    \divide\c@pgf@counta by\c@pgf@countb\relax%
+    \pgfutil@tempdima=\c@pgf@counta\pgf@yc\relax%
+    \ifdim\pgfutil@tempdima<\pgf@ya%
+      \advance\pgfutil@tempdima by\pgf@yc%
+    \fi%
+    \pgfutil@tempdimb\pgf@x
+    \pgfutil@loop%
+      {%
+        \pgf@xa=\pgfutil@tempdimb%
+        \pgf@ya=\pgfutil@tempdima%
+        \pgf@pos@transform{\pgf@xa}{\pgf@ya}
+        \pgf@nlt@moveto{\pgf@xa}{\pgf@ya}%
+        \pgf@xa=\pgf@xb%
+        \pgf@ya=\pgfutil@tempdima%
+        \pgf@pos@transform{\pgf@xa}{\pgf@ya}
+        \pgf@nlt@lineto{\pgf@xa}{\pgf@ya}%
+      }%
+    \advance\pgfutil@tempdima by\pgf@yc%
+    \ifdim\pgfutil@tempdima<\pgf@yb%
+    \pgfutil@repeat%
+    \advance\pgfutil@tempdima by-0.01pt\relax%
+    \ifdim\pgfutil@tempdima<\pgf@yb%
+      {%
+        \pgf@xa=\pgfutil@tempdimb%
+        \pgf@ya=\pgfutil@tempdima%
+        \pgf@pos@transform{\pgf@xa}{\pgf@ya}
+        \pgf@nlt@moveto{\pgf@xa}{\pgf@ya}%
+        \pgf@xa=\pgf@xb%
+        \pgf@ya=\pgfutil@tempdima%
+        \pgf@pos@transform{\pgf@xa}{\pgf@ya}
+        \pgf@nlt@lineto{\pgf@xa}{\pgf@ya}%
+      }%
+    \fi%
+  \fi%
+  \ifdim \pgf@xc > .01pt\relax%
+    \c@pgf@counta=\pgf@xa\relax%
+    \c@pgf@countb=\pgf@xc\relax%
+    \divide\c@pgf@counta by\c@pgf@countb\relax%
+    \pgfutil@tempdimb=\c@pgf@counta\pgf@xc\relax%
+    \ifdim\pgfutil@tempdimb<\pgf@xa%
+      \advance\pgfutil@tempdimb by\pgf@xc%
+    \fi%
+    \pgfutil@loop%
+      {%
+        \pgf@xc=\pgfutil@tempdimb%
+        \pgf@yc=\pgf@ya%
+        \pgf@pos@transform{\pgf@xc}{\pgf@yc}
+        \pgf@nlt@moveto{\pgf@xc}{\pgf@yc}%
+        \pgf@xc=\pgfutil@tempdimb%
+        \pgf@yc=\pgf@yb%
+        \pgf@pos@transform{\pgf@xc}{\pgf@yc}
+        \pgf@nlt@lineto{\pgf@xc}{\pgf@yc}%
+      }%
+      \advance\pgfutil@tempdimb by\pgf@xc%
+    \ifdim\pgfutil@tempdimb<\pgf@xb%
+    \pgfutil@repeat%
+    \advance\pgfutil@tempdimb by-0.01pt\relax%
+    \ifdim\pgfutil@tempdimb<\pgf@xb%
+      {%
+        \pgf@xc=\pgfutil@tempdimb%
+        \pgf@yc=\pgf@ya%
+        \pgf@pos@transform{\pgf@xc}{\pgf@yc}
+        \pgf@nlt@moveto{\pgf@xc}{\pgf@yc}%
+        \pgf@xc=\pgfutil@tempdimb%
+        \pgf@yc=\pgf@yb%
+        \pgf@pos@transform{\pgf@xc}{\pgf@yc}
+        \pgf@nlt@lineto{\pgf@xc}{\pgf@yc}%
+      }%
+    \fi%
+  \fi%
+  \pgf@process{#3}%
+  \pgf@pos@transform{\pgf@x}{\pgf@y}%
+  \pgf@nlt@moveto{\pgf@x}{\pgf@y}%
+}
+
+
+
+
+\def\pgfpathparabola#1#2{%
+  {%
+    \pgf@process{#2}%
+    \pgf@xb=\pgf@x%
+    \pgf@yb=\pgf@y%
+    \pgf@process{#1}%
+    \pgf@xc=\pgf@x%
+    \pgf@yc=\pgf@y%
+    \pgfutil@tempswatrue%
+    \ifdim\pgf@xb=0pt\relax%
+      \ifdim\pgf@yb=0pt\relax%
+        \pgfutil@tempswafalse%
+      \fi%
+    \fi%
+    {%
+      \ifpgfutil@tempswa%
+        \pgf@arccornersfalse
+      \else%
+      \fi%
+      \pgfutil@tempswatrue%
+      \ifdim\pgf@xc=0pt\relax%
+        \ifdim\pgf@yc=0pt\relax%
+          \pgfutil@tempswafalse%
+        \fi%
+      \fi%
+      \ifpgfutil@tempswa
+      {%
+        \pgf@pt@x=\pgf@path@lastx%
+        \pgf@pt@y=\pgf@path@lasty%
+        \pgfpathcurveto%
+          {\pgfqpoint{.1125\pgf@xc}{.225\pgf@yc}}%
+          {\pgfqpoint{.5\pgf@xc}{\pgf@yc}}%
+          {\pgfqpoint{\pgf@xc}{\pgf@yc}}%
+      }%
+      \fi%
+    }%
+    \ifpgfutil@tempswa%
+      \pgf@xc=\pgf@xb%
+      \pgf@yc=\pgf@yb%
+      {%
+        \pgf@pt@x=\pgf@path@lastx%
+        \pgf@pt@y=\pgf@path@lasty%
+        \pgfpathcurveto%
+          {\pgfqpoint{.5\pgf@xc}{0\pgf@yc}}%
+          {\pgfqpoint{.8875\pgf@xc}{.775\pgf@yc}}%
+          {\pgfqpoint{\pgf@xc}{\pgf@yc}}%
+      }%
+    \fi%
+  }%
+}
+
+
+
+
+
+\def\pgfpathsine#1{%
+  {%
+    \pgf@process{#1}%
+    \pgf@xc=\pgf@x%
+    \pgf@yc=\pgf@y%
+    \pgf@pt@x=\pgf@path@lastx%
+    \pgf@pt@y=\pgf@path@lasty%
+    \pgfpathcurveto%
+      {\pgfqpoint{.3260\pgf@xc}{.5120\pgf@yc}}%
+      {\pgfqpoint{.6380\pgf@xc}{\pgf@yc}}%
+      {\pgfqpoint{\pgf@xc}{\pgf@yc}}%
+  }%
+}
+
+
+\def\pgfpathcosine#1{%
+  {%
+    \pgf@process{#1}%
+    \pgf@xc=\pgf@x%
+    \pgf@yc=\pgf@y%
+    \pgf@pt@x=\pgf@path@lastx%
+    \pgf@pt@y=\pgf@path@lasty%
+    \pgfpathcurveto%
+      {\pgfqpoint{.3620\pgf@xc}{0pt}}%
+      {\pgfqpoint{.6740\pgf@xc}{.4880\pgf@yc}}%
+      {\pgfqpoint{\pgf@xc}{\pgf@yc}}%
+  }%
+}
+
+
+
+\def\pgfpathcurvebetweentime{\pgf@ignoremovetofalse\pgf@@pathcurvebetweentime}
+\def\pgfpathcurvebetweentimecontinue{\pgf@ignoremovetotrue\pgf@@pathcurvebetweentime}
+\newif\ifpgf@ignoremoveto
+
+\def\pgf@@pathcurvebetweentime#1#2#3#4#5#6{%
+  \pgfmathparse{#1}%
+  \let\pgf@time@s=\pgfmathresult%
+  \pgfmathparse{#2}%
+  \let\pgf@time@t=\pgfmathresult%
+  \ifdim\pgf@time@s pt>\pgf@time@t pt\relax%
+    \pgfmathsetmacro\pgf@time@s{1-#1}%
+    \pgfmathsetmacro\pgf@time@t{1-#2}%
+    \pgf@@@pathcurvebetweentime{\pgf@time@t}{#6}{#5}{#4}{#3}%
+  \else%
+    \pgf@@@pathcurvebetweentime{\pgf@time@t}{#3}{#4}{#5}{#6}%
+  \fi%
+}
+
+\def\pgf@@@pathcurvebetweentime#1#2#3#4#5{%
+  \pgf@process{#2}%
+  \pgf@xc=\pgf@x%
+  \pgf@yc=\pgf@y%
+  \pgf@process{%
+    \pgf@process{#3}%
+    \pgf@xa=#1\pgf@x%
+    \pgf@ya=#1\pgf@y%
+    \pgf@process{#2}%
+    \pgf@xb=\pgf@x%
+    \pgf@yb=\pgf@y%
+    \advance\pgf@x by-#1\pgf@xb%
+    \advance\pgf@y by-#1\pgf@yb%
+    \advance\pgf@x by\pgf@xa%
+    \advance\pgf@y by\pgf@ya%
+  }%
+  \pgf@xb=\pgf@x%
+  \pgf@yb=\pgf@y%
+  \pgf@process{%
+    \pgf@process{#4}%
+    \pgf@xa=#1\pgf@x%
+    \pgf@ya=#1\pgf@y%
+    \pgf@process{#3}%
+    \pgf@xc=\pgf@x%
+    \pgf@yc=\pgf@y%
+    \advance\pgf@xc by-#1\pgf@x%
+    \advance\pgf@yc by-#1\pgf@y%
+    \pgf@x=\pgf@xb%
+    \pgf@y=\pgf@yb%
+    \advance\pgf@x by#1\pgf@xa%
+    \advance\pgf@y by#1\pgf@ya%
+    \advance\pgf@x by-#1\pgf@xb%
+    \advance\pgf@y by-#1\pgf@yb%
+    \advance\pgf@x by#1\pgf@xc%
+    \advance\pgf@y by#1\pgf@yc%
+  }%
+  \pgf@xa=\pgf@x%
+  \pgf@ya=\pgf@y%
+  \pgf@process{\pgfpointcurveattime{#1}{#2}{#3}{#4}{#5}}%
+  \ifx#1\pgf@time@t%
+    \pgfmathdivide@{\pgf@time@s}{\pgf@time@t}%
+    \pgfmathadd@{-\pgfmathresult}{1}%
+    \let\pgf@time@s=\pgfmathresult%
+    \edef\pgf@marshal{%
+      \noexpand\pgf@@@pathcurvebetweentime{\noexpand\pgf@time@s}%
+        {\noexpand\pgfqpoint{\the\pgf@x}{\the\pgf@y}}{\noexpand\pgfqpoint{\the\pgf@xa}{\the\pgf@ya}}%
+        {\noexpand\pgfqpoint{\the\pgf@xb}{\the\pgf@yb}}{\noexpand\pgfqpoint{\the\pgf@xc}{\the\pgf@yc}}%
+    }%
+  \else%
+    \ifpgf@ignoremoveto%
+      \edef\pgf@marshal{%
+        \noexpand\pgfpathcurveto{\noexpand\pgfqpoint{\the\pgf@xa}{\the\pgf@ya}}%
+          {\noexpand\pgfqpoint{\the\pgf@xb}{\the\pgf@yb}}{\noexpand\pgfqpoint{\the\pgf@xc}{\the\pgf@yc}}%
+      }%
+    \else%
+      \edef\pgf@marshal{%
+        \noexpand\pgfpathmoveto{\noexpand\pgfqpoint{\the\pgf@x}{\the\pgf@y}}%
+        \noexpand\pgfpathcurveto{\noexpand\pgfqpoint{\the\pgf@xa}{\the\pgf@ya}}%
+          {\noexpand\pgfqpoint{\the\pgf@xb}{\the\pgf@yb}}{\noexpand\pgfqpoint{\the\pgf@xc}{\the\pgf@yc}}%
+      }%
+    \fi%
+  \fi%
+  \pgf@marshal%
+}
+
+
+\endinput

preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/basiclayer/pgfcorepathprocessing.code.tex

@@ -0,0 +1,417 @@
+
+\ProvidesFileRCS{pgfcorepathprocessing.code.tex}
+
+
+
+\def\pgfprocesssplitpath#1{%
+  \let\pgfprocessresultpathprefix\pgfutil@empty%
+  \let\pgfprocessresultpathsuffix\pgfutil@empty%
+  \let\pgf@next\pgf@process@split%
+  \expandafter\pgf@process@split#1\pgfsyssoftpath@movetotoken{}{}\pgf@stop%
+}
+
+\def\pgf@process@split#1\pgfsyssoftpath@movetotoken#2#3#4{%
+  \ifx#4\pgf@stop%
+    \expandafter\def\expandafter\pgfprocessresultpathsuffix\expandafter{\pgfprocessresultpathsuffix#1}%
+    \let\pgf@next\pgfutil@gobble%
+  \else%
+    \expandafter\expandafter\expandafter\def%
+    \expandafter\expandafter\expandafter\pgfprocessresultpathprefix%
+    \expandafter\expandafter\expandafter{\expandafter\pgfprocessresultpathprefix\pgfprocessresultpathsuffix#1}%
+    \def\pgfprocessresultpathsuffix{\pgfsyssoftpath@movetotoken{#2}{#3}}%
+  \fi%
+  \pgf@next#4%
+}
+
+
+
+
+\def\pgfprocesssplitsubpath#1{%
+  \let\pgf@tempa\pgfutil@emtpy%
+  \let\pgf@tempb\pgfutil@emtpy%
+  \let\pgf@tempc\pgfutil@emtpy%
+  \let\pgf@tempd\pgfutil@emtpy%
+  \let\pgfprocessresultsubpathprefix\pgfutil@empty%
+  \let\pgfprocessresultsubpathsuffix\pgfutil@empty%
+  \let\pgf@next\pgf@split@subpath%
+  \expandafter\pgf@split@subpath#1\pgf@stop%
+}
+
+\newif\ifpgf@split@move
+
+\def\pgf@split@subpath#1#2#3#4{%
+  \ifx#4\pgf@stop%
+    \expandafter\def\expandafter\pgfprocessresultsubpathsuffix\expandafter{\pgfprocessresultsubpathsuffix#1{#2}{#3}}%
+    \let\pgf@next\pgfutil@gobble%
+  \else%
+    \pgf@split@movetrue%
+    \ifx#1\pgfsyssoftpath@curvetosupportatoken%
+      \pgf@split@movefalse%
+    \else
+      \ifx#1\pgfsyssoftpath@curvetosupportbtoken%
+        \pgf@split@movefalse%
+      \fi%
+    \fi%
+    \ifpgf@split@move%
+      \expandafter\expandafter\expandafter\def%
+      \expandafter\expandafter\expandafter\pgfprocessresultsubpathprefix%
+      \expandafter\expandafter\expandafter{%
+        \expandafter\pgfprocessresultsubpathprefix\pgfprocessresultsubpathsuffix}%
+      \def\pgfprocessresultsubpathsuffix{#1{#2}{#3}}%
+    \else%
+      \expandafter\def\expandafter\pgfprocessresultsubpathsuffix\expandafter{\pgfprocessresultsubpathsuffix#1{#2}{#3}}%
+    \fi%
+  \fi%
+  \pgf@next#4%
+}
+
+
+
+
+
+\def\pgfprocesspathextractpoints#1{%
+  \ifx#1\pgfutil@empty%
+    \let\pgfpointfirstonpath=\pgfpointorigin%
+    \let\pgfpointsecondonpath=\pgfpointorigin%
+    \let\pgfpointsecondlastonpath=\pgfpointorigin%
+    \let\pgfpointlastonpath=\pgfpointorigin%
+  \else%
+    \expandafter\pgf@extractprocessorfirst#1\pgf@stop%
+  \fi%
+}
+
+\def\pgf@extractprocessorfirst#1#2#3#4{%
+  \def\pgfpointfirstonpath{\pgfqpoint{#2}{#3}}%
+  \ifx#4\pgf@stop%
+    \let\pgfpointsecondonpath=\pgfpointfirstonpath%
+    \let\pgfpointsecondlastonpath=\pgfpointfirstonpath%
+    \let\pgfpointlastonpath=\pgfpointfirstonpath%
+    \let\next=\pgfutil@gobble%
+  \else
+    \let\next=\pgf@extractprocessorsecond%
+  \fi%
+  \next#4%
+}
+
+\def\pgf@extractprocessorsecond#1{%
+  \ifx#1\pgfsyssoftpath@movetotoken%
+    \let\pgf@next=\pgf@extractprocessorfirst%
+  \else%
+    \let\pgf@next=\pgf@@extractprocessorsecond%
+  \fi%
+  \pgf@next#1%
+}
+\def\pgf@@extractprocessorsecond#1#2#3#4{%
+  \def\pgfpointsecondonpath{\pgfqpoint{#2}{#3}}%
+  \let\pgfpointsecondlastonpath=\pgfpointfirstonpath%
+  \let\pgfpointlastonpath=\pgfpointsecondonpath%
+  \ifx#4\pgf@stop%
+    \let\next=\pgfutil@gobble%
+  \else
+    \let\next=\pgf@extractprocessorother%
+  \fi%
+  \next#4%
+}
+
+\def\pgf@extractprocessorother#1{%
+  \ifx#1\pgfsyssoftpath@movetotoken%
+    \let\pgf@next=\pgf@extractprocessorfirst%
+  \else%
+    \let\pgf@next=\pgf@@extractprocessorother%
+  \fi%
+  \pgf@next#1%
+}
+\def\pgf@@extractprocessorother#1#2#3#4{%
+  \let\pgfpointsecondlastonpath=\pgfpointlastonpath%
+  \def\pgfpointlastonpath{\pgfqpoint{#2}{#3}}%
+  \ifx#4\pgf@stop%
+    \let\next=\pgfutil@gobble%
+  \fi%
+  \next#4%
+}
+
+
+
+
+\def\pgfprocesscheckclosed#1#2{%
+  {%
+    \global\let\pgf@proc@todo=\relax%
+    \let\pgfsyssoftpath@movetotoken=\pgfutil@gobbletwo%
+    \let\pgfsyssoftpath@linetotoken=\pgfutil@gobbletwo%
+    \let\pgfsyssoftpath@curvetosupportatoken=\pgfutil@gobbletwo%
+    \let\pgfsyssoftpath@curvetosupportbtoken=\pgfutil@gobbletwo%
+    \let\pgfsyssoftpath@curvetotoken=\pgfutil@gobbletwo%
+    \def\pgfsyssoftpath@rectcornertoken{\gdef\pgf@proc@todo{#2}\pgfutil@gobbletwo}%
+    \def\pgfsyssoftpath@rectsizetoken{\gdef\pgf@proc@todo{#2}\pgfutil@gobbletwo}%
+    \def\pgfsyssoftpath@closepathtoken{\gdef\pgf@proc@todo{#2}\pgfutil@gobbletwo}%
+    #1%
+  }%
+  \pgf@proc@todo%
+}
+
+
+
+\def\pgfprocessround#1#2{%
+  \expandafter\pgf@processroundcheck\expandafter#1\expandafter#2#1\pgfsyssoftpath@specialroundtoken\pgf@stop%
+}
+
+\def\pgf@processroundcheck#1#2#3\pgfsyssoftpath@specialroundtoken#4\pgf@stop{%
+  \def\pgf@test{#4}%
+  \ifx\pgf@test\pgfutil@empty%
+    \let#2=#1%
+  \else%
+    \pgf@@processround#1#2%
+  \fi%
+}
+
+
+\def\pgf@@processround#1#2{%
+  \let\pgfprocess@newpath\pgfutil@empty%
+  \let\pgfprocess@moveto\pgfutil@empty%
+  \let\pgfprocess@firstto\pgfutil@empty%
+  \let\pgfprocess@segment\pgfutil@empty%
+  \pgf@xa=0pt%
+  \pgf@ya=0pt%
+  \expandafter\pgfprocess@round#1\pgf@stop{0pt}{0pt}%
+  \expandafter\pgfutil@g@addto@macro\expandafter\pgfprocess@newpath\expandafter{\pgfprocess@moveto}%
+  \expandafter\pgfutil@g@addto@macro\expandafter\pgfprocess@newpath\expandafter{\pgfprocess@segment}%
+  \let#2=\pgfprocess@newpath%
+}
+
+\def\pgfprocess@round#1#2#3{%
+  \ifx#1\pgf@stop%
+    \let\next=\relax%
+  \else%
+    \ifx#1\pgfsyssoftpath@specialroundtoken%
+      \def\pgfprocess@savex{#2}%
+      \def\pgfprocess@savey{#3}%
+      \let\next=\pgfprocess@specialround%
+      \ifdim#2=0pt%
+        \ifdim#3=0pt%
+          \let\next=\pgfprocess@round%
+        \fi%
+      \fi%
+    \else%
+      \ifx\pgfprocess@firstto\pgfutil@empty%
+        \def\pgfprocess@firstto{{#2}{#3}}%
+      \fi%
+      \pgf@xa=#2%
+      \pgf@ya=#3%
+      \ifx#1\pgfsyssoftpath@movetotoken%
+        \expandafter\pgfutil@g@addto@macro\expandafter\pgfprocess@newpath\expandafter{\pgfprocess@moveto}%
+        \expandafter\pgfutil@g@addto@macro\expandafter\pgfprocess@newpath\expandafter{\pgfprocess@segment}%
+        \def\pgfprocess@moveto{#1{#2}{#3}}%
+        \let\pgfprocess@firstto=\pgfutil@empty%
+        \let\pgfprocess@segment=\pgfutil@empty%
+      \else%
+        \pgfutil@g@addto@macro\pgfprocess@segment{#1{#2}{#3}}%
+      \fi%
+      \let\next=\pgfprocess@round%
+    \fi%
+  \fi%
+  \next%
+}
+
+\def\pgfprocess@specialround#1#2#3{%
+  \ifx\pgfprocess@firstto\pgfutil@empty%
+    \def\pgfprocess@firstto{{#2}{#3}}%
+  \fi%
+  \let\next=\pgfprocess@round%
+  \ifx#1\pgfsyssoftpath@linetotoken%
+    \let\next=\pgfprocess@specialroundcope%
+  \else%
+    \ifx#1\pgfsyssoftpath@curvetosupportatoken%
+      \let\next=\pgfprocess@specialroundcurveto%
+    \else%
+      \ifx#1\pgfsyssoftpath@closepathtoken%
+        \let\next=\pgfprocess@specialroundclose%
+      \fi%
+    \fi%
+  \fi%
+  \next#1{#2}{#3}%
+}%
+
+\def\pgfprocess@specialroundcope#1#2#3#4#5#6{%
+  \let\next=\pgfprocess@round%
+  \let\pgfprocess@continueafterrounding=\pgfprocess@round%
+  \ifx#4\pgfsyssoftpath@linetotoken%
+    \pgf@xc=#5%
+    \pgf@yc=#6%
+    \let\next=\pgfprocess@@specialround%
+  \else%
+    \ifx#4\pgfsyssoftpath@curvetosupportatoken%
+      \pgf@xc=#5%
+      \pgf@yc=#6%
+      \let\next=\pgfprocess@@specialround%
+    \else%
+      \ifx#4\pgfsyssoftpath@closepathtoken%
+        \pgf@xc=#5%
+        \pgf@yc=#6%
+        \let\next=\pgfprocess@@specialround%
+      \else
+        \ifx#4\pgfsyssoftpath@specialroundtoken%
+          \let\next=\pgfprocess@@findrightcoordinates%
+        \fi%
+      \fi%
+    \fi%
+  \fi%
+  \next#1{#2}{#3}#4{#5}{#6}%
+}
+
+\def\pgfprocess@@findrightcoordinates#1#2#3#4#5#6#7#8#9{%
+  \pgf@xc=#8%
+  \pgf@yc=#9%
+  \pgfprocess@@specialround#1{#2}{#3}#4{#5}{#6}#7{#8}{#9}%
+}
+
+\def\pgfprocess@@specialround#1#2#3{%
+  \pgfutil@g@addto@macro\pgfprocess@segment{#1}%
+  \pgf@xb=#2%
+  \pgf@yb=#3%
+  \edef\pgf@marshal%
+  {\noexpand\pgfpointlineatdistance{\pgfprocess@savex}%
+    {\noexpand\pgfqpoint{\the\pgf@xb}{\the\pgf@yb}}%
+    {\noexpand\pgfqpoint{\the\pgf@xa}{\the\pgf@ya}}}%
+  \pgf@process{\pgf@marshal}%
+  \pgf@xa=\pgf@x%
+  \pgf@ya=\pgf@y%
+  \edef\pgfprocess@addition{{\the\pgf@x}{\the\pgf@y}}%
+  \expandafter\pgfutil@g@addto@macro\expandafter\pgfprocess@segment\expandafter{\pgfprocess@addition}%
+  \edef\pgf@marshal%
+  {\noexpand\pgfpointlineatdistance{\pgfprocess@savey}%
+    {\noexpand\pgfqpoint{\the\pgf@xb}{\the\pgf@yb}}%
+    {\noexpand\pgfqpoint{\the\pgf@xc}{\the\pgf@yc}}}%
+  \pgf@process{\pgf@marshal}%
+  \pgf@xc=\pgf@x%
+  \pgf@yc=\pgf@y%
+  {%
+    \pgf@x=\pgf@xb%
+    \pgf@y=\pgf@yb%
+    \advance\pgf@x by-\pgf@xa%
+    \advance\pgf@y by-\pgf@ya%
+    \advance\pgf@xa by 0.5522847\pgf@x%
+    \advance\pgf@ya by 0.5522847\pgf@y%
+    \edef\pgfprocess@addition{\noexpand\pgfsyssoftpath@curvetosupportatoken{\the\pgf@xa}{\the\pgf@ya}}%
+    \expandafter\pgfutil@g@addto@macro\expandafter\pgfprocess@segment\expandafter{\pgfprocess@addition}%
+  }%
+  {%
+    \pgf@x=\pgf@xb%
+    \pgf@y=\pgf@yb%
+    \advance\pgf@x by-\pgf@xc%
+    \advance\pgf@y by-\pgf@yc%
+    \advance\pgf@xc by 0.5522847\pgf@x%
+    \advance\pgf@yc by 0.5522847\pgf@y%
+    \edef\pgfprocess@addition{\noexpand\pgfsyssoftpath@curvetosupportbtoken{\the\pgf@xc}{\the\pgf@yc}}%
+    \expandafter\pgfutil@g@addto@macro\expandafter\pgfprocess@segment\expandafter{\pgfprocess@addition}%
+  }%
+  \edef\pgfprocess@addition{\noexpand\pgfsyssoftpath@curvetotoken{\the\pgf@xc}{\the\pgf@yc}}%
+  \expandafter\pgfutil@g@addto@macro\expandafter\pgfprocess@segment\expandafter{\pgfprocess@addition}%
+  \pgf@xa=#2%
+  \pgf@ya=#3%
+  \pgfprocess@continueafterrounding%
+}
+
+\def\pgfprocess@specialroundcurveto#1#2#3#4#5#6{%
+  \pgfutil@g@addto@macro\pgfprocess@segment{#1{#2}{#3}#4{#5}{#6}}%
+  \pgf@xa=#5%
+  \pgf@ya=#6%
+  \pgfprocess@specialroundcope}
+
+\def\pgfprocess@specialroundclose{%
+  \let\next=\pgfprocess@round%
+  \ifx\pgfprocess@moveto\pgfutil@empty%
+  \else%
+    \ifx\pgfprocess@firstto\pgfutil@empty%
+    \else%
+      \expandafter\pgfprocess@@specialclosetarget\pgfprocess@firstto%
+      \let\pgfprocess@continueafterrounding=\pgfprocess@cleanupafterclose%
+      \edef\next{%
+        \noexpand\pgfprocess@@specialround%
+        \expandafter\expandafter\expandafter\noexpand\expandafter\pgfprocess@@specialclosemoveto\pgfprocess@moveto%
+      }%
+    \fi%
+  \fi%
+  \next%
+}
+
+\def\pgfprocess@@specialclosetarget#1#2{%
+  \pgf@xc=#1%
+  \pgf@yc=#2%
+}
+
+\def\pgfprocess@@specialclosemoveto#1#2#3{%
+  \pgfsyssoftpath@linetotoken{#2}{#3}%
+}
+
+
+\def\pgfprocess@cleanupafterclose#1#2#3{%
+  \edef\pgfprocess@moveto{\noexpand\pgfsyssoftpath@movetotoken{\the\pgf@xc}{\the\pgf@yc}}%
+  \edef\pgf@marshal{\noexpand\pgfprocess@round\noexpand\pgfsyssoftpath@closepathtoken{\the\pgf@xc}{\the\pgf@yc}}%
+  \pgf@marshal%
+}
+
+
+
+\def\pgfprocesspathreplacestartandend#1#2#3{%
+  \ifx#1\pgfutil@empty%
+  \else%
+  {%
+    \pgfsyssoftpath@getcurrentpath\pgf@replace@origpath%
+    \let\pgf@prepath=\pgfutil@empty%
+    \pgf@process{#3}%
+    \pgf@xa=\pgf@x%
+    \pgf@ya=\pgf@y%
+    \pgf@process{#2}%
+    \expandafter\pgf@replaceprocessfirst#1\pgf@stop%
+    \pgfsyssoftpath@getcurrentpath\pgf@restpath%
+    \expandafter\expandafter\expandafter\expandafter\expandafter\expandafter\expandafter\gdef%
+    \expandafter\expandafter\expandafter\expandafter\expandafter\expandafter\expandafter#1%
+    \expandafter\expandafter\expandafter\expandafter\expandafter\expandafter\expandafter{%
+      \expandafter\expandafter\expandafter\pgf@prepath%
+      \expandafter\pgf@newstart\pgf@restpath}%
+    \pgfsyssoftpath@setcurrentpath\pgf@replace@origpath%
+  }%
+  \fi%
+}
+
+\def\pgf@replaceprocessfirst#1#2#3#4{%
+  \def\pgf@origstart{#1{#2}{#3}}%
+  \edef\pgf@newstart{\noexpand#1{\the\pgf@x}{\the\pgf@y}}%
+  \pgfsyssoftpath@setcurrentpath\pgfutil@empty%
+  \ifx#4\pgf@stop%
+    \let\pgf@next=\pgfutil@gobble%
+  \else%
+    \let\pgf@next=\pgf@replaceprocessother%
+    \let\pgf@@next=\pgf@@replaceprocessother%
+  \fi%
+  \pgf@next#4%
+}
+
+\def\pgf@replaceprocessother#1{%
+  \ifx#1\pgfsyssoftpath@movetotoken%
+    \pgf@replace@handle@move%
+  \fi%
+  \pgf@@next#1%
+}
+\def\pgf@@replaceprocessother#1#2#3#4{%
+  \ifx#4\pgf@stop%
+    \edef\pgf@restpathaddition{{\noexpand#1{\the\pgf@xa}{\the\pgf@ya}}}%
+    \expandafter\pgfsyssoftpath@addtocurrentpath\pgf@restpathaddition%
+    \let\pgf@next=\pgfutil@gobble%
+  \else%
+    \pgfsyssoftpath@addtocurrentpath{#1{#2}{#3}}%
+  \fi%
+  \pgf@next#4%
+}
+
+\def\pgf@replace@handle@move{%
+  \pgfsyssoftpath@getcurrentpath\pgf@restpath%
+  \expandafter\expandafter\expandafter\expandafter\expandafter\expandafter\expandafter\gdef%
+  \expandafter\expandafter\expandafter\expandafter\expandafter\expandafter\expandafter\pgf@prepath%
+  \expandafter\expandafter\expandafter\expandafter\expandafter\expandafter\expandafter{%
+    \expandafter\expandafter\expandafter\pgf@prepath%
+    \expandafter\pgf@origstart\pgf@restpath}%
+  \let\pgf@@next=\pgf@replaceprocessfirst%
+}
+
+\endinput

preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/basiclayer/pgfcorepathusage.code.tex

@@ -0,0 +1,510 @@
+
+\ProvidesFileRCS{pgfcorepathusage.code.tex}
+
+
+
+\pgfkeys{
+  /pgf/stroke/.code=\let\pgf@up@stroke\pgf@up@stroke@text\pgf@up@path@neededtrue,
+  /pgf/draw/.code=\let\pgf@up@stroke\pgf@up@stroke@text\pgf@up@path@neededtrue,
+  /pgf/fill/.code=\let\pgf@up@fill\pgf@up@fill@text\pgf@up@path@neededtrue,
+  /pgf/clip/.code=\let\pgf@up@clip\pgf@up@clip@text\pgf@up@path@neededtrue,
+  /pgf/discard/.code=,
+  /pgf/use as bounding box/.code=\let\pgf@up@bb\pgf@do@up@bb,
+  /pgf/arrow keys/flex/.code=\pgferror{You need to say \string\usetikzlibrary{bending} for flexing and bending arrows},
+  /pgf/arrow keys/flex'/.code=\pgferror{You need to say \string\usetikzlibrary{bending} for flexing and bending arrows},
+  /pgf/arrow keys/bend/.code=\pgferror{You need to say \string\usetikzlibrary{bending} for flexing and bending arrows},
+  /pgf/arrow keys/quick/.code=\pgfarrowsaddtooptions{\let\pgf@arrow@flex@mode\pgf@arrow@mode@is@quick},
+}
+
+\pgfkeys{
+  /pgf/.cd,
+  tips/.is choice,
+  tips/.default=true,
+  tips/proper/.code=\let\pgf@tips@mode\pgf@tips@mode@onproper,
+  tips/on proper draw/.code=\let\pgf@tips@mode\pgf@tips@mode@onproperdraw,
+  tips/true/.code=\let\pgf@tips@mode\pgf@tips@mode@true,
+  tips/on draw/.code=\let\pgf@tips@mode\pgf@tips@mode@ondraw,
+  tips/never/.code=\let\pgf@tips@mode\pgf@tips@mode@false,
+  tips/false/.code=\let\pgf@tips@mode\pgf@tips@mode@false,
+}
+\def\pgf@tips@mode@onproper{4}
+\def\pgf@tips@mode@onproperdraw{3}
+\def\pgf@tips@mode@true{2}
+\def\pgf@tips@mode@ondraw{1}
+\def\pgf@tips@mode@false{0}
+\let\pgf@tips@mode\pgf@tips@mode@ondraw
+
+
+\newif\ifpgf@precise@shortening
+\def\pgf@arrow@mode@is@quick{0}
+\let\pgf@arrow@flex@mode\pgf@arrow@mode@is@quick
+
+\newif\ifpgf@up@path@needed
+\newif\ifpgf@up@draw@arrows
+\def\pgf@up@stroke@text{stroke}
+\def\pgf@up@fill@text{fill}
+\def\pgf@up@clip@text{clip}
+\def\pgf@do@up@bb{\pgf@relevantforpicturesizefalse}
+
+\def\pgfusepath#1{%
+  \pgf@up@path@neededfalse%
+  \pgf@up@draw@arrowsfalse%
+  \let\pgf@up@stroke\pgfutil@empty%
+  \let\pgf@up@fill\pgfutil@empty%
+  \let\pgf@up@clip\pgfutil@empty%
+  \let\pgf@up@bb\pgfutil@empty%
+  \pgfset{#1}%
+  \expandafter\def\expandafter\pgf@up@action\expandafter{\csname pgfsys@\pgf@up@fill\pgf@up@stroke\endcsname}%
+  \ifnum\pgf@tips@mode=2\relax%
+    \pgf@up@path@neededtrue%
+  \fi%
+  \ifnum\pgf@tips@mode=4\relax%
+    \pgf@up@path@neededtrue%
+  \fi%
+  \ifpgf@up@path@needed%
+  \else%
+    \pgfsyssoftpath@setcurrentpath\pgfutil@empty%
+  \fi%
+  \ifx\pgf@up@stroke\pgfutil@empty%
+    \ifx\pgf@up@fill\pgfutil@empty%
+      \let\pgf@up@action=\pgfutil@empty%
+      \ifx\pgf@up@clip\pgfutil@empty%
+      \else%
+        \let\pgf@up@action=\pgfsys@discardpath%
+      \fi%
+    \fi%
+  \fi%
+  \pgfsyssoftpath@getcurrentpath\pgf@last@processed@path
+  \pgfprocessround{\pgf@last@processed@path}{\pgf@last@processed@path}%
+  \pgfsyssoftpath@setcurrentpath\pgf@last@processed@path%
+  \ifpgf@relevantforpicturesize%
+    \ifx\pgf@up@stroke\pgfutil@empty%
+    \else%
+      \ifdim\pgf@picmaxx=-16000pt\relax%
+      \else%
+        \pgf@x=\pgf@pathminx\advance\pgf@x by-.5\pgflinewidth%
+        \ifdim\pgf@x<\pgf@picminx\global\pgf@picminx\pgf@x\fi%
+        \pgf@y=\pgf@pathminy\advance\pgf@y by-.5\pgflinewidth%
+        \ifdim\pgf@y<\pgf@picminy\global\pgf@picminy\pgf@y\fi%
+        \pgf@x=\pgf@pathmaxx\advance\pgf@x by.5\pgflinewidth%
+        \ifdim\pgf@x>\pgf@picmaxx\global\pgf@picmaxx\pgf@x\fi%
+        \pgf@y=\pgf@pathmaxy\advance\pgf@y by.5\pgflinewidth%
+        \ifdim\pgf@y>\pgf@picmaxy\global\pgf@picmaxy\pgf@y\fi%
+      \fi%
+    \fi%
+  \fi%
+  \ifx\pgf@up@clip\pgfutil@empty%
+    \ifx\pgf@up@stroke\pgfutil@empty%
+      \ifx\pgf@up@action\pgfutil@empty%
+        \ifnum\pgf@tips@mode=2\relax%
+          \pgf@up@draw@arrows@only%
+        \fi%
+        \ifnum\pgf@tips@mode=4\relax%
+          \pgf@up@draw@arrows@only%
+        \fi%
+      \else%
+        \pgfsyssoftpath@invokecurrentpath%
+        \pgf@up@action%
+      \fi%
+    \else%
+      \pgfgetpath\pgf@arrowpath%
+      \pgf@path@setup@tempswa%
+      \pgfprocesscheckclosed{\pgf@arrowpath}{\pgfutil@tempswafalse}%
+      \pgf@path@check@proper%
+      \ifpgfutil@tempswa%
+        \pgf@check@for@arrow@and@animation%
+        \pgf@prepare@end@of@path%
+        \begingroup%
+          \pgf@prepare@start@of@path%
+      \fi%
+          \pgfsyssoftpath@invokecurrentpath%
+          \pgf@up@action%
+          \ifdim\pgfinnerlinewidth>0pt\relax%
+            \pgf@stroke@inner@line%
+          \fi%
+      \ifpgfutil@tempswa%
+          \pgf@add@arrow@at@start%
+        \endgroup%
+        \pgf@add@arrow@at@end%
+      \fi%
+    \fi%
+  \else%
+    \pgfsyssoftpath@invokecurrentpath%
+    \pgfsys@clipnext%
+    \pgf@up@action%
+    \pgf@relevantforpicturesizefalse%
+  \fi%
+  \pgf@up@bb%
+  \pgfsyssoftpath@setcurrentpath\pgfutil@empty%
+  \pgf@resetpathsizes%
+  \ignorespaces%
+}
+\def\pgf@path@setup@tempswa{%
+  \ifnum\pgf@tips@mode>0\relax
+    \pgfutil@tempswatrue%
+  \else
+    \pgfutil@tempswafalse%
+  \fi%
+}
+\def\pgf@up@draw@arrows@only{%
+  \pgfgetpath\pgf@arrowpath%
+  \pgfutil@tempswatrue%
+  \pgfprocesscheckclosed{\pgf@arrowpath}{\pgfutil@tempswafalse}%
+  \pgf@path@check@proper%
+  \ifpgfutil@tempswa%
+    \pgf@check@for@arrow@and@animation%
+    \pgf@prepare@end@of@path%
+    \begingroup%
+      \pgf@prepare@start@of@path%
+      \pgf@add@arrow@at@start%
+    \endgroup%
+    \pgf@add@arrow@at@end%
+  \fi%
+}
+
+\def\pgf@check@for@arrow@and@animation{\pgfsys@if@fresh@currentid{\pgf@check@for@arrow@and@animation@}{}}%
+\def\pgf@check@for@arrow@and@animation@{%
+  \expandafter\ifx\csname pgfsysanim@path@is@animated@\pgf@sys@id@current@id @\pgfsys@current@type\endcsname\pgfutil@empty%
+    \ifx\pgf@end@tip@sequence\pgfutil@empty%
+      \ifx\pgf@start@tip@sequence\pgfutil@empty%
+      \else%
+        \pgf@check@for@arrow@and@animation@error%
+      \fi%
+    \else%
+      \pgf@check@for@arrow@and@animation@error%
+    \fi%
+  \fi%
+}
+\def\pgf@check@for@arrow@and@animation@error{\pgferror{Animated path may not have normal arrow tips. Use a base path with arrow tips}}
+
+\def\pgf@path@check@proper{%
+  \ifpgfutil@tempswa%
+    \ifnum\pgf@tips@mode>2\relax%
+      \pgf@path@check@proper@%
+    \fi%
+  \fi%
+}
+
+\def\pgf@path@check@proper@{%
+  {%
+    \pgf@x0pt\pgf@y\pgf@x%
+    \pgfutil@tempswatrue%
+    \let\pgfsyssoftpath@movetotoken\pgf@path@proper@init%
+    \let\pgfsyssoftpath@linetotoken\pgf@path@proper@test%
+    \let\pgfsyssoftpath@curvetosupportatoken\pgf@path@proper@test%
+    \let\pgfsyssoftpath@curvetosupportbtoken=\pgf@path@proper@test%
+    \let\pgfsyssoftpath@curvetotoken\pgf@path@proper@test%
+    \let\pgfsyssoftpath@rectcornertoken\pgf@path@proper@test%
+    \let\pgfsyssoftpath@rectsizetoken\pgf@path@proper@zero@test%
+    \let\pgfsyssoftpath@closepathtoken\pgf@path@proper@test%
+    \pgf@arrowpath%
+    \expandafter
+  }%
+  \ifpgfutil@tempswa\pgfutil@tempswafalse\else\pgfutil@tempswatrue\fi%
+}
+
+\def\pgf@path@proper@init#1#2{\pgfutil@tempswatrue\pgf@x#1\pgf@y#2}%
+\def\pgf@path@proper@test#1#2{%
+  \ifdim\pgf@x=#1\relax\else\pgfutil@tempswafalse\fi%
+  \ifdim\pgf@y=#2\relax\else\pgfutil@tempswafalse\fi}
+\def\pgf@path@proper@zero@test#1#2{%
+  \ifdim\pgf@x=0pt\relax\else\pgfutil@tempswafalse\fi%
+  \ifdim\pgf@y=0pt\relax\else\pgfutil@tempswafalse\fi}
+
+
+
+
+\def\pgf@stroke@inner@line{%
+  \let\pgf@temp@save=\pgf@strokecolor@global
+  \pgfsys@beginscope%
+  {%
+    \pgfsys@setlinewidth{\pgfinnerlinewidth}%
+    \pgfsetstrokecolor{\pgfinnerstrokecolor}%
+    \pgfsyssoftpath@invokecurrentpath%
+    \pgfsys@stroke%
+  }%
+  \pgfsys@endscope%
+  \global\let\pgf@strokecolor@global=\pgf@temp@save
+}
+
+\let\pgf@prepare@start@of@path\relax%
+
+
+
+
+
+\def\pgfsetshortenstart#1{\pgfmathsetlength\pgf@shorten@start@additional{#1}}
+\def\pgfsetshortenend#1{\pgfmathsetlength\pgf@shorten@end@additional{#1}}
+
+\newdimen\pgf@shorten@end@additional
+\newdimen\pgf@shorten@start@additional
+
+
+
+
+\newif\ifpgf@worry
+
+
+
+\def\pgf@prepare@end@of@path{%
+  \let\pgfprocessresultpathsuffix\relax%
+  \let\pgfprocessresultsubpathsuffix\relax%
+  \pgfsyssoftpath@getcurrentpath\pgf@arrowpath%
+  \ifx\pgf@arrowpath\pgfutil@empty\else%
+    \pgf@worryfalse%
+    \ifx\pgf@end@tip@sequence\pgfutil@empty%
+    \else%
+      \pgf@worrytrue%
+    \fi%
+    \pgf@precise@shorteningfalse%
+    \pgf@arrow@compute@shortening\pgf@end@tip@sequence%
+    \advance\pgf@xa by\pgf@shorten@end@additional%
+    \advance\pgf@xb by\pgf@shorten@end@additional%
+    \ifdim\pgf@xa=0pt\relax\else\pgf@worrytrue\fi%
+    \edef\pgf@path@shortening@distance{\the\pgf@xa}%
+    \edef\pgf@arrow@tip@total@length{\the\pgf@xb}%
+    \ifpgf@worry%
+      \pgfprocesssplitpath{\pgf@arrowpath}%
+      \pgfprocesssplitsubpath{\pgfprocessresultpathsuffix}%
+      \expandafter\pgf@parse@end\pgfprocessresultsubpathsuffix\pgf@stop\pgf@stop\pgf@stop%
+      \pgf@prep@end%
+      \ifdim\pgf@path@shortening@distance=0pt\else\pgf@do@shorten@end\fi%
+      \expandafter\expandafter\expandafter\def%
+      \expandafter\expandafter\expandafter\pgf@arrowpath%
+      \expandafter\expandafter\expandafter{\expandafter\pgfprocessresultpathprefix\pgfprocessresultpathsuffix}%
+      \pgfsyssoftpath@setcurrentpath\pgf@arrowpath%
+    \fi%
+  \fi%
+}
+
+\def\pgf@parse@end#1#2#3#4#5#6{%
+  \ifx#4\pgf@stop%
+    \def\pgfpointlastonpath{\pgfqpoint{#2}{#3}}%
+    \let\pgf@next\relax%
+    \let\pgf@do@shorten@end\relax%
+    \let\pgf@do@draw@end\pgf@do@draw@straightend%
+    \let\pgf@prep@end\pgf@prep@movetoend%
+  \else\ifx#4\pgfsyssoftpath@curvetosupportatoken%
+    \def\pgfsubpathfourthlasttoken{#1}%
+    \def\pgfpointfourthlastonpath{\pgfqpoint{#2}{#3}}%
+    \def\pgfpointthirdlastonpath{\pgfqpoint{#5}{#6}}%
+    \ifpgf@precise@shortening%
+      \let\pgf@do@shorten@end\pgf@do@shorten@curvedend%
+      \let\pgf@do@draw@end\pgf@do@draw@curvedend%
+      \let\pgf@prep@end\pgf@prep@curveend%
+    \else%
+      \def\pgfsubpathstart{\noexpand#1{#2}{#3}\noexpand#4{#5}{#6}}%
+      \let\pgf@do@shorten@end\pgf@do@shorten@straightend%
+      \let\pgf@do@draw@end\pgf@do@draw@straightend%
+      \let\pgf@prep@end\pgf@prep@straightend%
+    \fi%
+    \let\pgf@next\pgf@parse@end@curve@cont%
+  \else%
+    \def\pgfsubpathstart{\noexpand#1{#2}{#3}\noexpand#4}%
+    \def\pgfpointsecondlastonpath{\pgfqpoint{#2}{#3}}%
+    \def\pgfpointlastonpath{\pgfqpoint{#5}{#6}}%
+    \let\pgfpointfourthlastonpath\relax%
+    \let\pgfpointthirdlastonpath\relax%
+    \let\pgf@next\pgf@parse@end@gobble@three%
+    \let\pgf@do@shorten@end\pgf@do@shorten@straightend%
+    \let\pgf@do@draw@end\pgf@do@draw@straightend%
+    \let\pgf@prep@end\pgf@prep@straightend%
+  \fi\fi%
+  \pgf@next%
+}
+
+\def\pgf@parse@end@gobble@three#1#2#3{}%
+\def\pgf@parse@end@curve@cont#1#2#3#4#5#6#7#8#9{%
+  \def\pgfpointsecondlastonpath{\pgfqpoint{#2}{#3}}%
+  \def\pgfpointlastonpath{\pgfqpoint{#5}{#6}}%
+  \ifpgf@precise@shortening%
+  \else%
+    \expandafter\def\expandafter\pgfsubpathstart\expandafter{\pgfsubpathstart\noexpand#1{#2}{#3}\noexpand#4}%
+  \fi%
+}
+
+\def\pgf@prep@movetoend{%
+  \pgf@process{\pgfpointlastonpath}%
+  \pgf@xb\pgf@x
+  \pgf@yb\pgf@y
+  \pgf@xc\pgf@x
+  \pgf@yc\pgf@y
+}
+\def\pgf@prep@straightend{%
+  \let\pgf@ref\pgfpointsecondlastonpath
+  \ifx\pgfpointlastonpath\pgfpointsecondlastonpath%
+    \ifx\pgfpointthirdlastonpath\relax%
+    \else%
+      \ifx\pgfpointlastonpath\pgfpointthirdlastonpath%
+        \let\pgf@ref\pgfpointfourthlastonpath%
+      \else
+        \let\pgf@ref\pgfpointthirdlastonpath%
+      \fi%
+    \fi%
+  \fi%
+  \pgfpointlineatdistance{\pgf@path@shortening@distance}{\pgfpointlastonpath}{\pgf@ref}%
+  \pgf@xa\pgf@x%
+  \pgf@ya\pgf@y%
+}
+
+
+\def\pgf@do@shorten@straightend{%
+  \edef\pgfprocessresultsubpathsuffix{\pgfsubpathstart{\the\pgf@xa}{\the\pgf@ya}}%
+  \expandafter\expandafter\expandafter\def%
+  \expandafter\expandafter\expandafter\pgfprocessresultpathsuffix%
+  \expandafter\expandafter\expandafter{\expandafter\pgfprocessresultsubpathprefix\pgfprocessresultsubpathsuffix}%
+}
+
+
+
+\def\pgf@add@arrow@at@end{%
+  \ifx\pgf@arrowpath\pgfutil@empty\else%
+    \ifx\pgf@end@tip@sequence\pgfutil@empty\else%
+      \pgf@do@draw@end%
+    \fi%
+  \fi%
+}
+
+\def\pgf@do@draw@straightend{%
+  {%
+    \pgftransformreset%
+    \pgftransformarrow{\pgfqpoint{\pgf@xc}{\pgf@yc}}{\pgfqpoint{\pgf@xb}{\pgf@yb}}%
+    \pgf@arrow@draw@arrow\pgf@end@tip@sequence\pgf@arrow@tip@total@length%
+  }%
+}
+
+
+
+
+
+
+
+\def\pgf@prepare@start@of@path{%
+  \ifx\pgf@arrowpath\pgfutil@empty\else%
+    \pgf@worryfalse%
+    \ifx\pgf@start@tip@sequence\pgfutil@empty\else\pgf@worrytrue\fi%
+    \pgf@precise@shorteningfalse%
+    \pgf@arrow@compute@shortening\pgf@start@tip@sequence%
+    \advance\pgf@xa by\pgf@shorten@start@additional%
+    \advance\pgf@xb by\pgf@shorten@start@additional%
+    \ifdim\pgf@xa=0pt\relax\else\pgf@worrytrue\fi%
+    \edef\pgf@path@shortening@distance{\the\pgf@xa}%
+    \edef\pgf@arrow@tip@total@length{\the\pgf@xb}%
+    \ifpgf@worry%
+      \ifx\pgfprocessresultpathsuffix\relax%
+        \pgfprocesssplitpath{\pgf@arrowpath}%
+      \fi%
+      \expandafter\pgf@parse@start\pgfprocessresultpathsuffix\pgf@stop\pgf@stop\pgf@stop%
+      \pgf@prep@start%
+      \ifdim\pgf@path@shortening@distance=0pt\else\pgf@do@shorten@start\fi%
+      \expandafter\expandafter\expandafter\def%
+      \expandafter\expandafter\expandafter\pgf@arrowpath%
+      \expandafter\expandafter\expandafter{\expandafter\pgfprocessresultpathprefix\pgfprocessresultpathsuffix}%
+      \pgfsyssoftpath@setcurrentpath\pgf@arrowpath%
+    \fi%
+  \fi%
+}
+
+\def\pgf@parse@start#1#2#3#4#5#6{%
+  \def\pgfpointfirstonpath{\pgfqpoint{#2}{#3}}%
+  \def\pgfpointsecondonpath{\pgfqpoint{#5}{#6}}%
+  \let\pgfpointthirdonpath\relax%
+  \let\pgfpointfourthonpath\relax%
+  \def\pgfsubpathfirsttoken{\noexpand#1}%
+  \def\pgfsubpathsecondtoken{\noexpand#4}%
+  \ifx#4\pgf@stop%
+    \let\pgf@next\relax%
+    \let\pgf@do@shorten@start\relax%
+    \let\pgf@prep@start\pgf@prep@movetostart%
+    \let\pgf@do@draw@start\pgf@do@draw@straightstart%
+  \else\ifx#4\pgfsyssoftpath@curvetosupportatoken%
+    \ifpgf@precise@shortening%
+      \let\pgf@next\pgf@parse@start@curve@cont%
+      \let\pgf@do@shorten@start\pgf@do@shorten@curvedstart%
+      \let\pgf@do@draw@start\pgf@do@draw@curvedstart%
+      \let\pgf@prep@start\pgf@prep@curvedstart%
+    \else%
+      \let\pgf@next\pgf@parse@start@curve@cont@straight%
+      \let\pgf@do@shorten@start\pgf@do@shorten@straightstart%
+      \let\pgf@do@draw@start\pgf@do@draw@straightstart%
+      \let\pgf@prep@start\pgf@prep@straightstart%
+    \fi%
+  \else%
+    \let\pgf@next\pgf@parse@start@till@stop%
+    \let\pgf@do@shorten@start\pgf@do@shorten@straightstart%
+    \let\pgf@do@draw@start\pgf@do@draw@straightstart%
+    \let\pgf@prep@start\pgf@prep@straightstart%
+  \fi\fi%
+  \pgf@next%
+}
+
+\def\pgf@parse@start@till@stop#1\pgf@stop\pgf@stop\pgf@stop{\def\pgfsubpathend{#1}}%
+
+\def\pgf@parse@start@curve@cont#1#2#3#4#5#6#7\pgf@stop\pgf@stop\pgf@stop{%
+  \def\pgfpointthirdonpath{\pgfqpoint{#2}{#3}}%
+  \def\pgfpointfourthonpath{\pgfqpoint{#5}{#6}}%
+  \def\pgfsubpathend{#7}%
+}
+
+\def\pgf@parse@start@curve@cont@straight#1#2#3#4#5#6#7\pgf@stop\pgf@stop\pgf@stop{%
+  \def\pgfpointthirdonpath{\pgfqpoint{#2}{#3}}%
+  \def\pgfpointfourthonpath{\pgfqpoint{#5}{#6}}%
+  \def\pgfsubpathend{#1{#2}{#3}#4{#5}{#6}#7}%
+}
+
+\def\pgf@prep@movetostart{%
+  \pgf@process{\pgfpointfirstonpath}%
+  \pgf@xb\pgf@x
+  \pgf@yb\pgf@y
+  \pgf@xc\pgf@x
+  \pgf@yc\pgf@y
+}
+\def\pgf@prep@straightstart{%
+  \let\pgf@ref\pgfpointsecondonpath
+  \ifx\pgfpointfirstonpath\pgfpointsecondonpath%
+    \ifx\pgfpointthirdonpath\relax%
+    \else%
+      \ifx\pgfpointfirstonpath\pgfpointthirdonpath%
+        \let\pgf@ref\pgfpointfourthonpath%
+      \else
+        \let\pgf@ref\pgfpointthirdonpath%
+      \fi%
+    \fi%
+  \fi%
+  \pgfpointlineatdistance{\pgf@path@shortening@distance}{\pgfpointfirstonpath}{\pgf@ref}%
+  \pgf@xa\pgf@x%
+  \pgf@ya\pgf@y%
+}
+
+\def\pgf@do@shorten@straightstart{%
+  \edef\pgfprocessresultpathsuffix{\pgfsubpathfirsttoken{\the\pgf@xa}{\the\pgf@ya}\pgfsubpathsecondtoken{\the\pgf@xc}{\the\pgf@yc}}%
+  \expandafter\expandafter\expandafter\def%
+  \expandafter\expandafter\expandafter\pgfprocessresultpathsuffix%
+  \expandafter\expandafter\expandafter{\expandafter\pgfprocessresultpathsuffix\pgfsubpathend}%
+}
+
+
+
+\def\pgf@add@arrow@at@start{%
+  \ifx\pgf@arrowpath\pgfutil@empty\else%
+    \ifx\pgf@start@tip@sequence\pgfutil@empty\else%
+      \pgf@do@draw@start%
+    \fi%
+  \fi%
+}
+
+\def\pgf@do@draw@straightstart{%
+  {%
+    \pgftransformreset%
+    \pgftransformarrow{\pgfqpoint{\pgf@xc}{\pgf@yc}}{\pgfqpoint{\pgf@xb}{\pgf@yb}}%
+    \pgf@arrow@draw@arrow\pgf@start@tip@sequence\pgf@arrow@tip@total@length%
+  }%
+}
+
+
+
+\let\pgf@shorten@end=\pgfutil@empty
+\let\pgf@shorten@start=\pgfutil@empty
+
+
+\endinput%

preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/basiclayer/pgfcorepatterns.code.tex

@@ -0,0 +1,197 @@
+
+\ProvidesFileRCS{pgfcorepatterns.code.tex}
+
+\def\pgfdeclarepatternformonly{%
+  \def\pgf@pattern@type{formonly}%
+  \pgfutil@ifnextchar[{\pgf@declarepattern@checkarg}{\pgf@declarepattern@checkarg[]}%
+}
+
+
+\def\pgfdeclarepatterninherentlycolored{%
+  \def\pgf@pattern@type{inherentlycolored}%
+  \pgfutil@ifnextchar[{\pgf@declarepattern@checkarg}{\pgf@declarepattern@checkarg[]}%
+}
+
+
+
+
+
+\def\pgf@declarepattern@checkarg[#1]{%
+  \def\pgf@pattern@tempvars{#1}%
+  \ifx\pgf@pattern@tempvars\pgfutil@empty%
+    \expandafter\let\expandafter\pgf@next\csname pgf@declarepattern\pgf@pattern@type\endcsname%
+  \else%
+    \expandafter\let\expandafter\pgf@next\csname pgf@declarepattern\pgf@pattern@type @mutable\endcsname%
+  \fi%
+  \pgf@next}
+
+\long\def\pgf@declarepatternformonly#1#2#3#4#5{\pgf@declarepattern{#1}{#2}{#3}{#4}{#5}{0}}
+
+\long\def\pgf@declarepatterninherentlycolored#1#2#3#4#5{\pgf@declarepattern{#1}{#2}{#3}{#4}{#5}{1}}
+
+\long\def\pgf@declarepatternformonly@mutable#1#2#3#4#5{%
+  \def\pgf@marshal{\pgf@declarepatternmutable{#1}}%
+  \expandafter\pgf@marshal\expandafter{\pgf@pattern@tempvars}{#2}{#3}{#4}{#5}{2}%
+}
+
+\long\def\pgf@declarepatterninherentlycolored@mutable#1#2#3#4#5#6{%
+  \def\pgf@marshal{\pgf@declarepatternmutable{#1}}%
+  \expandafter\pgf@marshal\expandafter{\pgf@pattern@tempvars}{#2}{#3}{#4}{#5}{3}%
+}
+
+\def\pgfsys@patternmatrix{{1.0}{0.0}{0.0}{1.0}{0.0pt}{0.0pt}}
+\def\pgf@declarepattern#1#2#3#4#5#6{%
+  \pgfutil@ifundefined{pgf@pattern@name@#1}{%
+  \pgfsysprotocol@getcurrentprotocol\pgf@pattern@temp%
+  {%
+    \pgfinterruptpath%
+      \pgfpicturetrue%
+      \pgf@relevantforpicturesizefalse%
+      \pgftransformreset%
+      \pgfsysprotocol@setcurrentprotocol\pgfutil@empty%
+      \pgfsysprotocol@bufferedtrue%
+      \pgfsys@beginscope%
+      \pgfsetarrows{-}%
+      #5%
+      \pgfsys@endscope%
+      \pgfsysprotocol@getcurrentprotocol\pgf@pattern@code%
+      \global\let\pgf@pattern@code=\pgf@pattern@code%
+    \endpgfinterruptpath%
+    \pgf@process{#2}%
+    \pgf@xa=\pgf@x%
+    \pgf@ya=\pgf@y%
+    \pgf@process{#3}%
+    \pgf@xb=\pgf@x%
+    \pgf@yb=\pgf@y%
+    \pgf@process{#4}%
+    \pgf@xc=\pgf@x%
+    \pgf@yc=\pgf@y%
+    \pgfutil@tempcnta=\pgf@pattern@number%
+    \advance\pgfutil@tempcnta by1\relax%
+    \xdef\pgf@pattern@number{\the\pgfutil@tempcnta}%
+    \expandafter\xdef\csname pgf@pattern@name@#1\endcsname{\the\pgfutil@tempcnta}%
+    \expandafter\gdef\csname pgf@pattern@type@#1\endcsname{#6}%
+    \xdef\pgf@marshal{\noexpand\pgfsys@declarepattern
+      {\csname pgf@pattern@name@#1\endcsname}%
+      {\the\pgf@xa}{\the\pgf@ya}{\the\pgf@xb}{\the\pgf@yb}%
+      {\the\pgf@xc}{\the\pgf@yc}%
+      \pgfsys@patternmatrix%
+      {\pgf@pattern@code}{#6}}%
+  }%
+  \pgfsysprotocol@setcurrentprotocol\pgf@pattern@temp%
+  \expandafter\global\expandafter\let\csname pgf@pattern@instantiate@#1\endcsname=\pgf@marshal%
+  }
+  {%
+    \pgferror{Pattern `#1' already defined}%
+  }%
+}
+
+\def\pgf@pattern@number{0}%
+
+\def\pgf@declarepatternmutable#1#2#3#4#5#6#7{%
+  \pgfutil@ifundefined{pgf@pattern@name@#1}{%
+    \expandafter\gdef\csname pgf@pattern@name@#1\endcsname{#1}%
+    \expandafter\gdef\csname pgf@pattern@variables@#1\endcsname{#2}%
+    \expandafter\gdef\csname pgf@pattern@lowerleft@#1\endcsname{#3}%
+    \expandafter\gdef\csname pgf@pattern@upperright@#1\endcsname{#4}%
+    \expandafter\gdef\csname pgf@pattern@tilesize@#1\endcsname{#5}%
+    \expandafter\long\expandafter\gdef\csname pgf@pattern@code@#1\endcsname{#6}%
+    \expandafter\gdef\csname pgf@pattern@type@#1\endcsname{#7}%
+  }{\pgferror{The pattern `#1' is already defined}}%
+}
+
+\def\pgf@ifpatternisinherentlycolored#1#2#3{%
+  \expandafter\ifodd\csname pgf@pattern@type@#1\endcsname\relax#2\else#3\fi%
+}
+
+\def\pgf@ifpatternismutable#1#2#3{%
+  \expandafter\ifnum\csname pgf@pattern@type@#1\endcsname>1\relax#2\else#3\fi%
+}
+
+\def\pgfpatternreleasename#1{\expandafter\let\csname pgf@pattern@name@#1\endcsname\relax}
+
+
+
+
+
+
+\def\pgfsetfillpattern#1#2{%
+  \pgfutil@ifundefined{pgf@pattern@name@#1}%
+  {%
+    \pgferror{Undefined pattern `#1'}%
+  }%
+  {%
+    \pgf@ifpatternismutable{#1}%
+    {%
+      \let\pgf@pattern@tempvars\pgfutil@empty%
+      \expandafter\expandafter\expandafter\pgf@pattern@check@vars%
+        \csname pgf@pattern@variables@#1\endcsname,\pgf@stop,%
+      \edef\pgf@pattern@nametemp{pgf@pattern@#1@\pgf@pattern@tempvars}%
+      \expandafter\pgfutil@ifundefined\expandafter{\pgf@pattern@nametemp}%
+      {%
+        \pgf@ifpatternisinherentlycolored{#1}%
+          {\let\pgf@set@fillpattern@declare\pgfdeclarepatterninherentlycolored}%
+          {\let\pgf@set@fillpattern@declare\pgfdeclarepatternformonly}%
+        \pgf@set@fillpattern@declare%
+          {\pgf@pattern@nametemp}%
+          {\csname pgf@pattern@lowerleft@#1\endcsname}%
+          {\csname pgf@pattern@upperright@#1\endcsname}%
+          {\csname pgf@pattern@tilesize@#1\endcsname}%
+          {\csname pgf@pattern@code@#1\endcsname}%
+      }%
+      {%
+      }%
+      \expandafter\pgf@set@fillpattern\expandafter{\pgf@pattern@nametemp}{#2}%
+      \expandafter\gdef\csname\pgf@pattern@nametemp\endcsname{#1}%
+    }%
+    {%
+      \pgf@set@fillpattern{#1}{#2}%
+    }%
+  }%
+}
+
+
+\def\pgf@set@fillpattern#1#2{%
+  \pgfutil@ifundefined{pgf@pattern@name@#1}{%
+    \pgferror{Undefined pattern `#1'}}
+  {%
+    \csname pgf@pattern@instantiate@#1\endcsname%
+    \expandafter\global\expandafter\let\csname pgf@pattern@instantiate@#1\endcsname=\relax%
+    \pgf@ifpatternisinherentlycolored{#1}{%
+      \pgfsys@setpatterncolored{\csname pgf@pattern@name@#1\endcsname}%
+    }{%
+      \pgfutil@colorlet{pgf@tempcolor}{#2}%
+      \pgfutil@ifundefined{applycolormixins}{}{\applycolormixins{pgf@tempcolor}}%
+      \pgfutil@extractcolorspec{pgf@tempcolor}{\pgf@tempcolor}%
+      \expandafter\pgfutil@convertcolorspec\pgf@tempcolor{rgb}{\pgf@rgbcolor}%
+      \expandafter\pgf@set@fill@patternuncolored\pgf@rgbcolor\relax{#1}%
+    }%
+  }%
+}
+
+\def\pgf@set@fill@patternuncolored#1,#2,#3\relax#4{%
+  \pgfsys@setpatternuncolored{\csname pgf@pattern@name@#4\endcsname}{#1}{#2}{#3}%
+}
+
+\def\pgf@pattern@check@vars#1,{%
+  \ifx#1\pgf@stop%
+    \let\pgf@next\relax%
+  \else%
+    \afterassignment\pgfmath@gobbletilpgfmath@%
+    \expandafter\let\expandafter\pgf@pattern@char#1#1\pgfmath@%
+    \ifx\pgf@pattern@char/%
+      \edef\pgf@pattern@tempvar{(\pgfkeysvalueof{#1})}%
+    \else%
+      \expandafter\ifcat\pgf@pattern@char\relax%
+        \edef\pgf@pattern@tempvar{(\the#1)}%
+      \else%
+        \edef\pgf@pattern@tempvar{(#1)}%
+      \fi%
+    \fi%
+    \edef\pgf@pattern@tempvars{\pgf@pattern@tempvars\pgf@pattern@tempvar}%
+    \let\pgf@next\pgf@pattern@check@vars%
+  \fi%
+  \pgf@next%
+}
+
+\endinput

preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/basiclayer/pgfcorepoints.code.tex

@@ -0,0 +1,724 @@
+
+\ProvidesFileRCS{pgfcorepoints.code.tex}
+
+\newdimen\pgf@picminx
+\newdimen\pgf@picmaxx
+\newdimen\pgf@picminy
+\newdimen\pgf@picmaxy
+
+\newdimen\pgf@pathminx
+\newdimen\pgf@pathmaxx
+\newdimen\pgf@pathminy
+\newdimen\pgf@pathmaxy
+
+\newif\ifpgf@relevantforpicturesize
+
+\def\pgf@process#1{{#1\global\pgf@x=\pgf@x\global\pgf@y=\pgf@y}}
+
+
+\def\pgfextract@process#1#2{%
+    \pgf@process{#2}%
+    \edef#1{\noexpand\global\pgf@x=\the\pgf@x\noexpand\relax\noexpand\global\pgf@y=\the\pgf@y\noexpand\relax}%
+}
+\let\pgfsavepgf@process\pgfextract@process%
+
+
+
+\def\pgfpoint#1#2{%
+  \pgfmathsetlength\pgf@x{#1}%
+  \pgfmathsetlength\pgf@y{#2}\ignorespaces}
+
+
+
+\def\pgfqpoint#1#2{\global\pgf@x=#1\relax\global\pgf@y=#2\relax}
+
+
+
+
+\def\pgfpointorigin{\global\pgf@x=0pt \global\pgf@y=\pgf@x\ignorespaces}
+
+
+
+
+\def\pgfpointtransformed#1{%
+  \pgf@process{%
+    #1%
+    \pgf@pos@transform@glob%
+  }%
+}
+
+
+
+\def\pgfpointdiff#1#2{%
+  \pgf@process{#1}%
+  \pgf@xa=\pgf@x%
+  \pgf@ya=\pgf@y%
+  \pgf@process{#2}%
+  \global\advance\pgf@x by-\pgf@xa\relax%
+  \global\advance\pgf@y by-\pgf@ya\relax\ignorespaces}
+
+
+\def\pgfpointadd#1#2{%
+  \pgf@process{#1}%
+  \pgf@xa=\pgf@x%
+  \pgf@ya=\pgf@y%
+  \pgf@process{#2}%
+  \global\advance\pgf@x by\pgf@xa%
+  \global\advance\pgf@y by\pgf@ya}
+
+
+
+
+\def\pgfpointscale#1#2{%
+  \pgf@process{#2}%
+  \pgfmathparse{#1}%
+  \global\pgf@x=\pgfmathresult\pgf@x%
+  \global\pgf@y=\pgfmathresult\pgf@y%
+}
+\def\pgfqpointscale#1#2{%
+  \pgf@process{#2}%
+  \global\pgf@x=#1\pgf@x%
+  \global\pgf@y=#1\pgf@y%
+}
+
+
+
+\def\pgfpointintersectionoflines#1#2#3#4{%
+  {%
+    \pgf@process{#2}%
+    \pgf@xa=\pgf@x%
+    \pgf@ya=\pgf@y%
+    \pgf@process{#1}%
+    \advance\pgf@xa by-\pgf@x%
+    \advance\pgf@ya by-\pgf@y%
+    \pgf@ya=-\pgf@ya%
+    \c@pgf@counta=\pgf@xa%
+    \ifnum\c@pgf@counta<0\relax%
+      \c@pgf@counta=-\c@pgf@counta\relax%
+    \fi%
+    \c@pgf@countb=\pgf@ya%
+    \ifnum\c@pgf@countb<0\relax%
+      \c@pgf@countb=-\c@pgf@countb\relax%
+    \fi%
+    \advance\c@pgf@counta by\c@pgf@countb\relax%
+    \divide\c@pgf@counta by 65536\relax%
+    \ifnum\c@pgf@counta>0\relax%
+      \divide\pgf@xa by\c@pgf@counta\relax%
+      \divide\pgf@ya by\c@pgf@counta\relax%
+    \fi%
+    \pgf@xc=\pgf@sys@tonumber{\pgf@ya}\pgf@x%
+    \advance\pgf@xc by\pgf@sys@tonumber{\pgf@xa}\pgf@y%
+    \pgf@process{#4}%
+    \pgf@xb=\pgf@x%
+    \pgf@yb=\pgf@y%
+    \pgf@process{#3}%
+    \advance\pgf@xb by-\pgf@x%
+    \advance\pgf@yb by-\pgf@y%
+    \pgf@yb=-\pgf@yb%
+    \c@pgf@counta=\pgf@xb%
+    \ifnum\c@pgf@counta<0\relax%
+      \c@pgf@counta=-\c@pgf@counta\relax%
+    \fi%
+    \c@pgf@countb=\pgf@yb%
+    \ifnum\c@pgf@countb<0\relax%
+      \c@pgf@countb=-\c@pgf@countb\relax%
+    \fi%
+    \advance\c@pgf@counta by\c@pgf@countb\relax%
+    \divide\c@pgf@counta by 65536\relax%
+    \ifnum\c@pgf@counta>0\relax%
+      \divide\pgf@xb by\c@pgf@counta\relax%
+      \divide\pgf@yb by\c@pgf@counta\relax%
+    \fi%
+    \pgf@yc=\pgf@sys@tonumber{\pgf@yb}\pgf@x%
+    \advance\pgf@yc by\pgf@sys@tonumber{\pgf@xb}\pgf@y%
+    \pgfsettransform{{\pgf@sys@tonumber\pgf@ya}{\pgf@sys@tonumber\pgf@yb}{\pgf@sys@tonumber\pgf@xa}{\pgf@sys@tonumber\pgf@xb}{0pt}{0pt}}%
+    \pgftransforminvert%
+    \pgf@process{\pgfpointtransformed{\pgfpoint{\pgf@xc}{\pgf@yc}}}%
+  }%
+}
+
+
+
+\def\pgfpointintersectionofcircles#1#2#3#4#5{%
+  {%
+    \pgf@process{#1}%
+    \pgf@xa=\pgf@x%
+    \pgf@ya=\pgf@y%
+    \pgfmathsetlength{\pgf@xc}{#3}%
+    \pgf@process{#2}%
+    \pgf@xb=\pgf@x%
+    \pgf@yb=\pgf@y%
+    \pgfmathsetlength{\pgf@yc}{#4}%
+    \c@pgf@counta=1\relax%
+    \loop%
+      \pgf@scale@downfalse%
+      \ifdim\pgf@xc>50pt\relax%
+        \pgf@scale@downtrue%
+      \fi%
+      \ifdim\pgf@yc>50pt\relax%
+        \pgf@scale@downtrue%
+      \fi%
+    \ifpgf@scale@down%
+      \multiply\c@pgf@counta by2\relax%
+      \divide\pgf@xa by2\relax%
+      \divide\pgf@ya by2\relax%
+      \divide\pgf@xb by2\relax%
+      \divide\pgf@yb by2\relax%
+      \divide\pgf@xc by2\relax%
+      \divide\pgf@yc by2\relax%
+    \repeat%
+    \dimen0=\pgf@xb%
+    \advance\dimen0 by-\pgf@xa%
+    \dimen1=\pgf@yb%
+    \advance\dimen1 by-\pgf@ya%
+    \pgf@x=\dimen0\relax%
+    \pgf@x=\pgf@sys@tonumber{\pgf@x}\pgf@x%
+    \dimen3=\pgf@x%
+    \pgf@x=\dimen1\relax%
+    \advance\dimen3 by\pgf@sys@tonumber{\pgf@x}\pgf@x%
+    \pgfmathparse{sqrt(\the\dimen3)}%
+    \dimen2=\pgfmathresult pt%
+    \pgfmathreciprocal@{\pgfmathresult}%
+    \dimen5=\pgfmathresult pt%
+    \dimen4=\dimen3\relax%
+    \pgf@x=\pgf@xc%
+    \advance\dimen4 by\pgf@sys@tonumber{\pgf@x}\pgf@x\relax%
+    \pgf@x=\pgf@yc%
+    \advance\dimen4 by-\pgf@sys@tonumber{\pgf@x}\pgf@x\relax%
+    \dimen4=.5\dimen4%
+    \dimen4=\pgf@sys@tonumber{\dimen5}\dimen4%
+    \dimen7=\pgf@sys@tonumber{\dimen4}\dimen4\relax%
+    \pgfmathparse{sqrt(\pgf@sys@tonumber{\pgf@xc}\pgf@xc-\the\dimen7)}%
+    \dimen6=\pgfmathresult pt%
+    \dimen8=\pgf@sys@tonumber{\dimen4}\dimen5\relax%
+    \dimen9=\pgf@sys@tonumber{\dimen6}\dimen5\relax%
+    \ifnum#5=1\relax%
+      \pgf@x=\pgf@xa%
+      \advance\pgf@x by\pgf@sys@tonumber{\dimen0}\dimen8\relax%
+      \advance\pgf@x by\pgf@sys@tonumber{\dimen1}\dimen9\relax%
+      \pgf@y=\pgf@ya%
+      \advance\pgf@y by\pgf@sys@tonumber{\dimen1}\dimen8\relax%
+        \pgf@xb=\pgf@sys@tonumber{\dimen0}\dimen9%
+        \pgf@xb=-\pgf@xb%
+      \advance\pgf@y by\pgf@xb\relax%
+    \else%
+      \pgf@x=\pgf@xa%
+      \advance\pgf@x by\pgf@sys@tonumber{\dimen0}\dimen8\relax%
+        \pgf@xb=\pgf@sys@tonumber{\dimen1}\dimen9%
+        \pgf@xb=-\pgf@xb%
+      \advance\pgf@x by\pgf@xb\relax%
+      \pgf@y=\pgf@ya%
+      \advance\pgf@y by\pgf@sys@tonumber{\dimen1}\dimen8\relax%
+      \advance\pgf@y by\pgf@sys@tonumber{\dimen0}\dimen9\relax%
+    \fi%
+    \pgf@x=\c@pgf@counta\pgf@x%
+    \pgf@y=\c@pgf@counta\pgf@y%
+    \pgf@process{}%
+  }%
+}
+\newif\ifpgf@scale@down
+
+
+
+\def\pgfpointlineattime#1#2#3{%
+  \pgf@process{#3}%
+  \pgf@xa\pgf@x%
+  \pgf@ya\pgf@y%
+  \pgf@xc\pgf@x%
+  \pgf@yc\pgf@y%
+  \pgf@process{#2}%
+  \pgf@xb\pgf@x%
+  \pgf@yb\pgf@y%
+  \pgfmathsetmacro\pgf@temp{#1}%
+  \advance\pgf@xa by-\pgf@x%
+  \advance\pgf@ya by-\pgf@y%
+  \global\advance\pgf@x by\pgf@temp\pgf@xa%
+  \global\advance\pgf@y by\pgf@temp\pgf@ya%
+}
+
+
+
+\def\pgfpointlineatdistance#1#2#3{%
+  \pgfmathsetlength\pgf@xa{#1}%
+  \pgf@process{#2}%
+  \pgf@xb\pgf@x%
+  \pgf@yb\pgf@y%
+  \pgf@process{#3}%
+  \pgf@xc\pgf@x%
+  \pgf@yc\pgf@y%
+  \global\advance\pgf@x by-\pgf@xb\relax%
+  \global\advance\pgf@y by-\pgf@yb\relax%
+  \pgf@process{\pgfpointnormalised{}}%
+  \pgf@ya=\pgf@xa\relax%
+  \pgf@xa=\pgf@sys@tonumber{\pgf@x}\pgf@xa%
+  \pgf@ya=\pgf@sys@tonumber{\pgf@y}\pgf@ya%
+  \global\pgf@x=\pgf@xb\relax%
+  \global\pgf@y=\pgf@yb\relax%
+  \global\advance\pgf@x by\pgf@xa\relax%
+  \global\advance\pgf@y by\pgf@ya\relax%
+}
+
+
+
+\def\pgfpointcurveattime#1#2#3#4#5{%
+  \pgfmathparse{#1}%
+  \let\pgf@time@s=\pgfmathresult%
+  \global\pgf@x=\pgfmathresult pt%
+  \global\pgf@x=-\pgf@x%
+  \advance\pgf@x by 1pt%
+  \edef\pgf@time@t{\pgf@sys@tonumber{\pgf@x}}%
+  \pgf@process{#5}%
+  \pgf@xc=\pgf@x%
+  \pgf@yc=\pgf@y%
+  \pgf@process{#4}%
+  \pgf@xb=\pgf@x%
+  \pgf@yb=\pgf@y%
+  \pgf@process{#3}%
+  \pgf@xa=\pgf@x%
+  \pgf@ya=\pgf@y%
+  \pgf@process{#2}%
+  \global\pgf@x=\pgf@time@t\pgf@x\global\advance\pgf@x by\pgf@time@s\pgf@xa%
+  \global\pgf@y=\pgf@time@t\pgf@y\global\advance\pgf@y by\pgf@time@s\pgf@ya%
+  \pgf@xa=\pgf@time@t\pgf@xa\advance\pgf@xa by\pgf@time@s\pgf@xb%
+  \pgf@ya=\pgf@time@t\pgf@ya\advance\pgf@ya by\pgf@time@s\pgf@yb%
+  \pgf@xb=\pgf@time@t\pgf@xb\advance\pgf@xb by\pgf@time@s\pgf@xc%
+  \pgf@yb=\pgf@time@t\pgf@yb\advance\pgf@yb by\pgf@time@s\pgf@yc%
+  \global\pgf@x=\pgf@time@t\pgf@x\global\advance\pgf@x by\pgf@time@s\pgf@xa%
+  \global\pgf@y=\pgf@time@t\pgf@y\global\advance\pgf@y by\pgf@time@s\pgf@ya%
+  \pgf@xa=\pgf@time@t\pgf@xa\advance\pgf@xa by\pgf@time@s\pgf@xb%
+  \pgf@ya=\pgf@time@t\pgf@ya\advance\pgf@ya by\pgf@time@s\pgf@yb%
+  \pgf@xb=\pgf@x%
+  \pgf@yb=\pgf@y%
+  \global\pgf@x=\pgf@time@t\pgf@x\global\advance\pgf@x by\pgf@time@s\pgf@xa%
+  \global\pgf@y=\pgf@time@t\pgf@y\global\advance\pgf@y by\pgf@time@s\pgf@ya%
+}
+
+
+
+
+\def\pgfpointarcaxesattime#1#2#3#4#5#6{%
+  \pgfmathsetmacro\pgf@angle@start{#5}%
+  \pgfmathsetmacro\pgf@angle@end{#6}%
+  \pgfmathparse{#1}%
+  \global\pgf@x=\pgfmathresult pt%
+  \global\pgf@x=-\pgf@x%
+  \advance\pgf@x by 1pt%
+  \pgfmathsetmacro\pgf@angle@mid{\pgf@angle@end*\pgfmathresult+\pgf@angle@start*\pgf@sys@tonumber{\pgf@x}}%
+  \pgfmathcos@{\pgf@angle@mid}%
+  \let\pgf@angle@cos\pgfmathresult%
+  \pgfmathsin@{\pgf@angle@mid}%
+  \let\pgf@angle@sin\pgfmathresult%
+  \pgf@process{#3}%
+  \edef\pgf@angle@zero@axis{\noexpand\pgfqpoint{\the\pgf@x}{\the\pgf@y}}
+  \pgf@process{#4}%
+  \edef\pgf@angle@ninety@axis{\noexpand\pgfqpoint{\the\pgf@x}{\the\pgf@y}}
+  \pgf@process{\pgfpointadd{\pgfpointscale{\pgf@angle@sin}{\pgf@angle@zero@axis}}%
+    {\pgfpointscale{-\pgf@angle@cos}{\pgf@angle@ninety@axis}}}%
+  \ifdim\pgf@angle@start pt>\pgf@angle@end pt%
+    \pgf@xa=\pgf@x%
+    \pgf@ya=\pgf@y%
+  \else%
+    \pgf@xa=-\pgf@x%
+    \pgf@ya=-\pgf@y%
+  \fi%
+  \pgf@process{\pgfpointadd{#2}{%
+      \pgfpointadd{\pgfpointscale{\pgf@angle@cos}{\pgf@angle@zero@axis}}%
+    {\pgfpointscale{\pgf@angle@sin}{\pgf@angle@ninety@axis}}}}%
+}
+
+
+
+\newdimen\pgf@xx
+\newdimen\pgf@xy
+\newdimen\pgf@yx
+\newdimen\pgf@yy
+\newdimen\pgf@zx
+\newdimen\pgf@zy
+
+
+
+
+\def\pgfpointpolar#1#2{%
+  \pgfutil@in@{and }{#2}%
+  \ifpgfutil@in@%
+    \pgf@polar@#2\@@%
+  \else%
+    \pgf@polar@#2 and #2\@@%
+  \fi%
+  \pgfmathparse{#1}%
+  \let\pgfpoint@angle=\pgfmathresult%
+  \pgfmathcos@{\pgfpoint@angle}%
+  \global\pgf@x=\pgfmathresult\pgf@x%
+  \pgfmathsin@{\pgfpoint@angle}%
+  \global\pgf@y=\pgfmathresult\pgf@y%
+}
+
+\def\pgf@polar@#1and #2\@@{%
+  \pgfmathsetlength{\pgf@y}{#2}%
+  \pgfmathsetlength{\pgf@x}{#1}%
+}
+
+
+\def\pgfqpointpolar#1#2{%
+  \global\pgf@x=#2%
+  \global\pgf@y=\pgf@x%
+  \pgfmathcos@{#1}%
+  \global\pgf@x=\pgfmathresult\pgf@x%
+  \pgfmathsin@{#1}%
+  \global\pgf@y=\pgfmathresult\pgf@y\relax%
+}
+
+
+
+
+
+\def\pgfpointpolarxy#1#2{%
+  \pgfutil@in@{and }{#2}%
+  \ifpgfutil@in@%
+    \pgf@polarxy@#2\@@%
+  \else%
+    \pgf@polarxy@#2and #2\@@%
+  \fi%
+  \pgfmathparse{#1}%
+  \let\pgfpoint@angle=\pgfmathresult%
+  \pgfmathcos@{\pgfpoint@angle}%
+  \pgf@xa=\pgfmathresult\pgf@xa%
+  \pgfmathsin@{\pgfpoint@angle}%
+  \pgf@ya=\pgfmathresult\pgf@ya%
+  \global\pgf@x=\pgf@sys@tonumber{\pgf@xa}\pgf@xx%
+  \global\advance\pgf@x by \pgf@sys@tonumber{\pgf@ya}\pgf@yx%
+  \global\pgf@y=\pgf@sys@tonumber{\pgf@xa}\pgf@xy%
+  \global\advance\pgf@y by \pgf@sys@tonumber{\pgf@ya}\pgf@yy}
+
+\def\pgf@polarxy@#1and #2\@@{%
+  \pgfmathsetlength{\pgf@xa}{#1}%
+  \pgfmathsetlength{\pgf@ya}{#2}%
+}
+
+
+
+
+\def\pgfpointcylindrical#1#2#3{%
+  \pgfpointpolarxy{#1}{#2}%
+  \pgfmathparse{#3}%
+  \global\advance\pgf@x by \pgfmathresult\pgf@zx%
+  \global\advance\pgf@y by \pgfmathresult\pgf@zy}
+
+
+
+\def\pgfpointspherical#1#2#3{%
+  \pgfmathparse{#1}%
+  \let\pgfpoint@angle=\pgfmathresult%
+  \pgfmathsin@{\pgfpoint@angle}%
+  \pgf@xb=\pgfmathresult\pgf@xx%
+  \pgf@yb=\pgfmathresult\pgf@xy%
+  \pgfmathcos@{\pgfpoint@angle}%
+  \advance\pgf@xb by \pgfmathresult\pgf@yx%
+  \advance\pgf@yb by \pgfmathresult\pgf@yy%
+  \pgfmathparse{#2}%
+  \let\pgfpoint@angle=\pgfmathresult%
+  \pgfmathcos@{\pgfpoint@angle}%
+  \pgf@xc=\pgfmathresult\pgf@xb%
+  \pgf@yc=\pgfmathresult\pgf@yb%
+  \pgfmathsin@{\pgfpoint@angle}%
+  \advance\pgf@xc by \pgfmathresult\pgf@zx%
+  \advance\pgf@yc by \pgfmathresult\pgf@zy%
+  \pgfmathparse{#3}%
+  \global\pgf@x=\pgfmathresult\pgf@xc%
+  \global\pgf@y=\pgfmathresult\pgf@yc\relax%
+}
+
+
+
+\def\pgfpointxy#1#2{%
+  \pgfmathparse{#1}%
+  \let\pgftemp@x=\pgfmathresult%
+  \pgfmathparse{#2}%
+  \let\pgftemp@y=\pgfmathresult%
+  \global\pgf@x=\pgftemp@x\pgf@xx%
+  \global\advance\pgf@x by \pgftemp@y\pgf@yx%
+  \global\pgf@y=\pgftemp@x\pgf@xy%
+  \global\advance\pgf@y by \pgftemp@y\pgf@yy}
+
+
+\def\pgfqpointxy#1#2{%
+  \global\pgf@x=#1\pgf@xx%
+  \global\advance\pgf@x by #2\pgf@yx%
+  \global\pgf@y=#1\pgf@xy%
+  \global\advance\pgf@y by #2\pgf@yy}
+
+
+\def\pgfpointxyz#1#2#3{%
+  \pgfmathparse{#1}%
+  \let\pgftemp@x=\pgfmathresult%
+  \pgfmathparse{#2}%
+  \let\pgftemp@y=\pgfmathresult%
+  \pgfmathparse{#3}%
+  \let\pgftemp@z=\pgfmathresult%
+  \global\pgf@x=\pgftemp@x\pgf@xx%
+  \global\advance\pgf@x by \pgftemp@y\pgf@yx%
+  \global\advance\pgf@x by \pgftemp@z\pgf@zx%
+  \global\pgf@y=\pgftemp@x\pgf@xy%
+  \global\advance\pgf@y by \pgftemp@y\pgf@yy%
+  \global\advance\pgf@y by \pgftemp@z\pgf@zy}
+
+\def\pgfqpointxyz#1#2#3{%
+  \global\pgf@x=#1\pgf@xx%
+  \global\advance\pgf@x by #2\pgf@yx%
+  \global\advance\pgf@x by #3\pgf@zx%
+  \global\pgf@y=#1\pgf@xy%
+  \global\advance\pgf@y by #2\pgf@yy%
+  \global\advance\pgf@y by #3\pgf@zy}
+
+
+
+
+\def\pgfsetxvec#1{%
+  \pgf@process{#1}%
+  \pgf@xx=\pgf@x%
+  \pgf@xy=\pgf@y%
+  \ignorespaces}
+
+
+
+\def\pgfsetyvec#1{%
+  \pgf@process{#1}%
+  \pgf@yx=\pgf@x%
+  \pgf@yy=\pgf@y%
+  \ignorespaces}
+
+
+
+\def\pgfsetzvec#1{%
+  \pgf@process{#1}%
+  \pgf@zx=\pgf@x%
+  \pgf@zy=\pgf@y%
+  \ignorespaces}
+
+
+
+\pgfsetxvec{\pgfpoint{1cm}{0cm}}
+\pgfsetyvec{\pgfpoint{0cm}{1cm}}
+\pgfsetzvec{\pgfpoint{-0.385cm}{-0.385cm}}
+
+
+
+
+
+\def\pgfpointnormalised#1{%
+  \pgf@process{#1}%
+  \pgfmathatantwo{\the\pgf@y}{\the\pgf@x}%
+  \let\pgf@tmp=\pgfmathresult%
+  \pgfmathcos@{\pgf@tmp}%
+  \pgf@x=\pgfmathresult pt\relax%
+  \pgfmathsin@{\pgf@tmp}%
+  \pgf@y=\pgfmathresult pt\relax%
+}
+
+
+
+
+
+
+\def\pgfpointborderrectangle#1#2{%
+  \pgf@process{#2}%
+  \pgf@xb=\pgf@x%
+  \pgf@yb=\pgf@y%
+  \pgf@process{#1}%
+  \pgf@xa=\pgf@x%
+  \pgf@ya=\pgf@y%
+  \ifnum\pgf@xa<0\relax%
+    \global\pgf@x=-\pgf@x%
+  \fi%
+  \ifnum\pgf@ya<0\relax%
+    \global\pgf@y=-\pgf@y%
+  \fi%
+  \pgf@xc=.125\pgf@x%
+  \pgf@yc=.125\pgf@y%
+  \c@pgf@counta=\pgf@xc%
+  \c@pgf@countb=\pgf@yc%
+  \ifnum\c@pgf@countb<\c@pgf@counta%
+    \ifnum\c@pgf@counta<255\relax%
+      \global\pgf@y=\pgf@yb\relax%
+      \global\pgf@x=0pt\relax%
+    \else%
+      \pgf@xc=8192pt%
+      \divide\pgf@xc by\c@pgf@counta%
+      \global\pgf@y=\pgf@sys@tonumber{\pgf@xc}\pgf@y%
+      \global\pgf@y=\pgf@sys@tonumber{\pgf@xb}\pgf@y%
+      \ifnum\pgf@y<\pgf@yb%
+        \global\pgf@x=\pgf@xb%
+      \else%
+        \ifnum\c@pgf@countb<255\relax%
+          \global\pgf@x=\pgf@xb\relax%
+          \global\pgf@y=0pt\relax%
+        \else%
+          \pgf@yc=8192pt%
+          \divide\pgf@yc by\c@pgf@countb%
+          \global\pgf@x=\pgf@sys@tonumber{\pgf@yc}\pgf@x%
+          \global\pgf@x=\pgf@sys@tonumber{\pgf@yb}\pgf@x%
+          \global\pgf@y=\pgf@yb%
+        \fi%
+      \fi%
+    \fi%
+  \else%
+    \ifnum\c@pgf@countb<255\relax%
+      \global\pgf@x=\pgf@xb\relax%
+      \global\pgf@y=0pt\relax%
+    \else%
+      \pgf@yc=8192pt%
+      \divide\pgf@yc by\c@pgf@countb%
+      \global\pgf@x=\pgf@sys@tonumber{\pgf@yc}\pgf@x%
+      \global\pgf@x=\pgf@sys@tonumber{\pgf@yb}\pgf@x%
+      \ifnum\pgf@x<\pgf@xb%
+        \global\pgf@y=\pgf@yb%
+      \else%
+        \ifnum\c@pgf@counta<255\relax%
+          \global\pgf@y=\pgf@yb\relax%
+          \global\pgf@x=0pt\relax%
+        \else%
+          \pgf@xc=8192pt%
+          \divide\pgf@xc by\c@pgf@counta%
+          \global\pgf@y=\pgf@sys@tonumber{\pgf@xc}\pgf@y%
+          \global\pgf@y=\pgf@sys@tonumber{\pgf@xb}\pgf@y%
+          \global\pgf@x=\pgf@xb%
+        \fi%
+      \fi%
+    \fi%
+  \fi%
+  \ifnum\pgf@xa<0\relax\global\pgf@x=-\pgf@x\fi%
+  \ifnum\pgf@ya<0\relax\global\pgf@y=-\pgf@y\fi%
+}
+
+
+
+
+
+\def\pgfpointborderellipse#1#2{%
+  \pgf@process{#2}%
+  \pgf@xa=\pgf@x%
+  \pgf@ya=\pgf@y%
+  \ifdim\pgf@xa=\pgf@ya%
+    \pgf@process{\pgfpointnormalised{#1}}%
+    \global\pgf@x=\pgf@sys@tonumber{\pgf@xa}\pgf@x%
+    \global\pgf@y=\pgf@sys@tonumber{\pgf@xa}\pgf@y%
+  \else%
+    \ifdim\pgf@xa<\pgf@ya%
+      \c@pgf@countb=\pgf@ya%
+      \divide\c@pgf@countb by65536\relax%
+      \global\divide\pgf@x by\c@pgf@countb%
+      \global\divide\pgf@y by\c@pgf@countb%
+      \pgf@xc=\pgf@x%
+      \pgf@yc=8192pt%
+      \global\pgf@y=.125\pgf@y%
+      \c@pgf@countb=\pgf@y%
+      \divide\pgf@yc by\c@pgf@countb%
+      \pgf@process{#1}%
+      \global\pgf@y=\pgf@sys@tonumber{\pgf@yc}\pgf@y%
+      \global\pgf@y=\pgf@sys@tonumber{\pgf@xc}\pgf@y%
+      \pgf@process{\pgfpointnormalised{}}%
+      \global\pgf@x=\pgf@sys@tonumber{\pgf@xa}\pgf@x%
+      \global\pgf@y=\pgf@sys@tonumber{\pgf@ya}\pgf@y%
+    \else%
+      \c@pgf@countb=\pgf@xa%
+      \divide\c@pgf@countb by65536\relax%
+      \global\divide\pgf@x by\c@pgf@countb%
+      \global\divide\pgf@y by\c@pgf@countb%
+      \pgf@yc=\pgf@y%
+      \pgf@xc=8192pt%
+      \global\pgf@x=.125\pgf@x%
+      \c@pgf@countb=\pgf@x%
+      \divide\pgf@xc by\c@pgf@countb%
+      \pgf@process{#1}%
+      \global\pgf@x=\pgf@sys@tonumber{\pgf@yc}\pgf@x%
+      \global\pgf@x=\pgf@sys@tonumber{\pgf@xc}\pgf@x%
+      \pgf@process{\pgfpointnormalised{}}%
+      \global\pgf@x=\pgf@sys@tonumber{\pgf@xa}\pgf@x%
+      \global\pgf@y=\pgf@sys@tonumber{\pgf@ya}\pgf@y%
+    \fi%
+  \fi%
+}
+
+
+
+
+
+
+\def\pgfextractx#1#2{%
+  \pgf@process{#2}%
+  #1=\pgf@x\relax}
+
+
+
+\def\pgfextracty#1#2{%
+  \pgf@process{#2}%
+  #1=\pgf@y\relax}
+
+
+\def\pgfgetlastxy#1#2{%
+    \edef#1{\the\pgf@x}%
+    \edef#2{\the\pgf@y}%
+}%
+
+
+\def\pgf@def#1#2#3{\expandafter\def\csname pgf@#1#2\endcsname{#3}}
+\pgf@def{cosfrac}{0}{1}
+\pgf@def{cosfrac}{1}{0.99995}    \pgf@def{cosfrac}{2}{0.9998}
+\pgf@def{cosfrac}{3}{0.99955}    \pgf@def{cosfrac}{4}{0.999201}
+\pgf@def{cosfrac}{5}{0.998752}   \pgf@def{cosfrac}{6}{0.998205}
+\pgf@def{cosfrac}{7}{0.997559}   \pgf@def{cosfrac}{8}{0.996815}
+\pgf@def{cosfrac}{9}{0.995974}   \pgf@def{cosfrac}{10}{0.995037}
+\pgf@def{cosfrac}{11}{0.994004}  \pgf@def{cosfrac}{12}{0.992877}
+\pgf@def{cosfrac}{13}{0.991656}  \pgf@def{cosfrac}{14}{0.990342}
+\pgf@def{cosfrac}{15}{0.988936}  \pgf@def{cosfrac}{16}{0.987441}
+\pgf@def{cosfrac}{17}{0.985856}  \pgf@def{cosfrac}{18}{0.984183}
+\pgf@def{cosfrac}{19}{0.982424}  \pgf@def{cosfrac}{20}{0.980581}
+\pgf@def{cosfrac}{21}{0.978653}  \pgf@def{cosfrac}{22}{0.976644}
+\pgf@def{cosfrac}{23}{0.974555}  \pgf@def{cosfrac}{24}{0.972387}
+\pgf@def{cosfrac}{25}{0.970143}  \pgf@def{cosfrac}{26}{0.967823}
+\pgf@def{cosfrac}{27}{0.965429}  \pgf@def{cosfrac}{28}{0.962964}
+\pgf@def{cosfrac}{29}{0.960429}  \pgf@def{cosfrac}{30}{0.957826}
+\pgf@def{cosfrac}{31}{0.955157}  \pgf@def{cosfrac}{32}{0.952424}
+\pgf@def{cosfrac}{33}{0.949629}  \pgf@def{cosfrac}{34}{0.946773}
+\pgf@def{cosfrac}{35}{0.943858}  \pgf@def{cosfrac}{36}{0.940887}
+\pgf@def{cosfrac}{37}{0.937862}  \pgf@def{cosfrac}{38}{0.934784}
+\pgf@def{cosfrac}{39}{0.931655}  \pgf@def{cosfrac}{40}{0.928477}
+\pgf@def{cosfrac}{41}{0.925252}  \pgf@def{cosfrac}{42}{0.921982}
+\pgf@def{cosfrac}{43}{0.918669}  \pgf@def{cosfrac}{44}{0.915315}
+\pgf@def{cosfrac}{45}{0.911922}  \pgf@def{cosfrac}{46}{0.90849}
+\pgf@def{cosfrac}{47}{0.905024}  \pgf@def{cosfrac}{48}{0.901523}
+\pgf@def{cosfrac}{49}{0.89799}   \pgf@def{cosfrac}{50}{0.894427}
+\pgf@def{cosfrac}{51}{0.890835}  \pgf@def{cosfrac}{52}{0.887217}
+\pgf@def{cosfrac}{53}{0.883573}  \pgf@def{cosfrac}{54}{0.879905}
+\pgf@def{cosfrac}{55}{0.876216}  \pgf@def{cosfrac}{56}{0.872506}
+\pgf@def{cosfrac}{57}{0.868777}  \pgf@def{cosfrac}{58}{0.865031}
+\pgf@def{cosfrac}{59}{0.861269}  \pgf@def{cosfrac}{60}{0.857493}
+\pgf@def{cosfrac}{61}{0.853704}  \pgf@def{cosfrac}{62}{0.849903}
+\pgf@def{cosfrac}{63}{0.846092}  \pgf@def{cosfrac}{64}{0.842271}
+\pgf@def{cosfrac}{65}{0.838444}  \pgf@def{cosfrac}{66}{0.834609}
+\pgf@def{cosfrac}{67}{0.83077}   \pgf@def{cosfrac}{68}{0.826927}
+\pgf@def{cosfrac}{69}{0.82308}   \pgf@def{cosfrac}{70}{0.819232}
+\pgf@def{cosfrac}{71}{0.815383}  \pgf@def{cosfrac}{72}{0.811534}
+\pgf@def{cosfrac}{73}{0.807687}  \pgf@def{cosfrac}{74}{0.803842}
+\pgf@def{cosfrac}{75}{0.8}       \pgf@def{cosfrac}{76}{0.796162}
+\pgf@def{cosfrac}{77}{0.792329}  \pgf@def{cosfrac}{78}{0.788502}
+\pgf@def{cosfrac}{79}{0.784682}  \pgf@def{cosfrac}{80}{0.780869}
+\pgf@def{cosfrac}{81}{0.777064}  \pgf@def{cosfrac}{82}{0.773268}
+\pgf@def{cosfrac}{83}{0.769481}  \pgf@def{cosfrac}{84}{0.765705}
+\pgf@def{cosfrac}{85}{0.761939}  \pgf@def{cosfrac}{86}{0.758185}
+\pgf@def{cosfrac}{87}{0.754443}  \pgf@def{cosfrac}{88}{0.750714}
+\pgf@def{cosfrac}{89}{0.746997}  \pgf@def{cosfrac}{90}{0.743294}
+\pgf@def{cosfrac}{91}{0.739605}  \pgf@def{cosfrac}{92}{0.735931}
+\pgf@def{cosfrac}{93}{0.732272}  \pgf@def{cosfrac}{94}{0.728628}
+\pgf@def{cosfrac}{95}{0.724999}  \pgf@def{cosfrac}{96}{0.721387}
+\pgf@def{cosfrac}{97}{0.717792}  \pgf@def{cosfrac}{98}{0.714213}
+\pgf@def{cosfrac}{99}{0.710651}  \pgf@def{cosfrac}{100}{0.707107}
+
+
+
+
+
+\let\pgfpointtransformednonlinear\pgfpointtransformed
+
+
+\endinput

preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/basiclayer/pgfcorequick.code.tex

@@ -0,0 +1,67 @@
+
+\ProvidesFileRCS{pgfcorequick.code.tex}
+
+
+
+\def\pgfpathqmoveto#1#2{\pgfsyssoftpath@moveto{#1}{#2}}
+
+
+
+\def\pgfpathqlineto#1#2{\pgfsyssoftpath@lineto{#1}{#2}}
+
+
+
+\def\pgfpathqcurveto#1#2#3#4#5#6{\pgfsyssoftpath@curveto{#1}{#2}{#3}{#4}{#5}{#6}}
+
+
+
+
+
+\def\pgfpathqcircle#1{%
+  {%
+    \pgf@x=#1%
+    \pgf@y=0.5522847\pgf@x%
+    \pgfsyssoftpath@moveto{\the\pgf@x}{0pt}%
+    \pgfsyssoftpath@curveto{\the\pgf@x}{\the\pgf@y}{\the\pgf@y}{\the\pgf@x}{0pt}{\the\pgf@x}%
+    \pgfsyssoftpath@curveto{-\the\pgf@y}{\the\pgf@x}{-\the\pgf@x}{\the\pgf@y}{-\the\pgf@x}{0pt}%
+    \pgfsyssoftpath@curveto{-\the\pgf@x}{-\the\pgf@y}{-\the\pgf@y}{-\the\pgf@x}{0pt}{-\the\pgf@x}%
+    \pgfsyssoftpath@curveto{\the\pgf@y}{-\the\pgf@x}{\the\pgf@x}{-\the\pgf@y}{\the\pgf@x}{0pt}%
+    \pgfsyssoftpath@closepath%
+  }%
+}
+
+
+
+
+\def\pgfusepathqstroke{%
+  \pgfsyssoftpath@flushcurrentpath%
+  \pgfsys@stroke%
+  \pgf@resetpathsizes%
+}
+
+
+
+\def\pgfusepathqfill{%
+  \pgfsyssoftpath@flushcurrentpath%
+  \pgfsys@fill%
+  \pgf@resetpathsizes%
+}
+
+
+
+\def\pgfusepathqfillstroke{%
+  \pgfsyssoftpath@flushcurrentpath%
+  \pgfsys@fillstroke%
+  \pgf@resetpathsizes%
+}
+
+
+\def\pgfusepathqclip{%
+  \pgfsyssoftpath@flushcurrentpath%
+  \pgfsys@clipnext%
+  \pgfsys@discardpath%
+  \pgf@resetpathsizes%
+}
+
+
+\endinput

preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/basiclayer/pgfcorerdf.code.tex

@@ -0,0 +1,83 @@
+
+\ProvidesFileRCS{pgfcorerdf.code.tex}
+
+
+
+
+
+
+
+
+
+\def\pgfrdfabout#1{\pgfsys@rdf@about{#1}}
+
+
+
+
+\def\pgfrdfcontent#1{\pgfsys@rdf@content{#1}}
+
+
+
+
+\def\pgfrdfdatatype#1{\pgfsys@rdf@datatype{#1}}
+
+
+
+
+\def\pgfrdfhref#1{\pgfsys@rdf@href{#1}}
+
+
+
+
+\def\pgfrdfinlist{\pgfsys@rdf@inlist}
+
+
+
+
+
+\def\pgfrdfprefix#1{\pgfsys@rdf@prefix{#1}}
+
+
+
+
+
+\def\pgfrdfproperty#1{\pgfsys@rdf@property{#1}}
+
+
+
+
+\def\pgfrdfrel#1{\pgfsys@rdf@rel{#1}}
+
+
+
+\def\pgfrdfresource#1{\pgfsys@rdf@resource{#1}}
+
+
+
+
+
+\def\pgfrdfrev#1{\pgfsys@rdf@rev{#1}}
+
+
+
+
+
+\def\pgfrdfsrc#1{\pgfsys@rdf@src{#1}}
+
+
+
+
+
+\def\pgfrdftypeof#1{\pgfsys@rdf@typeof{#1}}
+
+
+
+
+
+\def\pgfrdfvocab#1{\pgfsys@rdf@vocab{#1}}
+
+
+
+
+
+\endinput

preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/basiclayer/pgfcorescopes.code.tex

@@ -0,0 +1,496 @@
+
+\ProvidesFileRCS{pgfcorescopes.code.tex}
+
+
+\newbox\pgfpic
+\newbox\pgf@hbox
+
+\newbox\pgf@layerbox@main
+
+\newcount\pgf@picture@serial@count
+
+
+
+\newif\ifpgfrememberpicturepositiononpage
+
+
+
+
+
+
+
+\def\pgfscope{%
+  \pgfsyssoftpath@setcurrentpath\pgfutil@empty%
+  \pgfsys@beginscope%
+    \pgf@resetpathsizes%
+    \edef\pgfscope@linewidth{\the\pgflinewidth}%
+    \let\pgfscope@stroke@color=\pgf@strokecolor@global%
+    \let\pgfscope@fill@color=\pgf@fillcolor@global%
+    \begingroup}
+\def\endpgfscope{%
+    \endgroup%
+    \global\pgflinewidth=\pgfscope@linewidth%
+    \global\let\pgf@strokecolor@global=\pgfscope@stroke@color%
+    \global\let\pgf@fillcolor@global=\pgfscope@fill@color%
+  \pgfsys@endscope}
+
+
+
+
+
+\def\pgfqbox#1{%
+  \pgfsys@hbox#1%
+}
+
+
+
+\def\pgfqboxsynced#1{%
+  \pgfsys@hboxsynced#1%
+}
+
+
+
+\def\pgftext{\pgfutil@ifnextchar[\pgf@text{\pgf@text[]}}%
+\def\pgf@text[#1]{%
+  \def\pgf@text@options{#1}%
+  \pgf@maketext\pgf@after@text}
+\def\pgf@after@text{%
+  {%
+  \def\pgf@text@hshift{center}%
+  \def\pgf@text@vshift{center}%
+  \expandafter\pgf@text@setkeys\expandafter{\pgf@text@options}%
+  \csname pgf@halign\pgf@text@hshift\endcsname%
+  \csname pgf@valign\pgf@text@vshift\endcsname%
+  \pgfapproximatenonlineartransformation%
+  \pgf@process{\pgfpointtransformed{\pgfqpoint{0pt}{\dp\pgf@hbox}}}%
+  \pgf@protocolsizes{\pgf@x}{\pgf@y}%
+  \pgf@process{\pgfpointtransformed{\pgfqpoint{\wd\pgf@hbox}{\dp\pgf@hbox}}}%
+  \pgf@protocolsizes{\pgf@x}{\pgf@y}%
+  \pgf@process{\pgfpointtransformed{\pgfqpoint{0pt}{\ht\pgf@hbox}}}%
+  \pgf@protocolsizes{\pgf@x}{\pgf@y}%
+  \pgf@process{\pgfpointtransformed{\pgfqpoint{\wd\pgf@hbox}{\ht\pgf@hbox}}}%
+  \pgf@protocolsizes{\pgf@x}{\pgf@y}%
+  \pgfqboxsynced{\pgf@hbox}%
+  }%
+}
+\def\pgf@text@setkeys{\pgfqkeys{/pgf/text}}%
+
+\pgfkeys{/pgf/text/left/.code=\def\pgf@text@hshift{left}}
+\pgfkeys{/pgf/text/center/.code=}
+\pgfkeys{/pgf/text/right/.code=\def\pgf@text@hshift{right}}
+\pgfkeys{/pgf/text/top/.code=\def\pgf@text@vshift{top}}
+\pgfkeys{/pgf/text/bottom/.code=\def\pgf@text@vshift{bottom}}
+\pgfkeys{/pgf/text/base/.code=\def\pgf@text@vshift{base}}
+\pgfkeys{/pgf/text/at/.cd,.code=\pgftransformshift{#1},.value required}
+\pgfkeys{/pgf/text/x/.cd,.code=\pgftransformxshift{#1},.value required}
+\pgfkeys{/pgf/text/y/.cd,.code=\pgftransformyshift{#1},.value required}
+\pgfkeys{/pgf/text/rotate/.cd,.code=\pgftransformrotate{#1},.value required}
+
+\def\pgf@halignleft{}%
+\def\pgf@haligncenter{\pgftransformxshift{+-.5\wd\pgf@hbox}}
+\def\pgf@halignright{\pgftransformxshift{+-\wd\pgf@hbox}}%
+\def\pgf@valignbase{}%
+\def\pgf@valignbottom{\pgftransformyshift{+\dp\pgf@hbox}}%
+\def\pgf@valigncenter{\pgftransformyshift{+.5\dp\pgf@hbox}\pgftransformyshift{+-.5\ht\pgf@hbox}}%
+\def\pgf@valigntop{\pgftransformyshift{+-\ht\pgf@hbox}}%
+
+
+\def\pgf@maketext#1{%
+  \def\pgf@@maketextafter{#1}%
+  \setbox\pgf@hbox=\hbox\bgroup%
+    \pgfinterruptpicture%
+      \bgroup%
+        \aftergroup\pgf@collectresetcolor%
+        \let\next=%
+}
+\def\pgf@collectresetcolor{%
+  \pgfutil@ifnextchar\reset@color%
+  {\reset@color\afterassignment\pgf@collectresetcolor\let\pgf@temp=}%
+  {\pgf@textdone}%
+}
+\def\pgf@textdone{%
+    \endpgfinterruptpicture%
+  \egroup%
+  \pgf@@maketextafter%
+}
+
+\long\def\pgf@makehbox#1{%
+  \setbox\pgf@hbox=\hbox{{%
+    \pgfinterruptpicture%
+      #1%
+    \endpgfinterruptpicture%
+    }}}
+
+
+
+
+\def\pgfresetboundingbox{%
+    \global\pgf@picmaxx=-16000pt\relax%
+    \global\pgf@picminx=16000pt\relax%
+    \global\pgf@picmaxy=-16000pt\relax%
+    \global\pgf@picminy=16000pt\relax%
+}%
+
+\def\pgfpicture{%
+  \begingroup%
+    \pgfpicturetrue%
+    \global\advance\pgf@picture@serial@count by1\relax%
+    \edef\pgfpictureid{pgfid\the\pgf@picture@serial@count}%
+    \let\pgf@nodecallback=\pgfutil@gobble%
+    \pgf@picmaxx=-16000pt\relax%
+    \pgf@picminx=16000pt\relax%
+    \pgf@picmaxy=-16000pt\relax%
+    \pgf@picminy=16000pt\relax%
+    \pgf@relevantforpicturesizetrue%
+    \pgf@resetpathsizes%
+    \pgfutil@ifnextchar\bgroup\pgf@oldpicture\pgf@picture}
+\def\pgf@oldpicture#1#2#3#4{%
+  \pgfmathsetlength\pgf@picminx{#1}%
+  \pgfmathsetlength\pgf@picminy{#2}%
+  \pgfmathsetlength\pgf@picmaxx{#3}%
+  \pgfmathsetlength\pgf@picmaxy{#4}%
+  \pgf@relevantforpicturesizefalse%
+  \pgf@picture}
+
+\def\pgf@picture{%
+  \setbox\pgfpic\hbox to0pt\bgroup%
+    \begingroup%
+    \pgfsys@beginpicture%
+      \pgfsys@beginscope%
+        \begingroup%
+        \pgfsetcolor{.}%
+        \pgfsetlinewidth{0.4pt}%
+        \pgftransformreset%
+        \pgfsyssoftpath@setcurrentpath\pgfutil@empty%
+        \begingroup%
+          \let\pgf@setlengthorig=\setlength%
+          \let\pgf@addtolengthorig=\addtolength%
+          \let\pgf@selectfontorig=\selectfont%
+          \let\setlength=\pgf@setlength%
+          \let\addtolength=\pgf@addtolength%
+          \let\selectfont=\pgf@selectfont%
+          \nullfont\spaceskip0pt\xspaceskip0pt%
+          \tracinglostchars=%
+            \ifnum\tracinglostchars>2 2\else\tracinglostchars\fi
+          \setbox\pgf@layerbox@main\hbox to0pt\bgroup%
+            \begingroup%
+  }
+\def\endpgfpicture{%
+              \ifpgfrememberpicturepositiononpage%
+                \hbox to0pt{\pgfsys@markposition{\pgfpictureid}}%
+              \fi%
+              \ifdim\pgf@picmaxx=-16000pt\relax%
+                \global\pgf@picmaxx=0pt\relax%
+                \global\pgf@picminx=0pt\relax%
+                \global\pgf@picmaxy=0pt\relax%
+                \global\pgf@picminy=0pt\relax%
+              \fi%
+              \pgf@relevantforpicturesizefalse%
+              \pgf@process{\pgf@baseline}%
+              \xdef\pgf@shift@baseline{\the\pgf@y}%
+              \pgf@process{\pgf@trimleft}%
+              \global\advance\pgf@x by-\pgf@picminx
+              \xdef\pgf@trimleft@final{-\the\pgf@x}%
+              \pgf@process{\pgf@trimright}%
+              \global\advance\pgf@x by-\pgf@picmaxx
+              \xdef\pgf@trimright@final{\the\pgf@x}%
+        \pgf@remember@layerlist@globally
+            \endgroup%
+            \hss%
+          \egroup%
+      \pgf@restore@layerlist@from@global
+          \pgf@insertlayers%
+        \endgroup%
+        \pgfsys@discardpath%
+        \endgroup%
+      \pgfsys@endscope%
+    \pgfsys@endpicture%
+    \endgroup%
+    \hss
+  \egroup%
+  \pgfsys@typesetpicturebox\pgfpic%
+  \endgroup%
+}
+
+\def\pgf@remember@layerlist@globally{%
+  \global\let\pgf@layerlist@=\pgf@layerlist
+}%
+\def\pgf@restore@layerlist@from@global{%
+  \let\pgf@layerlist=\pgf@layerlist@
+}%
+\def\pgf@insertlayers{%
+  \box\pgf@layerbox@main%
+}
+
+\def\pgf@selectfont{\pgf@selectfontorig\nullfont}
+
+\def\pgf@setlength#1#2{%
+  \begingroup%
+    \pgfutil@selectfont%
+    \pgf@setlengthorig#1{#2}%
+    \expandafter%
+  \endgroup%
+  \expandafter#1\expandafter=\the#1\relax}
+\def\pgf@addtolength#1#2{%
+  \begingroup%
+    \pgfutil@selectfont%
+    \pgf@addtolengthorig#1{#2}%
+    \expandafter%
+  \endgroup%
+  \expandafter#1\expandafter=\the#1\relax}
+
+
+
+\def\pgfsetbaselinepointlater#1{\def\pgf@baseline{#1}}
+
+
+
+\def\pgfsetbaselinepointnow#1{%
+  \pgf@process{#1}%
+  \edef\pgf@setter@baseline{\noexpand\pgfpoint{\the\pgf@x}{\the\pgf@y}}%
+  \pgfsetbaselinepointlater{\pgf@setter@baseline}%
+}
+
+\def\pgf@default@text{default}%
+
+
+\def\pgfsetbaseline#1{%
+  \def\pgf@temp{#1}%
+  \ifx\pgf@temp\pgf@default@text
+    \pgfsetbaseline{\pgf@picminy}%
+  \else
+    \pgfsetbaselinepointlater{\pgfpoint{0pt}{#1}}%
+  \fi
+}
+\pgfsetbaseline{\pgf@picminy}
+
+\newif\ifpgf@trim@lowlevel
+\pgfkeys{
+  /pgf/trim lowlevel/.is if=pgf@trim@lowlevel,
+  /pgf/trim lowlevel/.default=true,
+}
+
+\def\pgfsettrimleftpointlater#1{\def\pgf@trimleft{#1}}
+\def\pgfsettrimleftpointnow#1{%
+  \pgf@process{#1}%
+  \edef\pgf@setter@baseline{\noexpand\pgfpoint{\the\pgf@x}{\the\pgf@y}}%
+  \pgfsettrimleftpointlater{\pgf@setter@baseline}%
+}
+\def\pgfsettrimleft#1{%
+  \def\pgf@temp{#1}%
+  \ifx\pgf@temp\pgf@default@text
+    \pgfsettrimleft{\pgf@picminx}
+  \else
+    \pgfsettrimleftpointlater{\pgfpoint{#1}{0pt}}%
+  \fi
+}
+\pgfsettrimleft{\pgf@picminx}
+
+\def\pgfsettrimrightpointlater#1{\def\pgf@trimright{#1}}
+\def\pgfsettrimrightpointnow#1{%
+  \pgf@process{#1}%
+  \edef\pgf@setter@baseline{\noexpand\pgfpoint{\the\pgf@x}{\the\pgf@y}}%
+  \pgfsettrimrightpointlater{\pgf@setter@baseline}%
+}
+\def\pgfsettrimright#1{%
+  \def\pgf@temp{#1}%
+  \ifx\pgf@temp\pgf@default@text
+    \pgfsettrimright{\pgf@picmaxx}%
+  \else
+    \pgfsettrimrightpointlater{\pgfpoint{#1}{0pt}}%
+  \fi
+}
+\pgfsettrimright{\pgf@picmaxx}
+
+
+
+\def\pgfinterruptpath
+{%
+  \begingroup%
+  \edef\pgf@interrupt@savex{\the\pgf@path@lastx}%
+  \edef\pgf@interrupt@savey{\the\pgf@path@lasty}%
+  \pgf@getpathsizes\pgf@interrupt@pathsizes%
+  \pgfsyssoftpath@getcurrentpath\pgf@interrupt@path%
+  \pgfsyssoftpath@setcurrentpath\pgfutil@empty%
+  \let\pgf@interrupt@lastmoveto=\pgfsyssoftpath@lastmoveto%
+  \begingroup%
+}
+\def\endpgfinterruptpath
+{%
+  \endgroup%
+  \pgfsyssoftpath@setcurrentpath\pgf@interrupt@path%
+  \pgf@setpathsizes\pgf@interrupt@pathsizes%
+  \global\pgf@path@lastx\pgf@interrupt@savex%
+  \global\pgf@path@lasty\pgf@interrupt@savey%
+  \global\let\pgfsyssoftpath@lastmoveto\pgf@interrupt@lastmoveto%
+  \endgroup%
+}
+
+
+
+
+\def\pgfinterruptboundingbox
+{%
+  \begingroup%
+    \edef\pgf@interrupt@savemaxx{\the\pgf@picmaxx}%
+    \edef\pgf@interrupt@saveminx{\the\pgf@picminx}%
+    \edef\pgf@interrupt@savemaxy{\the\pgf@picmaxy}%
+    \edef\pgf@interrupt@saveminy{\the\pgf@picminy}%
+    \pgf@picmaxx=-16000pt\relax%
+    \pgf@picminx=16000pt\relax%
+    \pgf@picmaxy=-16000pt\relax%
+    \pgf@picminy=16000pt\relax%
+    \pgf@size@hookedfalse%
+    \let\pgf@path@size@hook=\pgfutil@empty%
+}
+\def\endpgfinterruptboundingbox
+{%
+    \global\pgf@picmaxx=\pgf@interrupt@savemaxx%
+    \global\pgf@picmaxy=\pgf@interrupt@savemaxy%
+    \global\pgf@picminx=\pgf@interrupt@saveminx%
+    \global\pgf@picminy=\pgf@interrupt@saveminy%
+  \endgroup%
+}
+
+
+
+
+
+\def\pgfidscope{\pgfsys@begin@idscope}
+\def\endpgfidscope{\pgfsys@end@idscope}
+
+\let\startpgfidscope\pgfidscope
+\let\stoppgfidscope\pgfendidscope
+
+
+
+
+
+\def\pgfuseid#1{%
+  \edef\pgf@temp{#1}%
+  \ifx\pgf@temp\pgfutil@empty%
+  \else%
+    \pgf@lookup@id{#1}%
+    \pgfsys@use@id{\pgf@next@id}%
+    \expandafter\xdef\csname pgf@id@names@#1\endcsname{{\pgf@next@id}{}}%
+  \fi%
+}
+
+\def\pgf@lookup@id#1{%
+  \expandafter\let\expandafter\pgf@id@name\csname pgf@id@names@#1\endcsname%
+  \ifx\pgf@id@name\relax%
+    \let\pgf@prev@id\pgfutil@empty%
+    \let\pgf@next@id\pgfutil@empty%
+  \else%
+    \expandafter\pgf@id@parse\pgf@id@name%
+  \fi%
+  \ifx\pgf@next@id\pgfutil@empty%
+    \pgfsys@new@id\pgf@next@id%
+    \expandafter\xdef\csname pgf@id@names@#1\endcsname{{\pgf@prev@id}{\pgf@next@id}}%
+  \fi%
+}
+\def\pgf@id@parse#1#2{%
+  \def\pgf@prev@id{#1}%
+  \def\pgf@next@id{#2}%
+}
+
+
+
+
+\def\pgfclearid{%
+  \pgfsys@clear@id%
+}
+
+
+
+\def\pgfidrefnextuse#1#2{%
+  \edef\pgf@temp{#2}\ifx\pgf@temp\pgfutil@empty\pgferror{Missing name reference for ``\string#1''}\fi%
+  \pgf@lookup@id{#2}%
+  \let#1\pgf@next@id%
+}
+
+
+
+\def\pgfidrefprevuse#1#2{%
+  \edef\pgf@temp{#2}\ifx\pgf@temp\pgfutil@empty\pgferror{Missing name reference for ``\string#1''}\fi%
+  \pgf@lookup@id{#2}%
+  \let#1\pgf@prev@id%
+}
+
+
+
+\def\pgfusetype#1{%
+  \edef\pgf@temp{#1}%
+  \expandafter\pgfutil@ifnextchar\expandafter.\expandafter\pgf@id@use@type@add\expandafter\pgf@id@use@type@replace\pgf@temp\pgf@stop
+}
+\def\pgf@id@use@type@add.#1\pgf@stop{\pgfsys@append@type{#1}}
+\def\pgf@id@use@type@replace#1\pgf@stop{\pgfsys@use@type{#1}}
+
+
+\def\pgfpushtype{\pgfsys@push@type}
+
+
+
+\def\pgfpoptype{\pgfsys@pop@type}
+
+
+
+
+
+\def\pgfaliasid#1#2{%
+  \expandafter\let\expandafter\pgf@temp\csname pgf@id@names@#2\endcsname%
+  \expandafter\let\csname pgf@id@names@#1\endcsname\pgf@temp%
+}
+\def\pgfgaliasid#1#2{%
+  \expandafter\let\expandafter\pgf@temp\csname pgf@id@names@#2\endcsname%
+  \expandafter\global\expandafter\let\csname pgf@id@names@#1\endcsname\pgf@temp%
+}
+
+
+
+\def\pgfifidreferenced#1#2#3{%
+  \expandafter\let\expandafter\pgf@id@name\csname pgf@id@names@#1\endcsname%
+  \ifx\pgf@id@name\relax%
+    #3%
+  \else
+    \expandafter\pgf@id@parse\pgf@id@name%
+    \ifx\pgf@next@id\pgfutil@empty%
+      #3%
+    \else%
+      #2%
+    \fi%
+  \fi%
+}
+
+
+
+\def\pgfinterruptpicture
+{%
+  \begingroup%
+    \csname tikz@inside@picturefalse\endcsname%
+    \pgfinterruptboundingbox%
+      \pgftransformreset%
+      \pgfinterruptpath%
+        \ifx\pgf@selectfontorig\@undefined%
+        \else%
+          \let\setlength\pgf@setlengthorig%
+          \let\addtolength\pgf@addtolengthorig%
+          \let\selectfont\pgf@selectfontorig%
+        \fi%
+        \pgfutil@selectfont%
+        \pgfpicturefalse%
+        \let\pgf@positionnodelater@macro\relax%
+        \pgf@savelayers%
+}
+\def\endpgfinterruptpicture
+{%
+        \pgf@restorelayers%
+      \endpgfinterruptpath%
+    \endpgfinterruptboundingbox%
+  \endgroup%
+}
+
+\let\pgf@savelayers=\relax
+\let\pgf@restorelayers=\relax
+
+\endinput

preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/basiclayer/pgfcoreshade.code.tex

@@ -0,0 +1,700 @@
+
+\ProvidesFileRCS{pgfcoreshade.code.tex}
+
+\newdimen\pgf@max
+\newcount\pgf@sys@shading@range@num
+\def\pgf@parsefunc#1{%
+  \edef\temp{{#1}}%
+  \expandafter\pgf@convertstring\temp%
+  \edef\temp{{\pgf@conv}}%
+  \expandafter\pgf@@parsefunc\temp}
+\def\pgf@@parsefunc#1{%
+  \let\pgf@bounds=\pgfutil@empty%
+  \let\pgf@funcs=\pgfutil@empty%
+  \let\pgf@psfuncs=\pgfutil@empty%
+  \let\pgf@encode=\pgfutil@empty%
+  \let\pgf@sys@shading@ranges=\pgfutil@empty%
+  \pgf@sys@shading@range@num=0\relax%
+  \csname pgf@parsefirst\pgf@shading@model\endcsname[#1; ]%
+  \csname pgf@parselastdom\pgf@shading@model\endcsname[#1; ]%
+  \csname pgf@parsemid\pgf@shading@model\endcsname[#1; ]%
+  \ifx\pgf@bounds\pgfutil@empty%
+    \edef\pgf@pdfparseddomain{0 1}%
+    \edef\pgf@pdfparsedfunction{\pgf@singlefunc\space}%
+  \else%
+    \edef\pgf@pdfparseddomain{\pgf@doma\space\pgf@domb}%
+    \edef\pgf@pdfparsedfunction{%
+      << /FunctionType 3 /Domain [\pgf@doma\space\pgf@domb] /Functions
+      [\pgf@funcs\space] /Bounds [\pgf@bounds] /Encode [0 1 \pgf@encode]
+      >> }%
+  \fi%
+  \xdef\pgf@psfuncs{\pgf@psfuncs}%
+  }
+\def\pgf@parsefirstrgb[rgb(#1)=(#2,#3,#4)#5]{%
+  \pgfmathsetlength\pgf@x{#1}%
+  \edef\pgf@sys@shading@start@pos{\the\pgf@x}%
+  \pgf@sys@bp@correct\pgf@x%
+  \edef\pgf@doma{\pgf@sys@tonumber{\pgf@x}}%
+  \edef\pgf@prevx{\pgf@sys@tonumber{\pgf@x}}%
+  \pgf@getrgbtuplewithmixin{#2}{#3}{#4}%
+  \edef\pgf@sys@shading@start@rgb{\pgf@sys@rgb}%
+  \let\pgf@sys@prevcolor=\pgf@sys@shading@start@rgb%
+  \let\pgf@sys@prevpos=\pgf@sys@shading@start@pos%
+  \edef\pgf@prevcolor{\pgf@rgb}%
+  \edef\pgf@firstcolor{\pgf@rgb}}
+\def\pgf@parselastdomrgb[rgb(#1)=(#2,#3,#4); {%
+  \pgfutil@ifnextchar]{%
+    \pgfmathsetlength\pgf@x{#1}%
+    \edef\pgf@sys@shading@end@pos{\the\pgf@x}%
+    \pgf@max=\pgf@x\relax%
+    \pgf@sys@bp@correct\pgf@x%
+    \edef\pgf@domb{\pgf@sys@tonumber{\pgf@x}}%
+    \pgf@getrgbtuplewithmixin{#2}{#3}{#4}%
+    \edef\pgf@sys@shading@end@rgb{\pgf@sys@rgb}%
+    \pgfutil@gobble}{\pgf@parselastdomrgb[}}
+\def\pgf@parsemidrgb[rgb(#1)=(#2,#3,#4); {\pgf@parserestrgb[}
+\def\pgf@parserestrgb[rgb(#1)=(#2,#3,#4); {%
+  \advance\pgf@sys@shading@range@num by1\relax%
+  \pgfutil@ifnextchar]{%
+    \pgf@getrgbtuplewithmixin{#2}{#3}{#4}%
+    \edef\pgf@singlefunc{\space%
+      << /FunctionType 2 /Domain [0 1] /C0
+      [\pgf@prevcolor] /C1 [\pgf@rgb] /N 1 >> }%
+    \edef\pgf@funcs{\pgf@funcs\space%
+      << /FunctionType 2 /Domain [\pgf@doma\space\pgf@domb] /C0
+      [\pgf@prevcolor] /C1 [\pgf@rgb] /N 1 >> }%
+    \edef\pgf@psfuncs{\pgf@prevx\space \pgf@rgb\space \pgf@prevcolor\space pgfshade \pgf@psfuncs}%
+    \pgfmathsetlength\pgf@x{#1}%
+    \edef\pgf@sys@shading@ranges{\pgf@sys@shading@ranges{{\pgf@sys@prevpos}{\the\pgf@x}{\pgf@sys@prevcolor}{\pgf@sys@rgb}}}%
+    \edef\pgf@sys@prevpos{\the\pgf@x}%
+    \let\pgf@sys@prevcolor=\pgf@sys@rgb%
+    \pgfutil@gobble}{%
+    \pgfmathsetlength\pgf@x{#1}%
+    \pgf@getrgbtuplewithmixin{#2}{#3}{#4}%
+    \edef\pgf@sys@shading@ranges{\pgf@sys@shading@ranges{{\pgf@sys@prevpos}{\the\pgf@x}{\pgf@sys@prevcolor}{\pgf@sys@rgb}}}%
+    \edef\pgf@sys@prevpos{\the\pgf@x}%
+    \let\pgf@sys@prevcolor=\pgf@sys@rgb%
+    \edef\pgf@psfuncs{\pgf@prevx\space \pgf@rgb\space \pgf@prevcolor\space pgfshade \pgf@psfuncs}%
+    \pgf@sys@bp@correct\pgf@x%
+    \edef\pgf@prevx{\pgf@sys@tonumber{\pgf@x}}%
+    \edef\pgf@bounds{\pgf@bounds\space\pgf@sys@tonumber{\pgf@x}}%
+    \edef\pgf@encode{\pgf@encode\space0 1}%
+    \edef\pgf@singlefunc{\space%
+      << /FunctionType 2 /Domain [0 1] /C0
+      [\pgf@prevcolor] /C1 [\pgf@rgb] /N 1 >> }%
+    \edef\pgf@funcs{\pgf@funcs\space%
+      << /FunctionType 2 /Domain [\pgf@doma\space\pgf@domb] /C0
+      [\pgf@prevcolor] /C1 [\pgf@rgb] /N 1 >> }%
+    \edef\pgf@prevcolor{\pgf@rgb}%
+    \pgf@parserestrgb[}}
+
+\def\pgf@getrgbtuplewithmixin#1#2#3{%
+  \pgfutil@definecolor{pgfshadetemp}{rgb}{#1,#2,#3}%
+  \pgfutil@ifundefined{applycolormixins}{}{\applycolormixins{pgfshadetemp}}%
+  \pgfutil@extractcolorspec{pgfshadetemp}{\pgf@tempcolor}%
+  \expandafter\pgfutil@convertcolorspec\pgf@tempcolor{rgb}{\pgf@rgbcolor}%
+  \expandafter\pgf@getrgb@@\pgf@rgbcolor!}
+\def\pgf@getrgb@@#1,#2,#3!{%
+  \def\pgf@rgb{#1 #2 #3}%
+  \def\pgf@sys@rgb{{#1}{#2}{#3}}%
+}
+
+\def\pgf@parsefirstcmyk[cmyk(#1)=(#2,#3,#4,#5)#6]{%
+  \pgfmathsetlength\pgf@x{#1}%
+  \edef\pgf@sys@shading@start@pos{\the\pgf@x}%
+  \pgf@sys@bp@correct\pgf@x%
+  \edef\pgf@doma{\pgf@sys@tonumber{\pgf@x}}%
+  \edef\pgf@prevx{\pgf@sys@tonumber{\pgf@x}}%
+  \pgf@getcmyktuplewithmixin{#2}{#3}{#4}{#5}%
+  \edef\pgf@sys@shading@start@cmyk{\pgf@sys@cmyk}%
+  \let\pgf@sys@prevcolor=\pgf@sys@shading@start@cmyk%
+  \let\pgf@sys@prevpos=\pgf@sys@shading@start@pos%
+  \edef\pgf@prevcolor{\pgf@cmyk}%
+  \edef\pgf@firstcolor{\pgf@cmyk}}
+\def\pgf@parselastdomcmyk[cmyk(#1)=(#2,#3,#4,#5); {%
+  \pgfutil@ifnextchar]{%
+    \pgfmathsetlength\pgf@x{#1}%
+    \edef\pgf@sys@shading@end@pos{\the\pgf@x}%
+    \pgf@max=\pgf@x\relax%
+    \pgf@sys@bp@correct\pgf@x%
+    \edef\pgf@domb{\pgf@sys@tonumber{\pgf@x}}%
+    \pgf@getcmyktuplewithmixin{#2}{#3}{#4}{#5}%
+    \edef\pgf@sys@shading@end@cmyk{\pgf@sys@cmyk}%
+    \pgfutil@gobble}{\pgf@parselastdomcmyk[}}
+\def\pgf@parsemidcmyk[cmyk(#1)=(#2,#3,#4,#5); {\pgf@parserestcmyk[}
+\def\pgf@parserestcmyk[cmyk(#1)=(#2,#3,#4,#5); {%
+  \advance\pgf@sys@shading@range@num by1\relax%
+  \pgfutil@ifnextchar]{%
+    \pgf@getcmyktuplewithmixin{#2}{#3}{#4}{#5}%
+    \edef\pgf@singlefunc{\space%
+      << /FunctionType 2 /Domain [0 1] /C0
+      [\pgf@prevcolor] /C1 [\pgf@cmyk] /N 1 >> }%
+    \edef\pgf@funcs{\pgf@funcs\space%
+      << /FunctionType 2 /Domain [\pgf@doma\space\pgf@domb] /C0
+      [\pgf@prevcolor] /C1 [\pgf@cmyk] /N 1 >> }%
+    \edef\pgf@psfuncs{\pgf@prevx\space
+      \pgf@cmyk\space \pgf@prevcolor\space pgfshade \pgf@psfuncs}%
+    \pgfmathsetlength\pgf@x{#1}%
+    \edef\pgf@sys@shading@ranges{\pgf@sys@shading@ranges{%
+      {\pgf@sys@prevpos}{\the\pgf@x}{\pgf@sys@prevcolor}{\pgf@sys@cmyk}}}%
+    \edef\pgf@sys@prevpos{\the\pgf@x}%
+    \let\pgf@sys@prevcolor=\pgf@sys@cmyk%
+    \pgfutil@gobble}{%
+    \pgfmathsetlength\pgf@x{#1}%
+    \pgf@getcmyktuplewithmixin{#2}{#3}{#4}{#5}%
+    \edef\pgf@sys@shading@ranges{\pgf@sys@shading@ranges{%
+      {\pgf@sys@prevpos}{\the\pgf@x}{\pgf@sys@prevcolor}{\pgf@sys@cmyk}}}%
+    \edef\pgf@sys@prevpos{\the\pgf@x}%
+    \let\pgf@sys@prevcolor=\pgf@sys@cmyk%
+    \edef\pgf@psfuncs{\pgf@prevx\space \pgf@cmyk\space
+      \pgf@prevcolor\space pgfshade \pgf@psfuncs}%
+    \pgf@sys@bp@correct\pgf@x%
+    \edef\pgf@prevx{\pgf@sys@tonumber{\pgf@x}}%
+    \edef\pgf@bounds{\pgf@bounds\space\pgf@sys@tonumber{\pgf@x}}%
+    \edef\pgf@encode{\pgf@encode\space0 1}%
+    \edef\pgf@singlefunc{\space%
+      << /FunctionType 2 /Domain [0 1] /C0
+      [\pgf@prevcolor] /C1 [\pgf@cmyk] /N 1 >> }%
+    \edef\pgf@funcs{\pgf@funcs\space%
+      << /FunctionType 2 /Domain [\pgf@doma\space\pgf@domb] /C0
+      [\pgf@prevcolor] /C1 [\pgf@cmyk] /N 1 >> }%
+    \edef\pgf@prevcolor{\pgf@cmyk}%
+    \pgf@parserestcmyk[}}
+
+\def\pgf@getcmyktuplewithmixin#1#2#3#4{%
+  \pgfutil@definecolor{pgfshadetemp}{cmyk}{#1,#2,#3,#4}%
+  \pgfutil@ifundefined{applycolormixins}{}{\applycolormixins{pgfshadetemp}}%
+  \pgfutil@extractcolorspec{pgfshadetemp}{\pgf@tempcolor}%
+  \expandafter\pgfutil@convertcolorspec\pgf@tempcolor{cmyk}{\pgf@cmykcolor}%
+  \expandafter\pgf@getcmyk@@\pgf@cmykcolor!}
+\def\pgf@getcmyk@@#1,#2,#3,#4!{%
+  \def\pgf@cmyk{#1 #2 #3 #4}%
+  \def\pgf@sys@cmyk{{#1}{#2}{#3}{#4}}%
+}
+
+\def\pgf@parsefirstgray[gray(#1)=(#2)#3]{%
+  \pgfmathsetlength\pgf@x{#1}%
+  \edef\pgf@sys@shading@start@pos{\the\pgf@x}%
+  \pgf@sys@bp@correct\pgf@x%
+  \edef\pgf@doma{\pgf@sys@tonumber{\pgf@x}}%
+  \edef\pgf@prevx{\pgf@sys@tonumber{\pgf@x}}%
+  \pgf@getgraytuplewithmixin{#2}%
+  \edef\pgf@sys@shading@start@gray{\pgf@sys@gray}%
+  \let\pgf@sys@prevcolor=\pgf@sys@shading@start@gray%
+  \let\pgf@sys@prevpos=\pgf@sys@shading@start@pos%
+  \edef\pgf@prevcolor{\pgf@gray}%
+  \edef\pgf@firstcolor{\pgf@gray}}
+\def\pgf@parselastdomgray[gray(#1)=(#2); {%
+  \pgfutil@ifnextchar]{%
+    \pgfmathsetlength\pgf@x{#1}%
+    \edef\pgf@sys@shading@end@pos{\the\pgf@x}%
+    \pgf@max=\pgf@x\relax%
+    \pgf@sys@bp@correct\pgf@x%
+    \edef\pgf@domb{\pgf@sys@tonumber{\pgf@x}}%
+    \pgf@getgraytuplewithmixin{#2}%
+    \edef\pgf@sys@shading@end@gray{\pgf@sys@gray}%
+    \pgfutil@gobble}{\pgf@parselastdomgray[}}
+\def\pgf@parsemidgray[gray(#1)=(#2); {\pgf@parserestgray[}
+\def\pgf@parserestgray[gray(#1)=(#2); {%
+  \advance\pgf@sys@shading@range@num by1\relax%
+  \pgfutil@ifnextchar]{%
+    \pgf@getgraytuplewithmixin{#2}%
+    \edef\pgf@singlefunc{\space%
+      << /FunctionType 2 /Domain [0 1] /C0
+      [\pgf@prevcolor] /C1 [\pgf@gray] /N 1 >> }%
+    \edef\pgf@funcs{\pgf@funcs\space%
+      << /FunctionType 2 /Domain [\pgf@doma\space\pgf@domb] /C0
+      [\pgf@prevcolor] /C1 [\pgf@gray] /N 1 >> }%
+    \edef\pgf@psfuncs{\pgf@prevx\space \pgf@gray\space
+      \pgf@prevcolor\space pgfshade \pgf@psfuncs}%
+    \pgfmathsetlength\pgf@x{#1}%
+    \edef\pgf@sys@shading@ranges{\pgf@sys@shading@ranges{%
+      {\pgf@sys@prevpos}{\the\pgf@x}{\pgf@sys@prevcolor}{\pgf@sys@gray}}}%
+    \edef\pgf@sys@prevpos{\the\pgf@x}%
+    \let\pgf@sys@prevcolor=\pgf@sys@gray%
+    \pgfutil@gobble}{%
+    \pgfmathsetlength\pgf@x{#1}%
+    \pgf@getgraytuplewithmixin{#2}%
+    \edef\pgf@sys@shading@ranges{\pgf@sys@shading@ranges{%
+      {\pgf@sys@prevpos}{\the\pgf@x}{\pgf@sys@prevcolor}{\pgf@sys@gray}}}%
+    \edef\pgf@sys@prevpos{\the\pgf@x}%
+    \let\pgf@sys@prevcolor=\pgf@sys@gray%
+    \edef\pgf@psfuncs{\pgf@prevx\space \pgf@gray\space
+      \pgf@prevcolor\space pgfshade \pgf@psfuncs}%
+    \pgf@sys@bp@correct\pgf@x%
+    \edef\pgf@prevx{\pgf@sys@tonumber{\pgf@x}}%
+    \edef\pgf@bounds{\pgf@bounds\space\pgf@sys@tonumber{\pgf@x}}%
+    \edef\pgf@encode{\pgf@encode\space0 1}%
+    \edef\pgf@singlefunc{\space%
+      << /FunctionType 2 /Domain [0 1] /C0
+      [\pgf@prevcolor] /C1 [\pgf@gray] /N 1 >> }%
+    \edef\pgf@funcs{\pgf@funcs\space%
+      << /FunctionType 2 /Domain [\pgf@doma\space\pgf@domb] /C0
+      [\pgf@prevcolor] /C1 [\pgf@gray] /N 1 >> }%
+    \edef\pgf@prevcolor{\pgf@gray}%
+    \pgf@parserestgray[}}
+
+\def\pgf@getgraytuplewithmixin#1{%
+  \pgfutil@definecolor{pgfshadetemp}{gray}{#1}%
+  \pgfutil@ifundefined{applycolormixins}{}{\applycolormixins{pgfshadetemp}}%
+  \pgfutil@extractcolorspec{pgfshadetemp}{\pgf@tempcolor}%
+  \expandafter\pgfutil@convertcolorspec\pgf@tempcolor{gray}{\pgf@graycolor}%
+  \expandafter\pgf@getgray@@\pgf@graycolor!}
+\def\pgf@getgray@@#1!{%
+  \def\pgf@gray{#1}%
+  \def\pgf@sys@gray{{#1}}%
+}
+
+\def\pgf@convertstring#1{%
+  \def\pgf@conv{}%
+  \pgf@convert#1]%
+  }
+\def\pgf@convert{%
+  \pgfutil@ifnextchar]{\pgfutil@gobble}%
+  {%
+    \pgfutil@ifnextchar;{\pgf@grabsemicolor}%
+    {%
+      \pgfutil@ifnextchar c{\pgf@gobblec}%
+      {%
+        \pgfutil@ifnextchar g{\pgf@grabgray}%
+        {%
+          \pgfutil@ifnextchar o{\pgf@grabcolor}%
+          {%
+            \pgfutil@ifnextchar m{\pgf@grabcmyk}%
+            {%
+              \pgfutil@ifnextchar r{\pgf@grabrgb}%
+                {\pgferror{Illformed shading
+                 specification}\pgf@convert}%
+            }%
+          }%
+        }%
+      }%
+    }%
+  }%
+}
+\def\pgf@savecolor#1{%
+  \pgfutil@extractcolorspec{pgf@tempcol}{\pgf@tempcolor}%
+  \expandafter\pgfutil@convertcolorspec\pgf@tempcolor
+    {\pgf@shading@model}{\pgf@color}%
+  \expandafter\pgf@convget@\expandafter{\pgf@color}{#1}%
+}
+\def\pgf@grabsemicolor;{%
+  \edef\pgf@conv{\pgf@conv; }\pgf@convert}
+\def\pgf@gobblec c{\pgf@convert}
+\def\pgf@grabrgb rgb(#1)=(#2,#3,#4){%
+  \pgfutil@definecolor{pgf@tempcol}{rgb}{#2,#3,#4}%
+  \pgf@savecolor{#1}%
+}
+\def\pgf@grabcmyk myk(#1)=(#2,#3,#4,#5){%
+  \pgfutil@definecolor{pgf@tempcol}{cmyk}{#2,#3,#4,#5}%
+  \pgf@savecolor{#1}%
+}
+\def\pgf@grabgray gray(#1)=(#2){%
+  \pgfutil@definecolor{pgf@tempcol}{gray}{#2}%
+  \pgf@savecolor{#1}%
+}
+\def\pgf@grabcolor olor(#1)=(#2){%
+  \pgfutil@colorlet{pgf@tempcol}{#2}%
+  \pgf@savecolor{#1}%
+}
+\def\pgf@convget@#1#2{%
+  \edef\pgf@conv{\pgf@conv \pgf@shading@model(#2)=(#1)}\pgf@convert}
+
+
+\newcount\pgf@shadingcount
+\pgf@shadingcount=0
+{
+  \catcode`\/=0
+  \catcode`\\=12
+  /gdef/pgf@shadingnum{\/the/pgf@shadingcount\}
+}
+
+
+\newif\ifpgfshadingmodelrgb
+\newif\ifpgfshadingmodelcmyk
+\newif\ifpgfshadingmodelgray
+\def\pgf@setup@shading@model{%
+  \pgfshadingmodelrgbtrue
+  \pgfshadingmodelcmykfalse
+  \pgfshadingmodelgrayfalse
+  \XC@sdef\pgf@mod@test{\XC@tgt@mod{natural}}%
+  \def\pgf@shading@device{/DeviceRGB}%
+  \def\pgf@shading@ps@device{setrgbcolor}%
+  \def\pgf@shading@functional@range{0 1 0 1 0 1}%
+  \def\pgf@shading@model{rgb}%
+  \ifx\pgf@mod@test\XC@mod@cmyk
+    \def\pgf@shading@device{/DeviceCMYK}%
+    \def\pgf@shading@ps@device{setcmykcolor}%
+    \def\pgf@shading@functional@range{0 1 0 1 0 1 0 1}%
+    \def\pgf@shading@model{cmyk}%
+    \pgfshadingmodelrgbfalse
+    \pgfshadingmodelcmyktrue
+  \fi
+  \ifx\pgf@mod@test\XC@mod@gray
+    \def\pgf@shading@device{/DeviceGray}%
+    \def\pgf@shading@ps@device{setgray}%
+    \def\pgf@shading@functional@range{0 1}%
+    \def\pgf@shading@model{gray}%
+    \pgfshadingmodelrgbfalse
+    \pgfshadingmodelgraytrue
+  \fi
+  \edef\pgf@sys@driver@dvisvgm{pgfsys-dvisvgm.def}%
+  \ifx\pgfsysdriver\pgf@sys@driver@dvisvgm
+    \def\pgf@shading@model{rgb}%
+  \fi
+  \edef\pgf@sys@driver@texforht{pgfsys-tex4ht.def}%
+  \ifx\pgfsysdriver\pgf@sys@driver@texforht
+    \def\pgf@shading@model{rgb}%
+  \fi
+}
+
+
+
+\def\pgfdeclarehorizontalshading{%
+  \pgf@setup@shading@model
+  \pgfutil@ifnextchar[%
+    \pgf@declarehorizontalshading{\pgf@declarehorizontalshading[]}}
+\def\pgf@declarehorizontalshading[#1]#2#3#4{%
+  \expandafter\def\csname pgf@deps@pgfshading#2!\endcsname{#1}%
+  \expandafter\ifx\csname pgf@deps@pgfshading#2!\endcsname\pgfutil@empty%
+    \global\expandafter\let\csname pgf@num@pgfshading#2!\endcsname\pgfutil@empty
+    \pgfsys@horishading{#2}{#3}{#4}%
+  \else%
+    \global\advance\pgf@shadingcount 1\relax
+    \global\expandafter\edef\csname pgf@num@pgfshading#2!\endcsname{\pgf@shadingnum}%
+    \expandafter\def\csname pgf@func@pgfshading#2!\endcsname{\pgfsys@horishading}%
+    \expandafter\def\csname pgf@args@pgfshading#2!\endcsname{{#3}{#4}}%
+    \expandafter\let\csname @pgfshading#2!\endcsname=\pgfutil@empty%
+  \fi}
+
+
+
+\def\pgfdeclareverticalshading{%
+  \pgf@setup@shading@model
+  \pgfutil@ifnextchar[%
+    \pgf@declareverticalshading{\pgf@declareverticalshading[]}}
+\def\pgf@declareverticalshading[#1]#2#3#4{%
+  \expandafter\def\csname pgf@deps@pgfshading#2!\endcsname{#1}%
+  \expandafter\ifx\csname pgf@deps@pgfshading#2!\endcsname\pgfutil@empty%
+    \global\expandafter\let\csname pgf@num@pgfshading#2!\endcsname=\pgfutil@empty
+    \pgfsys@vertshading{#2}{#3}{#4}%
+  \else%
+    \global\advance\pgf@shadingcount 1\relax
+    \global\expandafter\edef\csname pgf@num@pgfshading#2!\endcsname{\pgf@shadingnum}%
+    \expandafter\def\csname pgf@func@pgfshading#2!\endcsname{\pgfsys@vertshading}%
+    \expandafter\def\csname pgf@args@pgfshading#2!\endcsname{{#3}{#4}}%
+    \expandafter\let\csname @pgfshading#2!\endcsname=\pgfutil@empty%
+  \fi}
+
+
+
+\def\pgfdeclareradialshading{%
+  \pgf@setup@shading@model
+  \pgfutil@ifnextchar[%
+    \pgf@declareradialshading{\pgf@declareradialshading[]}}
+\def\pgf@declareradialshading[#1]#2#3#4{%
+  \expandafter\def\csname pgf@deps@pgfshading#2!\endcsname{#1}%
+  \expandafter\ifx\csname pgf@deps@pgfshading#2!\endcsname\pgfutil@empty%
+    \global\expandafter\let\csname pgf@num@pgfshading#2!\endcsname=\pgfutil@empty
+    \pgfsys@radialshading{#2}{#3}{#4}%
+  \else%
+    \global\advance\pgf@shadingcount 1\relax
+    \global\expandafter\edef\csname pgf@num@pgfshading#2!\endcsname{\pgf@shadingnum}%
+    \expandafter\def\csname pgf@func@pgfshading#2!\endcsname{\pgfsys@radialshading}%
+    \expandafter\def\csname pgf@args@pgfshading#2!\endcsname{{#3}{#4}}%
+    \expandafter\let\csname @pgfshading#2!\endcsname=\pgfutil@empty%
+  \fi}
+
+
+
+
+
+\def\pgfdeclarefunctionalshading{%
+  \pgf@setup@shading@model
+  \pgfutil@ifnextchar[%
+    \pgf@declarefunctionalshading{\pgf@declarefunctionalshading[]}}
+\def\pgf@declarefunctionalshading[#1]#2#3#4#5#6{%
+  \expandafter\def\csname pgf@deps@pgfshading#2!\endcsname{#1}%
+  \expandafter\ifx\csname pgf@deps@pgfshading#2!\endcsname\pgfutil@empty%
+    \global\expandafter\let\csname pgf@num@pgfshading#2!\endcsname=\pgfutil@empty
+    \pgfshade@functionaldo{#2}{#3}{#4}{#5}{#6}%
+  \else%
+    \global\advance\pgf@shadingcount 1\relax
+    \global\expandafter\edef\csname pgf@num@pgfshading#2!\endcsname{\pgf@shadingnum}%
+    \expandafter\def\csname pgf@func@pgfshading#2!\endcsname{\pgfshade@functionaldo}%
+    \expandafter\def\csname pgf@args@pgfshading#2!\endcsname{{#3}{#4}{#5}{#6}}%
+    \expandafter\let\csname @pgfshading#2!\endcsname=\pgfutil@empty%
+  \fi}
+\def\pgfshade@functionaldo#1#2#3#4#5{%
+  \begingroup
+    #4%
+    \pgfsys@functionalshading{#1}{#2}{#3}{#5}%
+    \expandafter\pgfmath@smuggleone\csname @pgfshading#1!\endcsname
+  \endgroup
+}
+
+\def\pgfshadecolortorgb#1#2{%
+  \pgfutil@colorlet{pgf@tempcol}{#1}%
+  \pgfutil@extractcolorspec{pgf@tempcol}{\pgf@tempcolor}%
+  \expandafter\pgfutil@convertcolorspec\pgf@tempcolor{rgb}{\pgf@rgbcolor}%
+  \expandafter\pgfshading@rgb\pgf@rgbcolor\relax%
+  \edef#2{\pgf@sys@tonumber{\pgf@xa}\space\pgf@sys@tonumber{\pgf@xb}\space\pgf@sys@tonumber{\pgf@xc}\space}%
+  \c@pgf@counta\escapechar%
+  \escapechar-1\relax%
+  \expandafter\edef\csname\string#2red\endcsname{\pgf@sys@tonumber{\pgf@xa}\space}%
+  \expandafter\edef\csname\string#2green\endcsname{\pgf@sys@tonumber{\pgf@xb}\space}%
+  \expandafter\edef\csname\string#2blue\endcsname{\pgf@sys@tonumber{\pgf@xc}\space}%
+  \escapechar\c@pgf@counta%
+}
+\def\pgfshading@rgb#1,#2,#3\relax{%
+  \pgf@xa=#1pt%
+  \pgf@xb=#2pt%
+  \pgf@xc=#3pt%
+}
+
+\def\pgfshadecolortocmyk#1#2{%
+  \pgfutil@colorlet{pgf@tempcol}{#1}%
+  \pgfutil@extractcolorspec{pgf@tempcol}{\pgf@tempcolor}%
+  \expandafter\pgfutil@convertcolorspec\pgf@tempcolor{cmyk}{\pgf@cmykcolor}%
+  \expandafter\pgfshading@cmyk\pgf@cmykcolor\relax%
+  \edef#2{\pgf@sys@tonumber{\pgf@xa}\space\pgf@sys@tonumber{\pgf@xb}\space
+    \pgf@sys@tonumber{\pgf@xc}\space\pgf@sys@tonumber{\pgf@xd}\space}%
+  \c@pgf@counta\escapechar%
+  \escapechar-1\relax%
+  \expandafter\edef\csname\string#2cyan\endcsname{%
+    \pgf@sys@tonumber{\pgf@xa}\space}%
+  \expandafter\edef\csname\string#2magenta\endcsname{%
+    \pgf@sys@tonumber{\pgf@xb}\space}%
+  \expandafter\edef\csname\string#2yellow\endcsname{%
+    \pgf@sys@tonumber{\pgf@xc}\space}%
+  \expandafter\edef\csname\string#2black\endcsname{%
+    \pgf@sys@tonumber{\pgf@xd}\space}%
+  \escapechar\c@pgf@counta
+}
+\def\pgfshading@cmyk#1,#2,#3,#4\relax{%
+  \pgf@xa=#1pt%
+  \pgf@xb=#2pt%
+  \pgf@xc=#3pt%
+  \pgf@xd=#4pt%
+}
+
+\def\pgfshadecolortogray#1#2{%
+  \pgfutil@colorlet{pgf@tempcol}{#1}%
+  \pgfutil@extractcolorspec{pgf@tempcol}{\pgf@tempcolor}%
+  \expandafter\pgfutil@convertcolorspec\pgf@tempcolor{gray}{\pgf@graycolor}%
+  \expandafter\pgfshading@gray\pgf@graycolor\relax
+  \edef#2{\pgf@sys@tonumber{\pgf@xa}\space}%
+  \c@pgf@counta\escapechar
+  \escapechar-1\relax
+  \expandafter\edef\csname\string#2gray\endcsname{%
+    \pgf@sys@tonumber{\pgf@xa}\space}%
+  \escapechar\c@pgf@counta
+}
+\def\pgfshading@gray#1\relax{%
+  \pgf@xa=#1pt%
+}
+
+
+\def\pgffuncshadingrgbtocmyk{%
+  1.0 exch sub 3 1 roll
+  1.0 exch sub 3 1 roll
+  1.0 exch sub 3 1 roll
+  3 copy
+  2 copy gt { exch } if pop
+  2 copy gt { exch } if pop
+  dup 3 1 roll sub
+  0.0 2 copy lt { exch } if pop
+  1.0 2 copy gt { exch } if pop
+  4 1 roll
+  dup 3 1 roll sub
+  0.0 2 copy lt { exch } if pop
+  1.0 2 copy gt { exch } if pop
+  4 1 roll
+  dup 3 1 roll sub
+  0.0 2 copy lt { exch } if pop
+  1.0 2 copy gt { exch } if pop
+  4 1 roll
+}
+
+\def\pgffuncshadingrgbtogray{%
+  0.11 mul exch 0.59 mul add exch 0.3 mul add
+}
+
+\def\pgffuncshadingcmyktorgb{%
+  dup 3 1 roll add
+  1.0 2 copy gt { exch } if pop
+  4 1 roll
+  dup 3 1 roll add
+  1.0 2 copy gt { exch } if pop
+  4 1 roll
+  add
+  1.0 2 copy gt { exch } if pop
+  3 1 roll
+  1.0 exch sub
+  3 1 roll
+  1.0 exch sub
+  3 1 roll
+  1.0 exch sub
+  3 1 roll
+}
+
+\def\pgffuncshadingcmyktogray{%
+  exch 0.11 mul add exch 0.59 mul add exch 0.3 mul add
+  1.0 2 copy gt { exch } if pop
+  1.0 exch sub
+}
+
+\def\pgffuncshadinggraytorgb{%
+  dup dup
+}
+
+\def\pgffuncshadinggraytocmyk{%
+  0.0 0.0 0.0
+  4 3 roll
+}
+
+
+\def\pgfuseshading#1{%
+  \edef\pgf@shadingname{@pgfshading#1}%
+  \pgf@tryextensions{\pgf@shadingname}{\pgfalternateextension}%
+  \expandafter\pgfutil@ifundefined\expandafter{\pgf@shadingname}%
+  {\pgferror{Undefined shading "#1"}}%
+  {%
+    \edef\pgf@shade@adds{\csname pgf@num\pgf@shadingname\endcsname}%
+    \pgfutil@ifundefined{pgf@deps\pgf@shadingname}%
+    {}%
+    {%
+      \pgf@setup@shading@model
+      \begingroup
+        \pgfutil@globalcolorsfalse
+        \edef\@list{\csname pgf@deps\pgf@shadingname\endcsname}%
+        \pgfutil@for\@temp:=\@list\do{%
+          \pgfutil@ifundefined{applycolormixins}{}{\applycolormixins{\@temp}}%
+          \pgfutil@extractcolorspec{\@temp}{\pgf@tempcolor}%
+          \expandafter\pgfutil@convertcolorspec\pgf@tempcolor{\pgf@shading@model}{\pgf@color}%
+          \edef\pgf@shade@adds{\pgf@shade@adds,\pgf@color}%
+        }%
+        \pgfmath@smuggleone\pgf@shade@adds
+      \endgroup
+    }%
+    \expandafter\pgf@strip@shadename\pgf@shadingname!!%
+    \edef\pgf@shadingxname{@pgfshading\pgf@basename\pgf@shade@adds!}%
+    \pgfutil@ifundefined{\pgf@shadingxname}%
+    {%
+      \begingroup
+        \edef\@temp{\expandafter\noexpand\csname pgf@func\pgf@shadingname\endcsname}%
+        \edef\@args{{\pgf@basename\pgf@shade@adds}}%
+        \expandafter\expandafter\expandafter\def
+        \expandafter\expandafter\expandafter\@@args
+        \expandafter\expandafter\expandafter{\csname pgf@args\pgf@shadingname\endcsname}%
+        \expandafter\expandafter\expandafter\@temp\expandafter\@args\@@args
+        \expandafter\pgfmath@smuggleone\csname\pgf@shadingxname\endcsname
+      \endgroup
+    }%
+    {}%
+    \pgf@invokeshading{\csname\pgf@shadingxname\endcsname}%
+  }%
+}
+
+\def\pgf@strip@shadename @pgfshading#1!!!{\def\pgf@basename{#1}}
+
+\def\pgf@invokeshading#1{%
+  \ifpgfpicture%
+    \pgfsys@shadinginsidepgfpicture{#1}%
+  \else%
+    \pgfsys@shadingoutsidepgfpicture{#1}%
+  \fi%
+}
+
+
+
+\def\pgfaliasshading#1#2{%
+  \expandafter\let\expandafter\pgf@temp\expandafter=\csname @pgfshading#2!\endcsname%
+  \expandafter\let\csname @pgfshading#1!\endcsname=\pgf@temp%
+  \expandafter\let\expandafter\pgf@temp\expandafter=\csname pgf@num@pgfshading#2!\endcsname%
+  \expandafter\let\csname pgf@num@pgfshading#1!\endcsname=\pgf@temp%
+  \expandafter\let\expandafter\pgf@temp\expandafter=\csname pgf@deps@pgfshading#2!\endcsname%
+  \expandafter\let\csname pgf@deps@pgfshading#1!\endcsname=\pgf@temp%
+  \expandafter\let\expandafter\pgf@temp\expandafter=\csname pgf@func@pgfshading#2!\endcsname%
+  \expandafter\let\csname pgf@func@pgfshading#1!\endcsname=\pgf@temp%
+  \expandafter\let\expandafter\pgf@temp\expandafter=\csname pgf@args@pgfshading#2!\endcsname%
+  \expandafter\let\csname pgf@args@pgfshading#1!\endcsname=\pgf@temp%
+}
+
+
+
+
+
+\def\pgfshadepath#1#2{%
+  \ifdim\pgf@pathminx=16000pt%
+    \pgfwarning{No path specified that can be filled}%
+  \else%
+    \begingroup%
+      \pgf@xb=.5\pgf@pathmaxx%
+      \advance\pgf@xb by.5\pgf@pathminx%
+      \pgf@yb=.5\pgf@pathmaxy%
+      \advance\pgf@yb by.5\pgf@pathminy%
+      \pgfmathparse{#2}%
+      \let\pgfshade@angle=\pgfmathresult
+      \pgfmathsin@\pgfshade@angle
+      \let\pgfshade@sin=\pgfmathresult
+      \pgfmathcos@\pgfshade@angle
+      \let\pgfshade@cos=\pgfmathresult
+      \pgf@xa=\pgf@pathmaxx
+      \advance\pgf@xa by-\pgf@pathminx
+      \pgf@ya=\pgf@pathmaxy
+      \advance\pgf@ya by-\pgf@pathminy
+      \pgfmathabs@\pgfshade@sin
+      \let\pgfshade@abssin=\pgfmathresult
+      \pgfmathabs@\pgfshade@cos
+      \let\pgfshade@abscos=\pgfmathresult
+      \pgf@xc=\pgfshade@abscos\pgf@xa
+      \advance\pgf@xc by\pgfshade@abssin\pgf@ya
+      \pgf@yc=\pgfshade@abssin\pgf@xa
+      \advance\pgf@yc by\pgfshade@abscos\pgf@ya
+      \pgfmathadd@\pgfshade@abscos\pgfshade@abssin
+      \pgfmathdivide@{.01992528}{\pgfmathresult}%
+      \pgf@xc=\pgfmathresult\pgf@xc
+      \pgf@yc=\pgfmathresult\pgf@yc
+      \ifdim\pgf@xc<0.0001pt
+        \ifdim\pgf@xc>-0.0001pt
+          \pgf@no@shadetrue
+        \fi
+      \fi
+      \ifdim\pgf@yc<0.0001pt
+        \ifdim\pgf@yc>-0.0001pt
+          \pgf@no@shadetrue
+        \fi
+      \fi
+      \ifpgf@no@shade\else
+        \pgfsys@beginscope
+          \pgfsyssoftpath@invokecurrentpath
+          \pgfsys@clipnext
+          \pgfsys@discardpath
+          \pgfsys@transformcm{1}{0}{0}{1}{\the\pgf@xb}{\the\pgf@yb}%
+          \pgf@x=\pgfshade@sin pt%
+          \pgf@xa=-\pgf@x%
+          \pgfsys@transformcm{\pgfshade@cos}{\pgfshade@sin}{\pgf@sys@tonumber{\pgf@xa}}{\pgfshade@cos}{0pt}{0pt}%
+          \pgfsys@transformcm{\pgf@sys@tonumber{\pgf@xc}}{0}{0}{\pgf@sys@tonumber{\pgf@yc}}{0pt}{0pt}%
+          \ifx\pgf@shade@extra@transform\pgfutil@empty%
+          \else%
+            \pgflowlevel{\pgf@shade@extra@transform}%
+          \fi%
+          \pgfuseshading{#1}%
+        \pgfsys@endscope%
+      \fi%
+    \endgroup%
+  \fi%
+}
+
+\newif\ifpgf@no@shade
+
+
+\def\pgfsetadditionalshadetransform#1{\def\pgf@shade@extra@transform{#1}}
+\let\pgf@shade@extra@transform=\pgfutil@empty
+
+
+
+
+
+\endinput

preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/basiclayer/pgfcoretransformations.code.tex

@@ -0,0 +1,503 @@
+
+\ProvidesFileRCS{pgfcoretransformations.code.tex}
+
+
+
+\newdimen\pgf@pt@x
+\newdimen\pgf@pt@y
+
+\newdimen\pgf@pt@temp
+
+\newif\ifpgf@pt@identity
+\pgf@pt@identitytrue
+
+\def\pgf@pt@aa{1.0} \def\pgf@pt@ab{0.0}
+\def\pgf@pt@ba{0.0} \def\pgf@pt@bb{1.0}
+
+
+
+
+\def\pgfgettransform#1{%
+  \edef#1{{\pgf@pt@aa}{\pgf@pt@ab}{\pgf@pt@ba}{\pgf@pt@bb}{\the\pgf@pt@x}{\the\pgf@pt@y}}%
+}
+
+\def\pgfgettransformentries#1#2#3#4#5#6{%
+  \edef#1{\pgf@pt@aa}%
+  \edef#2{\pgf@pt@ab}%
+  \edef#3{\pgf@pt@ba}%
+  \edef#4{\pgf@pt@bb}%
+  \edef#5{\the\pgf@pt@x}%
+  \edef#6{\the\pgf@pt@y}%
+}%
+\def\pgfsettransformentries#1#2#3#4#5#6{%
+  \pgfsettransform{{#1}{#2}{#3}{#4}{#5}{#6}}%
+}%
+
+
+\def\pgfsettransform#1{%
+  \edef\pgf@temp{#1}%
+  \expandafter\pgf@settransform\pgf@temp%
+}
+\def\pgf@settransform#1#2#3#4#5#6{%
+  \def\pgf@pt@aa{#1}%
+  \def\pgf@pt@ab{#2}%
+  \def\pgf@pt@ba{#3}%
+  \def\pgf@pt@bb{#4}%
+  \pgf@pt@x=#5%
+  \pgf@pt@y=#6%
+  \edef\pgf@idtest{#1,#2,#3,#4}%
+  \ifx\pgf@idtest\pgf@idmatrixtext%
+    \pgf@pt@identitytrue%
+  \else%
+    \pgf@pt@identityfalse%
+  \fi%
+}
+
+\def\pgf@idmatrixtext{1.0,0.0,0.0,1.0}
+\def\pgf@zerozerotext{0.0,0.0}
+\def\pgf@one@text{1.0}
+\def\pgf@zero@text{0.0}
+
+
+\def\pgf@pos@transform#1#2{%
+  \ifpgf@pt@identity%
+  \else%
+    \pgf@pt@temp=#1%
+    #1=\pgf@pt@aa#1%
+    \advance#1 by\pgf@pt@ba#2%
+    #2=\pgf@pt@bb#2%
+    \advance#2 by\pgf@pt@ab\pgf@pt@temp%
+  \fi%
+  \advance#1 by\pgf@pt@x%
+  \advance#2 by\pgf@pt@y%
+}
+\def\pgf@pos@transform@glob{%
+  \ifpgf@pt@identity%
+  \else%
+    \pgf@pt@temp=\pgf@x%
+    \global\pgf@x=\pgf@pt@aa\pgf@x%
+    \global\advance\pgf@x by\pgf@pt@ba\pgf@y%
+    \global\pgf@y=\pgf@pt@bb\pgf@y%
+    \global\advance\pgf@y by\pgf@pt@ab\pgf@pt@temp%
+  \fi%
+  \global\advance\pgf@x by\pgf@pt@x%
+  \global\advance\pgf@y by\pgf@pt@y%
+}
+
+
+
+\def\pgftransforminvert{%
+  \pgf@pt@x=-\pgf@pt@x
+  \pgf@pt@y=-\pgf@pt@y
+  \ifpgf@pt@identity%
+  \else%
+    \edef\pgf@zerotest{\pgf@pt@ab,\pgf@pt@ba}%
+    \ifx\pgf@zerotest\pgf@zerozerotext%
+      \pgfmathreciprocal@{\pgf@pt@aa}%
+      \let\pgf@pt@aa\pgfmathresult%
+      \pgfmathreciprocal@{\pgf@pt@bb}%
+      \let\pgf@pt@bb\pgfmathresult%
+    \else%
+      {%
+        \pgfutil@tempdima=\pgf@pt@aa pt%
+        \pgfutil@tempdima=\pgf@pt@bb\pgfutil@tempdima%
+        \pgfutil@tempdimb=\pgf@pt@ba pt%
+        \pgfutil@tempdimb=\pgf@pt@ab\pgfutil@tempdimb%
+        \advance\pgfutil@tempdima by -\pgfutil@tempdimb%
+        \pgfmathreciprocal@{\pgf@sys@tonumber{\pgfutil@tempdima}}%
+        \pgfutil@tempdima=\pgfmathresult pt%
+        \pgf@x=\pgf@pt@bb\pgfutil@tempdima%
+        \xdef\pgf@new@pt@aa{\pgf@sys@tonumber{\pgf@x}}%
+        \pgf@x=\pgf@pt@aa\pgfutil@tempdima%
+        \xdef\pgf@new@pt@bb{\pgf@sys@tonumber{\pgf@x}}%
+        \pgfutil@tempdima=-\pgfutil@tempdima%
+        \pgf@x=\pgf@pt@ba\pgfutil@tempdima%
+        \xdef\pgf@new@pt@ba{\pgf@sys@tonumber{\pgf@x}}%
+        \pgf@x=\pgf@pt@ab\pgfutil@tempdima%
+        \xdef\pgf@new@pt@ab{\pgf@sys@tonumber{\pgf@x}}%
+      }%
+      \let\pgf@pt@aa\pgf@new@pt@aa%
+      \let\pgf@pt@ab\pgf@new@pt@ab%
+      \let\pgf@pt@ba\pgf@new@pt@ba%
+      \let\pgf@pt@bb\pgf@new@pt@bb%
+    \fi%
+    \pgf@pt@temp=\pgf@pt@x%
+    \pgf@pt@x=\pgf@pt@aa\pgf@pt@x%
+    \advance\pgf@pt@x by\pgf@pt@ba\pgf@pt@y%
+    \pgf@pt@y=\pgf@pt@bb\pgf@pt@y%
+    \advance\pgf@pt@y by\pgf@pt@ab\pgf@pt@temp%
+  \fi%
+}
+
+
+
+
+
+\def\pgftransformcm#1#2#3#4#5{%
+  \edef\pgf@marshal{\noexpand\pgf@transformcm{#1}{#2}{#3}{#4}}%
+  \pgf@marshal{#5}%
+}
+\def\pgf@transformcm#1#2#3#4#5{%
+  {%
+    \pgf@process{#5}%
+    \pgf@xc=\pgf@x%
+    \pgf@yc=\pgf@y%
+    \pgfmathsetlength\pgf@x{#1}%
+    \pgfmathsetlength\pgf@y{#2}%
+    \pgf@xa=\pgf@pt@aa\pgf@x%
+    \advance\pgf@xa by \pgf@pt@ba\pgf@y%
+    \pgf@ya=\pgf@pt@ab\pgf@x%
+    \advance\pgf@ya by \pgf@pt@bb\pgf@y%
+    \pgfmathsetlength\pgf@x{#3}%
+    \pgfmathsetlength\pgf@y{#4}%
+    \pgf@xb=\pgf@pt@aa\pgf@x%
+    \advance\pgf@xb by \pgf@pt@ba\pgf@y%
+    \pgf@yb=\pgf@pt@ab\pgf@x%
+    \advance\pgf@yb by \pgf@pt@bb\pgf@y%
+    \pgf@x=\pgf@pt@aa\pgf@xc%
+    \advance\pgf@x by\pgf@pt@ba\pgf@yc%
+    \advance\pgf@x by\pgf@pt@x%
+    \pgf@y=\pgf@pt@ab\pgf@xc%
+    \advance\pgf@y by\pgf@pt@bb\pgf@yc%
+    \advance\pgf@y by\pgf@pt@y%
+    \global\pgf@x=\pgf@x%
+    \global\pgf@y=\pgf@y%
+    \xdef\pgf@tempaa{\pgf@sys@tonumber{\pgf@xa}}%
+    \xdef\pgf@tempab{\pgf@sys@tonumber{\pgf@ya}}%
+    \xdef\pgf@tempba{\pgf@sys@tonumber{\pgf@xb}}%
+    \xdef\pgf@tempbb{\pgf@sys@tonumber{\pgf@yb}}%
+  }%
+  \pgf@pt@x=\pgf@x%
+  \pgf@pt@y=\pgf@y%
+  \let\pgf@pt@aa=\pgf@tempaa%
+  \let\pgf@pt@ba=\pgf@tempba%
+  \let\pgf@pt@ab=\pgf@tempab%
+  \let\pgf@pt@bb=\pgf@tempbb%
+  \edef\pgf@idtest{\pgf@pt@aa,\pgf@pt@ba,\pgf@pt@ab,\pgf@pt@bb}%
+  \ifx\pgf@idtest\pgf@idmatrixtext%
+    \pgf@pt@identitytrue%
+  \else%
+    \pgf@pt@identityfalse%
+  \fi%
+}
+
+
+
+
+\def\pgftransformtriangle#1#2#3{%
+  \pgf@process{#2}%
+  \pgf@xa=\pgf@x%
+  \pgf@ya=\pgf@y%
+  \pgf@process{#3}%
+  \pgf@xb=\pgf@x%
+  \pgf@yb=\pgf@y%
+  \pgf@process{#1}%
+  \advance\pgf@xa by-\pgf@x%
+  \advance\pgf@ya by-\pgf@y%
+  \advance\pgf@xb by-\pgf@x%
+  \advance\pgf@yb by-\pgf@y%
+  \pgftransformcm%
+  {\pgf@sys@tonumber\pgf@xa}{\pgf@sys@tonumber\pgf@ya}%
+  {\pgf@sys@tonumber\pgf@xb}{\pgf@sys@tonumber\pgf@yb}%
+  {\pgfpoint{\pgf@x}{\pgf@y}}%
+}
+
+
+
+
+\def\pgftransformreset{%
+  \pgf@pt@x=0pt%
+  \pgf@pt@y=0pt%
+  \let\pgf@pt@aa\pgf@one@text%
+  \let\pgf@pt@ba\pgf@zero@text%
+  \let\pgf@pt@ab\pgf@zero@text%
+  \let\pgf@pt@bb\pgf@one@text%
+  \pgf@pt@identitytrue%
+}
+
+
+
+\def\pgftransformresetnontranslations{%
+  \let\pgf@pt@aa\pgf@one@text%
+  \let\pgf@pt@ba\pgf@zero@text%
+  \let\pgf@pt@ab\pgf@zero@text%
+  \let\pgf@pt@bb\pgf@one@text%
+  \pgf@pt@identitytrue%
+}
+
+
+
+
+
+\def\pgftransformshift#1{\pgftransformcm{1}{0}{0}{1}{#1}}
+\def\pgftransformxshift#1{\pgftransformcm{1}{0}{0}{1}{\pgfpoint{#1}{+0pt}}}
+\def\pgftransformyshift#1{\pgftransformcm{1}{0}{0}{1}{\pgfpoint{+0pt}{#1}}}
+
+
+
+
+
+\def\pgftransformscale#1{\pgftransformcm{#1}{0}{0}{#1}{\pgfpointorigin}}
+\def\pgftransformxscale#1{\pgftransformcm{#1}{0}{0}{1.0}{\pgfpointorigin}}
+\def\pgftransformyscale#1{\pgftransformcm{1.0}{0}{0}{#1}{\pgfpointorigin}}
+
+
+
+
+\def\pgftransformxslant#1{\pgftransformcm{1.0}{0}{#1}{1.0}{\pgfpointorigin}}
+\def\pgftransformyslant#1{\pgftransformcm{1.0}{#1}{0}{1.0}{\pgfpointorigin}}
+
+
+
+
+\def\pgftransformrotate#1{%
+  \pgfmathparse{#1}%
+  \let\pgftransform@angle=\pgfmathresult%
+  \pgfmathsin@{\pgftransform@angle}%
+  \let\pgftransform@sin=\pgfmathresult%
+  \pgfmathcos@{\pgftransform@angle}%
+  \let\pgftransform@cos=\pgfmathresult%
+  \pgf@x=\pgftransform@sin pt%
+  \pgf@xa=-\pgf@x%
+  \pgftransformcm{\pgftransform@cos}{\pgftransform@sin}{\pgf@sys@tonumber{\pgf@xa}}{\pgftransform@cos}{\pgfpointorigin}%
+}
+
+
+
+
+\newif\ifpgfslopedattime
+\newif\ifpgfallowupsidedownattime
+\newif\ifpgfresetnontranslationattime
+
+
+\def\pgftransformlineattime#1#2#3{%
+  \pgf@process{#2}%
+  \pgf@xb=\pgf@x%
+  \pgf@yb=\pgf@y%
+  \pgf@process{#3}%
+  \pgf@xc=\pgf@x%
+  \pgf@yc=\pgf@y%
+  \pgftransformshift{\pgfpointlineattime{#1}{\pgfqpoint{\pgf@xb}{\pgf@yb}}{\pgfqpoint{\pgf@xc}{\pgf@yc}}}%
+  \ifpgfresetnontranslationattime%
+    \pgftransformresetnontranslations%
+  \fi%
+  \ifpgfslopedattime%
+    \advance\pgf@xc by-\pgf@xb%
+    \advance\pgf@yc by-\pgf@yb%
+    \ifpgfallowupsidedownattime%
+    \else%
+      \ifdim\pgf@xc<0pt%
+        \pgf@xc=-\pgf@xc%
+        \pgf@yc=-\pgf@yc%
+      \fi%
+    \fi%
+    \pgf@x=\pgf@xc%
+    \pgf@y=\pgf@yc%
+    \pgfpointnormalised{}%
+    \pgf@ya=-\pgf@y%
+    \pgftransformcm%
+    {\pgf@sys@tonumber{\pgf@x}}{\pgf@sys@tonumber{\pgf@y}}%
+    {\pgf@sys@tonumber{\pgf@ya}}{\pgf@sys@tonumber{\pgf@x}}{\pgfpointorigin}%
+  \fi%
+}
+
+
+
+\def\pgftransformarcaxesattime#1#2#3#4#5#6{%
+  \pgfpointarcaxesattime{#1}{#2}{#3}{#4}{#5}{#6}%
+  \pgftransformshift{\pgfqpoint{\pgf@x}{\pgf@y}}%
+  \ifpgfresetnontranslationattime%
+    \pgftransformresetnontranslations%
+  \fi%
+  \ifpgfslopedattime%
+    \pgf@x=\pgf@xa%
+    \pgf@y=\pgf@ya%
+    \pgf@process{\pgfpointnormalised{}}%
+    \ifpgfallowupsidedownattime%
+    \else%
+      \ifdim\pgf@x<0pt%
+        \pgf@x=-\pgf@x%
+        \pgf@y=-\pgf@y%
+      \fi%
+    \fi%
+    \pgf@ya=-\pgf@y%
+    \pgftransformcm%
+    {\pgf@sys@tonumber{\pgf@x}}{\pgf@sys@tonumber{\pgf@y}}%
+    {\pgf@sys@tonumber{\pgf@ya}}{\pgf@sys@tonumber{\pgf@x}}{\pgfpointorigin}%
+  \fi%
+}
+
+
+
+
+\def\pgftransformcurveattime#1#2#3#4#5{%
+  \pgfpointcurveattime{#1}{#2}{#3}{#4}{#5}%
+  \pgftransformshift{\pgfqpoint{\pgf@x}{\pgf@y}}%
+  \ifpgfresetnontranslationattime%
+    \pgftransformresetnontranslations%
+  \fi%
+  \ifpgfslopedattime%
+    \pgf@x=\pgf@xa%
+    \pgf@y=\pgf@ya%
+    \advance\pgf@x by-\pgf@xb%
+    \advance\pgf@y by-\pgf@yb%
+    \ifpgfallowupsidedownattime%
+    \else%
+      \ifdim\pgf@x<0pt%
+        \pgf@x=-\pgf@x%
+        \pgf@y=-\pgf@y%
+      \fi%
+    \fi%
+    \pgfpointnormalised{}%
+    \pgf@ya=-\pgf@y%
+    \pgftransformcm%
+    {\pgf@sys@tonumber{\pgf@x}}{\pgf@sys@tonumber{\pgf@y}}%
+    {\pgf@sys@tonumber{\pgf@ya}}{\pgf@sys@tonumber{\pgf@x}}{\pgfpointorigin}%
+  \fi%
+}
+
+
+
+
+
+
+\def\pgftransformarrow#1#2{%
+  \pgf@process{#2}%
+  \pgftransformshift{}%
+  \pgf@xa=\pgf@x%
+  \pgf@ya=\pgf@y%
+  \pgf@process{#1}%
+  \advance\pgf@xa by-\pgf@x%
+  \advance\pgf@ya by-\pgf@y%
+  \pgf@x=\pgf@xa%
+  \pgf@y=\pgf@ya%
+  \pgfpointnormalised{}%
+  \pgf@ya=-\pgf@y%
+  \pgftransformcm%
+  {\pgf@sys@tonumber{\pgf@x}}{\pgf@sys@tonumber{\pgf@y}}%
+  {\pgf@sys@tonumber{\pgf@ya}}{\pgf@sys@tonumber{\pgf@x}}{\pgfqpoint{0pt}{0pt}}%
+}
+
+
+
+
+
+\def\pgftransformationadjustments{%
+  \ifpgf@pt@identity%
+    \let\pgfhorizontaltransformationadjustment\pgf@one@text%
+    \let\pgfverticaltransformationadjustment\pgf@one@text%
+  \else%
+    {%
+      \pgf@pt@x0pt%
+      \pgf@pt@y0pt%
+      \pgfpointtransformed{\pgfqpoint{1pt}{0pt}}%
+      \pgfmathveclen@{\pgf@sys@tonumber\pgf@x}{\pgf@sys@tonumber\pgf@y}%
+      \pgfmathreciprocal@{\pgfmathresult}%
+      \global\let\pgf@temp@hori\pgfmathresult
+      \pgfpointtransformed{\pgfqpoint{0pt}{1pt}}%
+      \pgfmathveclen@{\pgf@sys@tonumber\pgf@x}{\pgf@sys@tonumber\pgf@y}%
+      \pgfmathreciprocal@{\pgfmathresult}%
+      \global\let\pgf@temp@vert\pgfmathresult
+      \xdef\pgf@marshal@b{\def\noexpand\pgfverticaltransformationadjustment{\pgfmathresult}}
+    }%
+    \let\pgfhorizontaltransformationadjustment\pgf@temp@hori%
+    \let\pgfverticaltransformationadjustment\pgf@temp@vert%
+  \fi%
+}
+
+\let\pgfhorizontaltransformationadjustment\pgf@one@text
+\let\pgfverticaltransformationadjustment\pgf@one@text
+
+
+
+
+\def\pgflowlevelsynccm{%
+  \pgfsys@transformcm%
+  {\pgf@pt@aa}{\pgf@pt@ab}%
+  {\pgf@pt@ba}{\pgf@pt@bb}%
+  {\pgf@pt@x}{\pgf@pt@y}%
+  \pgftransformreset%
+  \pgf@relevantforpicturesizefalse%
+}
+
+
+
+
+\def\pgflowlevel#1{%
+  {%
+    \pgftransformreset%
+    #1%
+    \pgflowlevelsynccm%
+  }%
+  \pgf@relevantforpicturesizefalse%
+}
+
+\def\pgflowlevelscope#1{\pgfscope\pgflowlevel{#1}}
+\def\endpgflowlevelscope{\endpgfscope}
+
+\long\def\pgflowlevelobj#1#2{\pgfscope{\pgflowlevel{#1}#2}\endpgfscope}
+
+
+
+
+
+\def\pgfviewboxscope#1#2#3#4#5{%
+  {%
+    \pgf@process{#1}%
+    \pgf@pos@transform@glob
+    \pgf@xa=\pgf@x%
+    \pgf@ya=\pgf@y%
+    \pgf@process{#2}%
+    \pgf@pos@transform@glob
+    \ifdim\pgf@x<\pgf@xa%
+      \pgf@xb\pgf@x%
+      \pgf@xc\pgf@xa%
+    \else%
+      \pgf@xb\pgf@xa%
+      \pgf@xc\pgf@x%
+    \fi%
+    \ifdim\pgf@y<\pgf@ya%
+      \pgf@yb\pgf@y%
+      \pgf@yc\pgf@ya%
+    \else%
+      \pgf@yb\pgf@ya%
+      \pgf@yc\pgf@y%
+    \fi%
+    \pgf@process{#3}%
+    \pgf@pos@transform@glob
+    \pgf@xa=\pgf@x%
+    \pgf@ya=\pgf@y%
+    \pgf@process{#4}%
+    \pgf@pos@transform@glob
+    \ifdim\pgf@x<\pgf@xa%
+    \else%
+      \pgfutil@tempdima\pgf@x
+      \pgf@x\pgf@xa%
+      \pgf@xa\pgfutil@tempdima%
+    \fi%
+    \ifdim\pgf@y<\pgf@ya%
+    \else%
+      \pgfutil@tempdima\pgf@y
+      \pgf@y\pgf@ya%
+      \pgf@ya\pgfutil@tempdima%
+    \fi%
+    \pgfusetype{.view}%
+    \edef\pgf@marshal{\expandafter\noexpand\csname pgfsys@viewbox#5\endcsname{\the\pgf@x}{\the\pgf@y}{\the\pgf@xa}{\the\pgf@ya}{\the\pgf@xb}{\the\pgf@yb}{\the\pgf@xc}{\the\pgf@yc}}%
+    \pgf@marshal%
+  }%
+  \pgf@relevantforpicturesizefalse%
+}
+
+\def\endpgfviewboxscope{\pgfsys@endviewbox}
+
+\let\startpgfviewboxscope=\pgfviewboxscope
+\let\stoppgfviewboxscope=\endpgfviewboxscope
+
+
+\let\pgfapproximatenonlineartranslation\relax
+\let\pgfapproximatenonlineartransformation\relax
+\def\pgftransformnonlinear#1{\pgferror{You need to say
+    \string\usepgfmodule{nonlineartransformations} to use nonlinear transformations}}
+
+
+\endinput

preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/basiclayer/pgfcoretransparency.code.tex

@@ -0,0 +1,146 @@
+
+\ProvidesFileRCS{pgfcoretransparency.code.tex}
+
+
+
+\def\pgfsetstrokeopacity#1{%
+  \pgfmathparse{#1}%
+  \expandafter\pgfsys@stroke@opacity\expandafter{\pgfmathresult}}
+
+
+
+\def\pgfsetfillopacity#1{%
+  \pgfmathparse{#1}%
+  \expandafter\pgfsys@fill@opacity\expandafter{\pgfmathresult}}
+
+
+
+
+\def\pgfsetblendmode#1{\pgfsys@blend@mode{#1}}
+
+
+
+\def\pgfdeclarefading#1#2{%
+  \setbox\pgfutil@tempboxa=\hbox{{\pgfsys@beginscope\pgfutil@color{white}\ignorespaces#2\pgfsys@endscope}}%
+  \pgfsys@fadingfrombox{#1}\pgfutil@tempboxa%
+}
+
+\pgfutil@colorlet{pgftransparent}{black}
+
+
+
+\def\pgfsetfading#1#2{%
+  {%
+    \pgftransformreset%
+    #2%
+    \pgfgettransform{\pgftrans@temp}%
+    \edef\pgf@marshal{\noexpand\pgfsys@usefading{#1}\pgftrans@temp}%
+    \pgf@marshal%
+  }%
+}
+
+
+
+
+\def\pgfsetfadingforcurrentpath#1#2{%
+  \ifdim\pgf@pathminx=16000pt%
+    \pgfsetfading{#1}{#2}%
+  \else%
+    \pgfsetfading{#1}{%
+      \pgf@xb=.5\pgf@pathmaxx%
+      \advance\pgf@xb by.5\pgf@pathminx%
+      \pgf@yb=.5\pgf@pathmaxy%
+      \advance\pgf@yb by.5\pgf@pathminy%
+      \pgf@xc=\pgf@pathmaxx%
+      \advance\pgf@xc by-\pgf@pathminx%
+      \ifdim\pgf@xc<0.1pt\pgf@xc=0.1pt\fi%
+      \pgf@yc=\pgf@pathmaxy%
+      \advance\pgf@yc by-\pgf@pathminy%
+      \ifdim\pgf@yc<0.1pt\pgf@yc=0.1pt\fi%
+      \pgf@xc=.02\pgf@xc%
+      \pgf@yc=.02\pgf@yc%
+      \pgftransformcm{1}{0}{0}{1}{\pgfqpoint{\pgf@xb}{\pgf@yb}}%
+      \pgftransformcm{\pgf@sys@tonumber{\pgf@xc}}{0}{0}{\pgf@sys@tonumber{\pgf@yc}}{\pgfpointorigin}%
+      \pgfsys@clipfading%
+      #2%
+    }%
+  \fi%
+}
+
+
+
+
+
+\def\pgfsetfadingforcurrentpathstroked#1#2{%
+  \ifdim\pgf@pathminx=16000pt%
+    \pgfsetfading{#1}{#2}%
+  \else%
+    \pgfsetfading{#1}{%
+      \pgf@xb=.5\pgf@pathmaxx%
+      \advance\pgf@xb by.5\pgf@pathminx%
+      \pgf@yb=.5\pgf@pathmaxy%
+      \advance\pgf@yb by.5\pgf@pathminy%
+      \pgf@xc=\pgf@pathmaxx%
+      \advance\pgf@xc by-\pgf@pathminx%
+      \advance\pgf@xc by\pgflinewidth%
+      \ifdim\pgf@xc<0.1pt\pgf@xc=0.1pt\fi%
+      \pgf@yc=\pgf@pathmaxy%
+      \advance\pgf@yc by-\pgf@pathminy%
+      \advance\pgf@yc by\pgflinewidth%
+      \ifdim\pgf@yc<0.1pt\pgf@yc=0.1pt\fi%
+      \pgf@xc=.02\pgf@xc%
+      \pgf@yc=.02\pgf@yc%
+      \pgftransformcm{1}{0}{0}{1}{\pgfqpoint{\pgf@xb}{\pgf@yb}}%
+      \pgftransformcm{\pgf@sys@tonumber{\pgf@xc}}{0}{0}{\pgf@sys@tonumber{\pgf@yc}}{\pgfpointorigin}%
+      \pgfsys@clipfading%
+      #2%
+    }%
+  \fi%
+}
+
+
+
+\def\pgftransparencygroup{%
+  \pgfutil@ifnextchar[{\pgftransparencygroup@}{\pgftransparencygroup@[]}%
+}
+\def\pgftransparencygroup@[#1]{%
+  \begingroup%
+    \pgfkeys{/pgf/transparency group options/.cd,%
+      isolated=false,
+      knockout=false,
+      #1}%
+    \setbox\pgfutil@tempboxa=\hbox\bgroup%
+}
+\pgfkeys{
+  /pgf/transparency group options/.cd,
+  isolated/.is if=pgfsys@transparency@group@isolated,
+  knockout/.is if=pgfsys@transparency@group@knockout
+}
+
+\def\endpgftransparencygroup{%
+    \egroup%
+    \ifdim\pgf@picminx=16000pt%
+    \else%
+      \advance\pgf@picminx by-1cm%
+      \advance\pgf@picmaxx by1cm%
+      \advance\pgf@picminy by-1cm%
+      \advance\pgf@picmaxy by1cm%
+      \setbox\pgfutil@tempboxa=\hbox{%
+        \vrule width0pt height\pgf@picmaxy depth-\pgf@picminy%
+        \hskip-\pgf@picminx%
+        \box\pgfutil@tempboxa%
+        \hskip\pgf@picmaxx%
+      }%
+      \pgfsys@transparencygroupfrombox\pgfutil@tempboxa%
+      \wd\pgfutil@tempboxa=0pt%
+      \ht\pgfutil@tempboxa=0pt%
+      \dp\pgfutil@tempboxa=0pt%
+      \hskip\pgf@picminx\box\pgfutil@tempboxa\hskip-\pgf@picminx%
+    \fi%
+  \endgroup%
+}
+
+\let\startpgftransparencygroup=\pgftransparencygroup
+\let\stoppgftransparencygroup=\endpgftransparencygroup
+
+\endinput

preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/circuits/tikzlibrarycircuits.code.tex

@@ -0,0 +1,205 @@
+
+\usetikzlibrary{calc,decorations.markings}%
+
+
+\tikzset{
+  circuit/.style={
+    every circuit/.try,
+    /utils/exec=\tikz@lib@circ@on@tofalse,
+    execute at begin to={
+      \tikz@lib@circ@on@totrue
+      \let\tikz@lib@circ@start@node\pgfutil@empty
+      \def\tikz@lib@circ@end{-- (\tikztotarget) \tikztonodes}
+    }
+  }
+}%
+
+\newif\iftikz@lib@circ@on@to
+
+
+
+\tikzset{
+  circuit handle symbol/.code={%
+    \global\advance\tikz@lib@circ@count by1\relax%
+    \iftikz@lib@circ@on@to
+      {%
+        \pgfkeys{
+          /pgf/key filters/active families or no family/.install key filter={/pgf/key filters/false}{/pgf/key filters/false},
+          /tikz/circuits/pos grabber/.activate family}
+        \pgfqkeysfiltered{/tikz}{pos=.5,#1}%
+        \expandafter%
+      }%
+      \expandafter\def\expandafter\tikz@lib@circ@pos\expandafter{\tikz@time}%
+      \pgfkeysalso{to path={
+         \pgfextra{\tikz@lib@circ@on@tofalse}
+         decorate [decoration={markings,mark connection node=mark node}]
+          {
+            \tikz@lib@circ@start@node
+            \tikz@lib@circ@end
+          }
+        }}
+      \ifdim\tikz@lib@circ@pos pt=0pt\relax%
+        \def\tikz@lib@circ@start@node{%
+          {\pgfextra{\tikz@lib@circ@compute@direction{\tikz@lib@circ@start}}%
+          node[alias=tikz@lib@circ@node@start,at={(0,0)},#1,pos=]{}}(tikz@lib@circ@node@start)}%
+      \else%
+        \ifdim\tikz@lib@circ@pos pt=1pt\relax%
+          \def\tikz@lib@circ@end{
+            {\pgfextra{\tikz@lib@circ@compute@direction{\tikz@lib@circ@target}}%
+              node[alias=tikz@lib@circ@node\the\tikz@lib@circ@count,at={(0,0)},#1,pos=]{}}
+            --(tikz@lib@circ@node\the\tikz@lib@circ@count)\tikztonodes
+          }%
+        \else%
+          \edef\tikz@marshal{mark=at position \tikz@lib@circ@pos\space with}%
+          \def\tikz@marshala{decoration=}%
+          \expandafter\expandafter\expandafter\tikzset%
+          \expandafter\expandafter\expandafter{\expandafter\tikz@marshala\expandafter{\tikz@marshal{\node[alias=mark node,#1,pos=]{};}}}
+        \fi%
+      \fi%
+    \else
+      \pgfkeysalso{#1}
+    \fi
+  }
+}%
+\newcount\tikz@lib@circ@count
+
+\def\tikz@lib@circ@compute@direction#1{%
+  \tikz@scan@one@point\tikz@lib@circ@save@start(\tikztostart)%
+  \tikz@scan@one@point\tikz@lib@circ@save@target(\tikztotarget)%
+  \pgf@process{\pgfpointnormalised{\pgfpointdiff{\tikz@lib@circ@start}{\tikz@lib@circ@target}}}%
+  \pgf@ya=-\pgf@y%
+  \pgftransformcm{\the\pgf@x}{\the\pgf@y}{\the\pgf@ya}{\the\pgf@x}{#1}%
+}%
+\def\tikz@lib@circ@save@start#1{\def\tikz@lib@circ@start{#1}}%
+\def\tikz@lib@circ@save@target#1{\def\tikz@lib@circ@target{#1}}%
+
+\tikzset{
+  circuits/pos grabber/.is family,
+  pos/.belongs to family=/tikz/circuits/pos grabber,
+  at start/.belongs to family=/tikz/circuits/pos grabber,
+  very near start/.belongs to family=/tikz/circuits/pos grabber,
+  near start/.belongs to family=/tikz/circuits/pos grabber,
+  midway/.belongs to family=/tikz/circuits/pos grabber,
+  near end/.belongs to family=/tikz/circuits/pos grabber,
+  very near end/.belongs to family=/tikz/circuits/pos grabber,
+  at end/.belongs to family=/tikz/circuits/pos grabber
+}%
+
+
+\tikzset{
+  circuit declare symbol/.style args={#1}{
+    #1/.style={circuit handle symbol={
+        inner sep=0.5pt,
+        every circuit symbol,
+        #1/graphic,
+        every #1/.try,
+        ##1}
+    },
+    #1/graphic/.style={},
+    set #1 graphic/.style={#1/graphic/.style={##1}}
+  },
+  circuit symbol unit/.code=\pgfmathsetlength\tikzcircuitssizeunit{#1},
+  circuit symbol size/.style args={width #1 height #2}{
+    minimum width={(#1)*\tikzcircuitssizeunit},
+    minimum height={(#2)*\tikzcircuitssizeunit}
+  },
+  huge circuit symbols/.style={circuit symbol unit=10pt},
+  large circuit symbols/.style={circuit symbol unit=8pt},
+  medium circuit symbols/.style={circuit symbol unit=7pt},
+  small circuit symbols/.style={circuit symbol unit=6pt},
+  tiny circuit symbols/.style={circuit symbol unit=5pt},
+}%
+
+\newdimen\tikzcircuitssizeunit
+\tikzcircuitssizeunit=7pt
+
+
+
+\tikzset{
+  circuit declare annotation/.style args={#1#2#3}{%
+    #1/.style={
+      append after command={%
+        \bgroup
+          [current point is local=true]
+          [every circuit annotation/.try]
+          [every #1/.try]
+          [shift={(\tikzlastnode.north)}]
+          [annotation arrow,->]
+          [label distance=#2,##1]
+          #3
+          \tikz@after@path%
+        \egroup%
+      }
+    },
+    #1'/.style={
+      append after command={%
+        \bgroup
+          [current point is local=true]
+          [every circuit annotation/.try]
+          [every #1/.try]
+          [shift={(\tikzlastnode.south)},yscale=-1]
+          [annotation arrow,->]
+          [label distance=#2,##1]
+          #3
+          \tikz@after@path%
+        \egroup%
+      }
+    }
+  },
+  annotation arrow/.style = {
+    /utils/exec={\pgfsetarrowoptions{direction ee}{.4*\the\tikzcircuitssizeunit+.3*\the\pgflinewidth}},
+    >=direction ee
+  }
+}%
+
+
+
+\tikzset{
+  point up/.style={rotate=90},
+  point down/.style={rotate=-90},
+  point left/.style={rotate=180},
+  point right/.style={}
+}%
+
+
+
+
+\tikzset{
+  every circuit symbol/.style={},
+  circuit symbol open/.style={draw},
+  circuit symbol filled/.style={draw,fill=black},
+  circuit symbol lines/.style={draw},
+  circuit symbol wires/.style={draw},
+}%
+
+
+
+
+
+
+\tikzset{
+  info/.code={\pgfutil@ifnextchar[\tikz@lib@circ@lab@plain{\tikz@lib@circ@lab@plain[]}#1\pgf@stop},%
+  info'/.code={\pgfutil@ifnextchar[\tikz@lib@circ@labp@plain{\tikz@lib@circ@labp@plain[]}#1\pgf@stop},%
+  info sloped/.code={\pgfutil@ifnextchar[\tikz@lib@circ@lab@sloped@plain{\tikz@lib@circ@lab@sloped@plain[]}#1\pgf@stop},%
+  info' sloped/.code={\pgfutil@ifnextchar[\tikz@lib@circ@lab@slopedp@plain{\tikz@lib@circ@lab@slopedp@plain[]}#1\pgf@stop},%
+  circuit declare unit/.style 2 args={
+    #1/.code={\pgfutil@ifnextchar[\tikz@lib@circ@lab{\tikz@lib@circ@lab[]}##1\pgf@stop{#2}{#1}},%
+    #1 sloped/.code={\pgfutil@ifnextchar[\tikz@lib@circ@lab@sloped{\tikz@lib@circ@lab@sloped[]}##1\pgf@stop{#2}{#1}},%
+    #1'/.code={\pgfutil@ifnextchar[\tikz@lib@circ@labp{\tikz@lib@circ@labp[]}##1\pgf@stop{#2}{#1}},%
+    #1' sloped/.code={\pgfutil@ifnextchar[\tikz@lib@circ@lab@slopedp{\tikz@lib@circ@lab@slopedp[]}##1\pgf@stop{#2}{#1}}%
+  }
+}%
+
+\def\tikz@lib@circ@lab[#1]#2\pgf@stop#3#4{\tikzset{label={[every info/.try,every #4/.try,#1]$\mathrm{#2#3}$}}}%
+\def\tikz@lib@circ@lab@sloped[#1]#2\pgf@stop#3#4{\tikzset{label={[every info/.try,every #4/.try,transform shape,#1]$\mathrm{#2#3}$}}}%
+\def\tikz@lib@circ@labp[#1]#2\pgf@stop#3#4{\tikzset{label={[label position=below,every info/.try,every #4/.try,#1]$\mathrm{#2#3}$}}}%
+\def\tikz@lib@circ@lab@slopedp[#1]#2\pgf@stop#3#4{\tikzset{label={[label position=below,every info/.try,every #4/.try,transform shape,#1]$\mathrm{#2#3}$}}}%
+
+\def\tikz@lib@circ@lab@plain[#1]#2\pgf@stop{\tikzset{label={[every info/.try,#1]#2}}}%
+\def\tikz@lib@circ@lab@sloped@plain[#1]#2\pgf@stop{\tikzset{label={[every info/.try,transform shape,#1]#2}}}%
+\def\tikz@lib@circ@labp@plain[#1]#2\pgf@stop{\tikzset{label={[label position=below,every info/.try,#1]#2}}}%
+\def\tikz@lib@circ@lab@slopedp@plain[#1]#2\pgf@stop{\tikzset{label={[label position=below,every info/.try,transform shape,#1]#2}}}%
+
+
+
+\endinput

preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/circuits/tikzlibrarycircuits.ee.IEC.code.tex

@@ -0,0 +1,371 @@
+
+\usetikzlibrary{arrows}%
+\usetikzlibrary{circuits.ee}%
+
+\usepgflibrary{shapes.gates.ee.IEC}%
+
+
+
+\tikzset{
+  circuit ee IEC/.style=
+  {
+    circuit ee,
+    set resistor graphic              = resistor IEC graphic,
+    set inductor graphic              = inductor IEC graphic,
+    set capacitor graphic             = capacitor IEC graphic,
+    set contact graphic               = contact IEC graphic,
+    set ground graphic                = ground IEC graphic,
+    set battery graphic               = battery IEC graphic,
+    set diode graphic                 = diode IEC graphic,
+    set Zener diode graphic           = Zener diode IEC graphic,
+    set tunnel diode graphic          = tunnel diode IEC graphic,
+    set backward diode graphic        = backward diode IEC graphic,
+    set Schottky diode graphic        = Schottky diode IEC graphic,
+    set breakdown diode graphic       = breakdown diode IEC graphic,
+    set bulb graphic                  = bulb IEC graphic,
+    set voltage source graphic        = voltage source IEC graphic,
+    set current source graphic        = current source IEC graphic,
+    set make contact graphic          = make contact IEC graphic,
+    set break contact graphic         = break contact IEC graphic,
+    set amperemeter graphic           = amperemeter graphic,
+    set voltmeter graphic             = voltmeter graphic,
+    set ohmmeter graphic              = ohmmeter graphic,
+    set ac source graphic             = ac source graphic,
+    set dc source graphic             = dc source graphic,
+  },
+}%
+
+
+
+\tikzset{
+  resistor IEC graphic/.style={
+    circuit symbol open,
+    circuit symbol size=width 4 height 1,
+    shape=rectangle ee,
+    transform shape,
+  },
+  var resistor IEC graphic/.style={
+    circuit symbol lines,
+    circuit symbol size=width 4.8 height 0.8,
+    shape=var resistor IEC,
+    transform shape,
+    outer sep=0pt,
+    cap=round,
+  },
+}%
+
+
+
+
+\tikzset{
+  inductor IEC graphic/.style={
+    circuit symbol lines,
+    circuit symbol size=width 4 height .5,
+    transform shape,
+    shape=inductor IEC,
+    outer sep=0pt,
+    cap=round,
+  },
+  var inductor IEC graphic/.style={
+    circuit symbol filled,
+    circuit symbol size=width 4 height 1,
+    transform shape,
+    shape=rectangle ee,
+  },
+}%
+
+
+
+
+\tikzset{
+  capacitor IEC graphic/.style={
+    circuit symbol lines,
+    circuit symbol size=width .5 height 2,
+    transform shape,
+    shape=capacitor IEC,
+  },
+}%
+
+
+
+
+\tikzset{
+  ground IEC graphic/.style={
+    circuit symbol lines,
+    circuit symbol size=width .75 height 2,
+    transform shape,
+    shape=ground IEC,
+  },
+}%
+
+
+
+
+
+\tikzset{
+  battery IEC graphic/.style={
+    circuit symbol lines,
+    circuit symbol size=width .5 height 2.5,
+    transform shape,
+    shape=battery IEC,
+    transform shape,
+  },
+}%
+
+
+
+
+\tikzset{
+  diode IEC graphic/.style={
+    circuit symbol open,
+    circuit symbol size=width 1.25 height 1.25,
+    transform shape,
+    shape=generic diode IEC,
+    /pgf/generic diode IEC/before background={
+      \pgfpathmoveto{\pgfqpoint{0pt}{-1pt}}
+      \pgfpathlineto{\pgfqpoint{0pt}{1pt}}
+      \pgfusepathqstroke
+    },
+  },
+  var diode IEC graphic/.style={
+    diode IEC graphic,
+    circuit symbol filled,
+  },
+}%
+
+\tikzset{
+  Zener diode IEC graphic/.style={
+    diode IEC graphic,
+    /pgf/generic diode IEC/before background={
+      \pgfpathmoveto{\pgfqpoint{-.5pt}{-1pt}}
+      \pgfpathlineto{\pgfqpoint{0pt}{-1pt}}
+      \pgfpathlineto{\pgfqpoint{0pt}{1pt}}
+      \pgfusepathqstroke
+    },
+  },
+  var Zener diode IEC graphic/.style={
+    Zener diode IEC graphic,
+    circuit symbol filled,
+  },
+}%
+
+\tikzset{
+  Schottky diode IEC graphic/.style={
+    diode IEC graphic,
+    /pgf/generic diode IEC/before background={
+      \pgfpathmoveto{\pgfqpoint{-.4pt}{-.6pt}}
+      \pgfpathlineto{\pgfqpoint{-.4pt}{-1pt}}
+      \pgfpathlineto{\pgfqpoint{0pt}{-1pt}}
+      \pgfpathlineto{\pgfqpoint{0pt}{1pt}}
+      \pgfpathlineto{\pgfqpoint{.4pt}{1pt}}
+      \pgfpathlineto{\pgfqpoint{.4pt}{.6pt}}
+      \pgfusepathqstroke
+    },
+  },
+  var Schottky diode IEC graphic/.style={
+    Schottky diode IEC graphic,
+    circuit symbol filled,
+  },
+}%
+
+\tikzset{
+  tunnel diode IEC graphic/.style={
+    diode IEC graphic,
+    /pgf/generic diode IEC/before background={
+      \pgfpathmoveto{\pgfqpoint{-.5pt}{-1pt}}
+      \pgfpathlineto{\pgfqpoint{0pt}{-1pt}}
+      \pgfpathlineto{\pgfqpoint{0pt}{1pt}}
+      \pgfpathlineto{\pgfqpoint{-.5pt}{1pt}}
+      \pgfusepathqstroke
+    },
+  },
+  var tunnel diode IEC graphic/.style={
+    tunnel diode IEC graphic,
+    circuit symbol filled,
+  },
+}%
+
+\tikzset{
+  backward diode IEC graphic/.style={
+    diode IEC graphic,
+    /pgf/generic diode IEC/before background={
+      \pgfpathmoveto{\pgfqpoint{-.5pt}{-1pt}}
+      \pgfpathlineto{\pgfqpoint{.5pt}{-1pt}}
+      \pgfpathmoveto{\pgfqpoint{0pt}{-1pt}}
+      \pgfpathlineto{\pgfqpoint{0pt}{1pt}}
+      \pgfpathmoveto{\pgfqpoint{-.5pt}{1pt}}
+      \pgfpathlineto{\pgfqpoint{.5pt}{1pt}}
+      \pgfusepathqstroke
+    },
+  },
+  var backward diode IEC graphic/.style={
+    backward diode IEC graphic,
+    circuit symbol filled,
+  },
+}%
+
+
+\tikzset{
+  breakdown diode IEC graphic/.style={
+    circuit symbol open,
+    circuit symbol size=width 2.5 height 1.25,
+    transform shape,
+    shape=breakdown diode IEC,
+  },
+  var breakdown diode IEC graphic/.style={
+    breakdown diode IEC graphic,
+    circuit symbol filled,
+  },
+}%
+
+
+
+
+\tikzset{
+  contact IEC graphic/.style={
+    circuit symbol filled,
+    circuit symbol size=width .5 height .5,
+    shape=circle ee,
+    outer sep=.25\pgflinewidth,
+  },
+}%
+
+
+
+\tikzset{
+  bulb IEC graphic/.style={
+    circuit symbol lines,
+    circuit symbol size=width 1.5 height 1.5,
+    shape=generic circle IEC,
+    /pgf/generic circle IEC/before background={
+      \pgfpathmoveto{\pgfpointpolar{-135}{1pt}}
+      \pgfpathlineto{\pgfpointpolar{45}{1pt}}
+      \pgfpathmoveto{\pgfpointpolar{-45}{1pt}}
+      \pgfpathlineto{\pgfpointpolar{135}{1pt}}
+      \pgfusepathqstroke
+    },
+    transform shape,
+  },
+}%
+
+
+
+\tikzset{
+  current source IEC graphic/.style={
+    circuit symbol lines,
+    circuit symbol size=width 2 height 2,
+    shape=generic circle IEC,
+    /pgf/generic circle IEC/before background={
+      \pgfpathmoveto{\pgfqpoint{0pt}{-1pt}}
+      \pgfpathlineto{\pgfqpoint{0pt}{1pt}}
+      \pgfusepathqstroke
+    },
+    transform shape,
+  },
+  voltage source IEC graphic/.style={
+    circuit symbol lines,
+    circuit symbol size=width 2 height 2,
+    shape=generic circle IEC,
+    /pgf/generic circle IEC/before background={
+      \pgfpathmoveto{\pgfqpoint{-1pt}{0pt}}
+      \pgfpathlineto{\pgfqpoint{1pt}{0pt}}
+      \pgfusepathqstroke
+    },
+    transform shape,
+  },
+}%
+
+
+
+
+\tikzset{
+  make contact IEC graphic/.style={
+    circuit symbol wires,
+    circuit symbol size=width 2 height 1,
+    transform shape,
+    shape=make contact IEC,
+    outer sep=0pt,
+    cap=round,
+  },
+  var make contact IEC graphic/.style={
+    circuit symbol wires,
+    circuit symbol size=width 2.4 height 1,
+    transform shape,
+    shape=var make contact IEC,
+    outer sep=0pt,
+    cap=round,
+  },
+}%
+
+
+\tikzset{
+  break contact IEC graphic/.style={
+    circuit symbol wires,
+    circuit symbol size=width 2 height 1,
+    transform shape,
+    shape=break contact IEC,
+    outer sep=0pt,
+    cap=round,
+  },
+}%
+
+
+
+
+\tikzset{
+  amperemeter graphic/.style={
+    circuit symbol open,
+    circuit symbol size=width 2 height 2,
+    transform shape,
+    shape=generic circle IEC,
+    info=center:A,
+  },
+  voltmeter graphic/.style={
+    circuit symbol open,
+    circuit symbol size=width 2 height 2,
+    transform shape,
+    shape=generic circle IEC,
+    info=center:V,
+  },
+  ohmmeter graphic/.style={
+    circuit symbol open,
+    circuit symbol size=width 2 height 2,
+    transform shape,
+    shape=generic circle IEC,
+    info=center:$\Omega$,
+  },
+}%
+
+
+
+
+\tikzset{
+  ac source graphic/.style={
+    circuit symbol lines,
+    circuit symbol size=width 2 height 2,
+    shape=generic circle IEC,
+    /pgf/generic circle IEC/before background={
+      \pgfpathmoveto{\pgfqpoint{0.7pt}{0pt}}
+      \pgfpathquadraticcurveto{\pgfqpoint{ 0.35pt}{-0.5pt}}{\pgfqpoint{0pt}{0pt}}
+      \pgfpathquadraticcurveto{\pgfqpoint{-0.35pt}{ 0.5pt}}{\pgfqpoint{-0.7pt}{0pt}}
+      \pgfusepathqstroke
+    },
+    transform shape,
+  },
+  dc source graphic/.style={
+    circuit symbol lines,
+    circuit symbol size=width 2 height 2,
+    shape=generic circle IEC,
+    /pgf/generic circle IEC/before background={
+      \pgfpathmoveto{\pgfqpoint{ 0.7pt}{ 0.2pt}}
+      \pgfpathlineto{\pgfqpoint{-0.7pt}{ 0.2pt}}
+      \pgfusepathqstroke
+      \pgfpathmoveto{\pgfqpoint{ 0.7pt}{-0.2pt}}
+      \pgfpathlineto{\pgfqpoint{-0.7pt}{-0.2pt}}
+      \pgfusepathqstroke
+    },
+    transform shape,
+  },
+}%
+
+\endinput

preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/circuits/tikzlibrarycircuits.ee.code.tex

@@ -0,0 +1,121 @@
+
+
+\usetikzlibrary{circuits}%
+\usepgflibrary{shapes.gates.ee}%
+
+
+\tikzset{
+  circuit ee/.style={
+    circuit,
+    every circuit ee/.try
+  }
+}%
+
+
+
+\tikzset{
+  circuit declare symbol = resistor,
+  circuit declare symbol = inductor,
+  circuit declare symbol = capacitor,
+  circuit declare symbol = contact,
+  circuit declare symbol = ground,
+  circuit declare symbol = battery,
+  circuit declare symbol = diode,
+  circuit declare symbol = Zener diode,
+  circuit declare symbol = Schottky diode,
+  circuit declare symbol = tunnel diode,
+  circuit declare symbol = backward diode,
+  circuit declare symbol = breakdown diode,
+  circuit declare symbol = bulb,
+  circuit declare symbol = current source,
+  circuit declare symbol = voltage source,
+  circuit declare symbol = current direction,
+  circuit declare symbol = current direction',
+  circuit declare symbol = make contact,
+  circuit declare symbol = break contact,
+  circuit declare symbol = amperemeter,
+  circuit declare symbol = voltmeter,
+  circuit declare symbol = ohmmeter,
+  circuit declare symbol = ac source,
+  circuit declare symbol = dc source,
+  set current direction graphic  = current direction ee graphic,
+  set current direction' graphic = current direction' ee graphic,
+}%
+
+
+
+\tikzset{
+  circuit declare unit={ampere}{A},
+  circuit declare unit={volt}{V},
+  circuit declare unit={ohm}{\Omega},
+  circuit declare unit={siemens}{S},
+  circuit declare unit={henry}{H},
+  circuit declare unit={farad}{F},
+  circuit declare unit={coulomb}{C},
+  circuit declare unit={voltampere}{VA},
+  circuit declare unit={watt}{W},
+  circuit declare unit={hertz}{Hz},
+}%
+
+
+
+
+\tikzset{
+  current direction arrow/.style = {
+    /utils/exec={\pgfsetarrowoptions{direction ee}{1.3065*.5*\the\tikzcircuitssizeunit+1.3065*.3*\the\pgflinewidth}},
+    >=direction ee,
+    direction ee arrow = direction ee,
+  }
+}%
+
+
+
+
+\tikzset{
+  current direction ee graphic/.style = {
+    shape=direction ee,
+    circuit symbol filled,
+    current direction arrow,
+    minimum width  = .5*\the\tikzcircuitssizeunit+.3*\the\pgflinewidth,
+    minimum height = .5*\the\tikzcircuitssizeunit+.3*\the\pgflinewidth,
+    transform shape
+  },
+  current direction' ee graphic/.style = {
+    current direction ee graphic,
+    rotate=180
+  }
+}%
+
+
+
+
+\tikzset{
+  circuit declare annotation={direction info}{.5\tikzcircuitssizeunit}
+  {
+    (-1.25\tikzcircuitssizeunit,.3333\tikzcircuitssizeunit) edge[line to] (1.25\tikzcircuitssizeunit,.3333\tikzcircuitssizeunit)
+  },
+  circuit declare annotation={light emitting}{1.75\tikzcircuitssizeunit}
+  {
+    (-.2\tikzcircuitssizeunit,.65\tikzcircuitssizeunit) edge[line to] ++(45:1.25\tikzcircuitssizeunit)
+    (.2\tikzcircuitssizeunit,.25\tikzcircuitssizeunit) edge[line to] ++(45:1.25\tikzcircuitssizeunit)
+  },
+  circuit declare annotation={light dependent}{1.75\tikzcircuitssizeunit}
+  {
+    [shift=(135:1.25\tikzcircuitssizeunit)]
+    (.2\tikzcircuitssizeunit,.65\tikzcircuitssizeunit) edge[line to] ++(-45:1.25\tikzcircuitssizeunit)
+    (-.2\tikzcircuitssizeunit,.25\tikzcircuitssizeunit) edge[line to] ++(-45:1.25\tikzcircuitssizeunit)
+  },
+  circuit declare annotation={adjustable}{1.5\tikzcircuitssizeunit}
+  {
+    [shift=(\tikzlastnode.center)]
+    (-1.5\tikzcircuitssizeunit,-1.5\tikzcircuitssizeunit) edge[line to] (1.5\tikzcircuitssizeunit,1.5\tikzcircuitssizeunit)
+  },
+  circuit declare annotation={adjustable'}{1.5\tikzcircuitssizeunit}
+  {
+    [shift=(\tikzlastnode.center)]
+    (-1.5\tikzcircuitssizeunit,1.5\tikzcircuitssizeunit) edge[line to] (1.5\tikzcircuitssizeunit,-1.5\tikzcircuitssizeunit)
+  }
+}%
+
+
+\endinput

preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/circuits/tikzlibrarycircuits.logic.CDH.code.tex

@@ -0,0 +1,20 @@
+
+\usetikzlibrary{circuits.logic.US}%
+
+\tikzset{
+  circuit logic CDH/.style =
+  {
+    circuit logic US,
+    set and gate graphic    = and gate CDH graphic,
+    set nand gate graphic   = nand gate CDH graphic,
+  }
+}%
+
+\tikzset{
+  circuit logic US make graphic=and gate CDH,
+  circuit logic US make graphic=nand gate CDH,
+}%
+
+
+
+\endinput

preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/circuits/tikzlibrarycircuits.logic.IEC.code.tex

@@ -0,0 +1,59 @@
+
+\usetikzlibrary{circuits.logic}%
+\usepgflibrary{shapes.gates.logic.IEC}%
+
+
+
+\tikzset{
+  circuit logic IEC/.style=
+  {
+    circuit logic,
+    set and gate graphic    = and gate IEC graphic,
+    set nand gate graphic   = nand gate IEC graphic,
+    set or gate graphic     = or gate IEC graphic,
+    set nor gate graphic    = nor gate IEC graphic,
+    set xor gate graphic    = xor gate IEC graphic,
+    set xnor gate graphic   = xnor gate IEC graphic,
+    set not gate graphic    = not gate IEC graphic,
+    set buffer gate graphic = buffer gate IEC graphic,
+    and gate IEC symbol    = {$\scriptstyle\char`\&$},
+    nand gate IEC symbol   = {$\scriptstyle\char`\&$},
+    or gate IEC symbol     = {$\scriptstyle\geq1$},
+    nor gate IEC symbol    = {$\scriptstyle\geq1$},
+    xor gate IEC symbol    = {$\scriptstyle=1$},
+    xnor gate IEC symbol   = {$\scriptstyle=1$},
+    not gate IEC symbol    = {$\scriptstyle1$},
+    buffer gate IEC symbol = {$\scriptstyle1$},
+  },
+}%
+
+
+\tikzset{
+  circuit logic IEC make graphic/.style=
+  {
+    #1 graphic/.style={
+      circuit symbol open,
+      circuit symbol size=width 2.5 height 4,
+      shape=#1,
+      inner sep=.5ex
+    }
+  }
+}%
+
+
+\tikzset{
+  circuit logic IEC make graphic=and gate IEC,
+  circuit logic IEC make graphic=nand gate IEC,
+  circuit logic IEC make graphic=or gate IEC,
+  circuit logic IEC make graphic=nor gate IEC,
+  circuit logic IEC make graphic=xor gate IEC,
+  circuit logic IEC make graphic=xnor gate IEC,
+  circuit logic IEC make graphic=not gate IEC,
+  circuit logic IEC make graphic=buffer gate IEC,
+  circuit logic IEC make graphic=and gate CDH,
+  circuit logic IEC make graphic=nand gate CDH,
+}%
+
+
+
+\endinput

preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/circuits/tikzlibrarycircuits.logic.US.code.tex

@@ -0,0 +1,49 @@
+
+\usetikzlibrary{circuits.logic}%
+\usepgflibrary{shapes.gates.logic.US}%
+
+
+
+\tikzset{
+  circuit logic US/.style=
+  {
+    circuit logic,
+    set and gate graphic    = and gate US graphic,
+    set nand gate graphic   = nand gate US graphic,
+    set or gate graphic     = or gate US graphic,
+    set nor gate graphic    = nor gate US graphic,
+    set xor gate graphic    = xor gate US graphic,
+    set xnor gate graphic   = xnor gate US graphic,
+    set not gate graphic    = not gate US graphic,
+    set buffer gate graphic = buffer gate US graphic
+  }
+}%
+
+
+\tikzset{
+  circuit logic US make graphic/.style=
+  {
+    #1 graphic/.style={
+      circuit symbol open,
+      circuit symbol size=width 0 height 2.5,
+      shape=#1,
+      transform shape
+    }
+  }
+}%
+
+
+\tikzset{
+  circuit logic US make graphic=and gate US,
+  circuit logic US make graphic=nand gate US,
+  circuit logic US make graphic=or gate US,
+  circuit logic US make graphic=nor gate US,
+  circuit logic US make graphic=xor gate US,
+  circuit logic US make graphic=xnor gate US,
+  circuit logic US make graphic=not gate US,
+  circuit logic US make graphic=buffer gate US,
+}%
+
+
+
+\endinput

preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/circuits/tikzlibrarycircuits.logic.code.tex

@@ -0,0 +1,31 @@
+
+\usetikzlibrary{circuits}%
+
+
+
+
+\tikzset{
+  circuit logic/.style={
+    circuit,
+    inputs/.style={logic gate inputs={##1}},
+    logic gate inverted radius=.25\tikzcircuitssizeunit,
+    every circuit logic/.try,
+  }
+}%
+
+
+
+
+\tikzset{
+  circuit declare symbol = and gate,
+  circuit declare symbol = nand gate,
+  circuit declare symbol = or gate,
+  circuit declare symbol = nor gate,
+  circuit declare symbol = xor gate,
+  circuit declare symbol = xnor gate,
+  circuit declare symbol = not gate,
+  circuit declare symbol = buffer gate
+}%
+
+
+\endinput

preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/datavisualization/tikzlibrarydatavisualization.3d.code.tex

@@ -0,0 +1,61 @@
+
+\ProvidesFileRCS{tikzlibrarydatavisualization.3d.code.tex}
+
+\usetikzlibrary{datavisualization}%
+
+
+
+
+
+
+
+\tikzdatavisualizationset{
+  school book 3d plot/.style={
+    xyz Cartesian,
+    x axis={
+      visualize axis={y axis={goto=0},z axis={goto=0},styling/.style=->},
+      visualize ticks={common={y axis={goto=0},z axis={goto=0},direction axis=y axis},only ticks={tick text at min extend}},
+    },
+    y axis={
+      visualize axis={x axis={goto=0},z axis={goto=0},styling/.style=->},
+      visualize ticks={common={x axis={goto=0},z axis={goto=0},direction axis=x axis},only ticks={tick text at min extend}},
+    },
+    z axis={
+      visualize axis={x axis={goto=0},y axis={goto=0},styling/.style=->},
+      visualize ticks={common={x axis={goto=0},y axis={goto=0},direction axis=x axis},only ticks={tick text at min extend}},
+    },
+    new line plot,
+    every school book plot/.try,
+  },
+}%
+
+
+
+\tikzdatavisualizationset{
+  scientific 3d plot/length/.initial=100pt,
+  scientific 3d plot/.style={
+    xyz Cartesian,
+    x axis={
+      length=\pgfkeysvalueof{/tikz/data visualization/scientific 3d plot/length},
+      visualize axis={y axis={goto=min},z axis={goto=min}},
+      visualize axis={y axis={goto=max},z axis={goto=min}},
+      visualize axis={y axis={goto=min},z axis={goto=max}},
+      visualize axis={y axis={goto=max},z axis={goto=max}},
+    },
+    y axis={
+      length=\pgfkeysvalueof{/tikz/data visualization/scientific 3d plot/length},
+      visualize axis={x axis={goto=min},z axis={goto=min}},
+      visualize axis={x axis={goto=max},z axis={goto=min}},
+      visualize axis={x axis={goto=min},z axis={goto=max}},
+      visualize axis={x axis={goto=max},z axis={goto=max}},
+    },
+    z axis={
+      length=\pgfkeysvalueof{/tikz/data visualization/scientific 3d plot/length},
+      visualize axis={x axis={goto=min},y axis={goto=min}},
+      visualize axis={x axis={goto=max},y axis={goto=min}},
+      visualize axis={x axis={goto=min},y axis={goto=max}},
+      visualize axis={x axis={goto=max},y axis={goto=max}},
+    },
+    new line plot,
+  },
+}%

preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/datavisualization/tikzlibrarydatavisualization.barcharts.code.tex

@@ -0,0 +1,35 @@
+
+\ProvidesFileRCS{tikzlibrarydatavisualization.barcharts.code.tex}
+
+\usetikzlibrary{datavisualization}%
+\usepgflibrary{datavisualization.barcharts}%
+
+
+\tikzdatavisualizationset{%
+  candle stick plot/.style={
+    new object={
+      store=/tikz/data visualization/count,
+      class=count,
+      arg1=day
+    },
+    new axis=y axis,
+    y axis/source=dax,
+    y axis/source max=100,
+    y axis/vec=\pgfqpoint{0cm}{1cm},
+    new object={
+      store=/tikz/data visualization/x line trans,
+      class=line transformer,
+      arg1=day,
+      arg2=\pgfqpoint{3mm}{0mm}
+    },
+    new object={
+      store=/tikz/data visualization/index,
+      class=candle stick visualizer,
+      arg1 from key=index/source
+    },
+  },
+  index/source/.initial=index,
+}%
+
+
+\endinput

preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/datavisualization/tikzlibrarydatavisualization.code.tex

@@ -0,0 +1,2355 @@
+
+\ProvidesFileRCS{tikzlibrarydatavisualization.code.tex}
+
+\usepgfmodule{datavisualization}%
+\usetikzlibrary{backgrounds}%
+
+
+\tikzset{/tikz/data visualization/.is family,
+  /tikz/data visualization/.unknown/.code={
+    \let\tikz@dv@key\pgfkeyscurrentname%
+    \pgfkeys{/tikz/\tikz@dv@key/.try={#1}}%
+    \ifpgfkeyssuccess%
+    \else%
+      \edef\pgf@temp{/errors/unknown key={/tikz/data visualization/\tikz@dv@key}}%
+      \expandafter\pgfkeys\expandafter{\pgf@temp{#1}}%
+    \fi%
+  },
+  /tikz/data visualization/data/.unknown/.code={%
+    \let\tikz@dv@key\pgfkeyscurrentname%
+    \pgfkeys{/pgf/data/\tikz@dv@key/.try={#1}}%
+    \ifpgfkeyssuccess%
+    \else%
+      \edef\pgf@temp{/errors/unknown key={/pgf/data/\tikz@dv@key}}%
+      \expandafter\pgfkeys\expandafter{\pgf@temp{#1}}%
+    \fi%
+  },
+}%
+
+\def\tikzdatavisualizationset{\pgfqkeys{/tikz/data visualization}}%
+
+
+
+
+
+\def\tikz@lib@datavisualization{
+  \begingroup%
+    \let\tikz@path@do@at@end=\relax%
+    \pgfoonew \tikz@main@dv=new data visualization()%
+    \pgfset{local bounding box=data visualization bounding box}%
+    \pgfkeyslet{/tikz/data visualization/axes list}\pgfutil@empty%
+    \pgfkeyslet{/tikz/data visualization/axes actions}\pgfutil@empty%
+    \pgfkeyslet{/tikz/data visualization/label actions}\pgfutil@empty%
+    \pgfkeyslet{/tikz/data visualization/legend actions}\pgfutil@empty%
+    \pgfkeyslet{/tikz/data visualization/grid actions}\pgfutil@empty%
+    \pgfkeyslet{/tikz/data visualization/major grid actions}\pgfutil@empty%
+    \pgfkeyslet{/tikz/data visualization/minor grid actions}\pgfutil@empty%
+    \pgfkeyslet{/tikz/data visualization/subminor grid actions}\pgfutil@empty%
+    \pgfkeyslet{/tikz/data visualization/ticks actions}\pgfutil@empty%
+    \pgfkeyslet{/tikz/data visualization/major ticks actions}\pgfutil@empty%
+    \pgfkeyslet{/tikz/data visualization/minor ticks actions}\pgfutil@empty%
+    \pgfkeyslet{/tikz/data visualization/subminor ticks actions}\pgfutil@empty%
+    \tikz@main@dv.before visualization(%
+    )%
+    \tikz@main@dv.after visualization(%
+      \tikz@lib@dv@alias@dv@bb
+      \pgfkeysvalueof{/tikz/data visualization/grid actions}
+      \pgfkeysvalueof{/tikz/data visualization/subminor grid actions}
+      \pgfkeysvalueof{/tikz/data visualization/minor grid actions}
+      \pgfkeysvalueof{/tikz/data visualization/major grid actions}
+      \pgfkeysvalueof{/tikz/data visualization/ticks actions}
+      \pgfkeysvalueof{/tikz/data visualization/subminor ticks actions}
+      \pgfkeysvalueof{/tikz/data visualization/minor ticks actions}
+      \pgfkeysvalueof{/tikz/data visualization/major ticks actions}
+      \pgfkeysvalueof{/tikz/data visualization/axes actions}
+      \pgfkeysvalueof{/tikz/data visualization/label actions}
+      \pgfkeysvalueof{/tikz/data visualization/legend actions}
+    )%
+    \pgfset{/pgf/data/continue code=\tikz@lib@dv@parse@loop}%
+    \tikz@lib@dv@parse@loop
+}%
+
+\def\tikz@lib@dv@parse@loop{%
+  \pgfutil@ifnextchar d\tikz@lib@dv@handle@data{%
+    \pgfutil@ifnextchar ;\tikz@lib@dv@parse@end{%
+      \pgfutil@ifnextchar \par\tikz@lib@dv@handle@par{%
+        \pgfutil@ifnextchar s\tikz@lib@dv@handle@beginscope{%
+          \pgfutil@ifnextchar i\tikz@lib@dv@handle@info{%
+            \pgfutil@ifnextchar [\tikz@lib@dv@handle@options{%
+              \pgfutil@ifnextchar \egroup\tikz@lib@dv@handle@endscope{%
+                \tikzerror{Semicolon expected}%
+                \endgroup%
+              }%
+            }%
+          }%
+        }%
+      }%
+    }%
+  }%
+}%
+\def\tikz@lib@dv@parse@end;{%
+    \tikz@main@dv.survey()%
+    \tikz@main@dv.visualize()%
+  \endgroup%
+  \tikz@path@do@at@end%
+}%
+\def\tikz@lib@dv@handle@par\par{\tikz@lib@dv@parse@loop}%
+
+\def\tikz@lib@dv@handle@options[#1]{%
+  \tikzdatavisualizationset{#1}%
+  \tikz@lib@dv@parse@loop%
+}%
+
+\def\tikz@lib@dv@handle@beginscope scope{%
+  \begingroup%
+    \pgfutil@ifnextchar[\tikz@lib@dv@beg@opt{\tikz@lib@dv@beg@opt[]}%
+}%
+\def\tikz@lib@dv@beg@opt[#1]{%
+  \pgfkeys{/pgf/data/.cd,/pgf/every data/.try,#1}%
+  \pgf@dv@do@adddata{\pgfkeysvalueof{/pgf/data visualization/obj}.add data({{\begingroup\pgfkeys{/pgf/data/.cd,/pgf/every data/.try,#1}}})}%
+  \pgfutil@ifnextchar\bgroup{
+    \afterassignment\tikz@lib@dv@parse@loop%
+    \let\tikz@dummy=%
+  }{%
+    \tikzerror{Opening brace expected}%
+    \tikz@lib@dv@parse@loop%
+  }%
+}%
+\def\tikz@lib@dv@handle@endscope{%
+    \pgf@dv@do@adddata{\pgfkeysvalueof{/pgf/data visualization/obj}.add data(\endgroup)}%
+  \endgroup%
+  \afterassignment\tikz@lib@dv@parse@loop%
+  \let\tikz@dummy=%
+}%
+
+\def\tikz@lib@dv@handle@data data{%
+  \pgfutil@ifnextchar g{\tikz@lib@dv@handle@data@group}{%
+    \pgfutil@ifnextchar p{\tikz@lib@dv@handle@data@point}{%
+      \pgfdata}}}%
+
+\def\tikz@lib@dv@handle@data@group group{\pgfutil@ifnextchar[{\tikz@lib@dv@handle@data@group@opt}{\tikz@lib@dv@handle@data@group@opt[]}}%
+
+\def\tikz@lib@dv@handle@data@group@opt[#1]#2{%
+  \pgfutil@ifnextchar={\tikz@lib@dv@handle@data@group@def{#1}{#2}}{%
+    \pgfutil@ifnextchar+{\tikz@lib@dv@handle@data@group@extend{#1}{#2}}{%
+      \tikz@lib@dv@handle@data@group@use{#1}{#2}}}}%
+
+\def\tikz@lib@dv@handle@data@group@def#1#2={%
+  \pgfkeys{/pgf/data/new group={#2}}%
+  \tikz@lib@dv@handle@data@group@extend{#1}{#2}+=%
+}%
+
+\def\tikz@lib@dv@handle@data@group@extend#1#2+={%
+  \pgfutil@ifnextchar\bgroup{
+    \begingroup%
+      \pgfkeys{/pgf/data/store in group={#2}}%
+      \pgf@dv@do@adddata{\pgfkeysvalueof{/pgf/data visualization/obj}.add data({{\begingroup\pgfkeys{/pgf/data/.cd,/pgf/every data/.try,#1}}})}%
+      \afterassignment\tikz@lib@dv@parse@loop%
+      \let\tikz@dummy=%
+  }{%
+    \tikzerror{Opening brace expected}%
+    \tikz@lib@dv@parse@loop%
+  }%
+}%
+
+\def\tikz@lib@dv@handle@data@group@use#1#2{%
+  \pgfdata[#1,use group=#2]%
+}%
+
+\def\tikz@lib@dv@handle@data@point point{\pgfutil@ifnextchar[{\tikz@lib@dv@handle@data@point@opt}{\tikz@lib@dv@handle@data@point@opt[]}}%
+\def\tikz@lib@dv@handle@data@point@opt[#1]{%
+  \pgf@dv@do@adddata{\pgfkeysvalueof{/pgf/data visualization/obj}.add data({{\bgroup\pgfkeys{/data point/.cd,#1}\pgfdatapoint\egroup}})}%
+  \tikz@lib@dv@parse@loop%
+}%
+
+\def\tikz@lib@dv@handle@info info{%
+  \pgfutil@ifnextchar'{\tikz@lib@dv@handle@info@prime}{\tikz@lib@dv@handle@info@noprime}}%
+\def\tikz@lib@dv@handle@info@noprime{%
+  \pgfutil@ifnextchar[{\tikz@lib@dv@handle@info@block@opt}{\tikz@lib@dv@handle@info@block@opt[]}}%
+\def\tikz@lib@dv@handle@info@block@opt[#1]#2{%
+  \tikz@main@dv.after visualization({\scope[#1]#2\endscope})%
+  \tikz@lib@dv@parse@loop
+}%
+\def\tikz@lib@dv@handle@info@prime'{%
+  \pgfutil@ifnextchar[{\tikz@lib@dv@handle@info@block@opt@prime}{\tikz@lib@dv@handle@info@block@opt@prime[]}}%
+\def\tikz@lib@dv@handle@info@block@opt@prime[#1]#2{%
+  \tikz@main@dv.before visualization({\scope[#1]#2\endscope})%
+  \tikz@lib@dv@parse@loop
+}%
+
+
+\pgfset{/pgf/every data/.style={/tikz/every data/.try,/tikz/data visualization/every data/.try}}%
+
+
+
+\tikzdatavisualizationset{
+  before survey/.code=\tikz@main@dv.before survey({#1}),
+  after survey/.code=\tikz@main@dv.after survey({#1}),
+  before visualization/.code=\tikz@main@dv.before visualization({#1}),
+  after visualization/.code=\tikz@main@dv.after visualization({#1}),
+  at start survey/.code=\tikz@main@dv.at start survey({#1}),
+  at end survey/.code=\tikz@main@dv.at end survey({#1}),
+  at start visualization/.code=\tikz@main@dv.at start visualization({#1}),
+  at end visualization/.code=\tikz@main@dv.at end visualization({#1}),
+}%
+
+
+\def\tikz@lib@dv@alias@dv@bb{
+  \pgfnodealias{data bounding box}{data visualization bounding box}%
+  \pgfkeys{/pgf/freeze local bounding box=data bounding box}%
+}%
+
+\tikzdatavisualizationset{
+  data point/.code={
+    \pgf@dv@do@adddata{\pgfkeysvalueof{/pgf/data visualization/obj}.add data({{\bgroup\pgfkeys{/data point/.cd,#1}\pgfdatapoint\egroup}})}%
+  }
+}%
+
+
+
+
+\tikzdatavisualizationset{%
+  new object/.code={%
+    \def\tikz@dv@grabbed@when{before survey}%
+    \let\tikz@dv@grabbed@store\pgfutil@empty
+    \pgfkeys{/tikz/data visualization/new object/grab/.cd,#1}%
+    \ifx\tikz@dv@grabbed@store\pgfutil@empty
+    \else
+      \pgfkeyslet{\tikz@dv@grabbed@store}\pgfutil@empty%
+    \fi
+    \edef\tikz@marshal{\noexpand\tikz@main@dv.\tikz@dv@grabbed@when(\noexpand\tikz@dv@newobject{\tikz@dv@grabbed@store}}%
+    \tikz@marshal{#1})%
+  },
+  new object/grab/store/.store in=\tikz@dv@grabbed@store,
+  new object/grab/when/.store in=\tikz@dv@grabbed@when,
+  new object/grab/.unknown/.code={},%
+}%
+
+\def\tikz@dv@newobject#1#2{%
+  \def\tikz@dv@new@obj@store{#1}%
+  \ifx\tikz@dv@new@obj@store\pgfutil@empty%
+    \let\tikz@dv@new@obj=\pgfutil@empty%
+  \else%
+    \pgfkeysgetvalue\tikz@dv@new@obj@store\tikz@dv@new@obj%
+  \fi%
+  \ifx\tikz@dv@new@obj\pgfutil@empty
+    \let\tikz@dv@arg@a=\tikz@lib@notused%
+    \let\tikz@dv@arg@b=\tikz@lib@notused%
+    \let\tikz@dv@arg@c=\tikz@lib@notused%
+    \let\tikz@dv@arg@d=\tikz@lib@notused%
+    \let\tikz@dv@arg@e=\tikz@lib@notused%
+    \let\tikz@dv@arg@f=\tikz@lib@notused%
+    \let\tikz@dv@arg@g=\tikz@lib@notused%
+    \let\tikz@dv@arg@h=\tikz@lib@notused%
+    \let\tikz@dv@new@after=\relax%
+    \pgfkeys{/tikz/data visualization/new object/parse/.cd,#2}
+    \edef\pgf@marshal{\noexpand\pgfoonew\noexpand\tikzdvobj=new \tikz@dv@new@class(}%
+    \tikz@dv@add@arg{}\tikz@dv@arg@a%
+    \tikz@dv@add@arg{\expandafter,}\tikz@dv@arg@b%
+    \tikz@dv@add@arg{\expandafter,}\tikz@dv@arg@c%
+    \tikz@dv@add@arg{\expandafter,}\tikz@dv@arg@d%
+    \tikz@dv@add@arg{\expandafter,}\tikz@dv@arg@e%
+    \tikz@dv@add@arg{\expandafter,}\tikz@dv@arg@f%
+    \tikz@dv@add@arg{\expandafter,}\tikz@dv@arg@g%
+    \tikz@dv@add@arg{\expandafter,}\tikz@dv@arg@h%
+    \expandafter\def\expandafter\pgf@marshal\expandafter{\pgf@marshal)}%
+    \pgf@marshal%
+    \tikzdvobj.default connects()%
+    \ifx\tikz@dv@new@obj@store\pgfutil@empty%
+    \else%
+      \pgfkeyslet\tikz@dv@new@obj@store\tikzdvobj%
+    \fi%
+    \tikz@dv@new@after%
+  \fi
+}%
+\def\tikz@lib@notused{\tikz@lib@notused}%
+
+\def\tikz@dv@add@arg#1#2{%
+  \ifx#2\tikz@lib@notused%
+  \else%
+    \expandafter\expandafter\expandafter\def%
+    \expandafter\expandafter\expandafter\pgf@marshal%
+    \expandafter\expandafter\expandafter{\expandafter\pgf@marshal#1#2}%
+  \fi%
+}%
+
+\tikzdatavisualizationset{%
+  new object/parse/.cd,
+  store/.code=,%
+  when/.code=,%
+  class/.store in=\tikz@dv@new@class,
+  before creation/.code={#1},
+  after creation/.store in=\tikz@dv@new@after,
+  arg1/.store in=\tikz@dv@arg@a,
+  arg2/.store in=\tikz@dv@arg@b,
+  arg3/.store in=\tikz@dv@arg@c,
+  arg4/.store in=\tikz@dv@arg@d,
+  arg5/.store in=\tikz@dv@arg@e,
+  arg6/.store in=\tikz@dv@arg@f,
+  arg7/.store in=\tikz@dv@arg@g,
+  arg8/.store in=\tikz@dv@arg@h,
+  arg1 from key/.code=\pgfkeysgetvalue{#1}{\tikz@dv@arg@a},
+  arg2 from key/.code=\pgfkeysgetvalue{#1}{\tikz@dv@arg@b},
+  arg3 from key/.code=\pgfkeysgetvalue{#1}{\tikz@dv@arg@c},
+  arg4 from key/.code=\pgfkeysgetvalue{#1}{\tikz@dv@arg@d},
+  arg5 from key/.code=\pgfkeysgetvalue{#1}{\tikz@dv@arg@e},
+  arg6 from key/.code=\pgfkeysgetvalue{#1}{\tikz@dv@arg@f},
+  arg7 from key/.code=\pgfkeysgetvalue{#1}{\tikz@dv@arg@g},
+  arg8 from key/.code=\pgfkeysgetvalue{#1}{\tikz@dv@arg@h}
+  arg1 handle from key/.code=\tikz@dv@handle@from@key{#1}{\tikz@dv@handle@a}{\tikz@dv@arg@a},
+  arg2 handle from key/.code=\tikz@dv@handle@from@key{#1}{\tikz@dv@handle@b}{\tikz@dv@arg@b},
+  arg3 handle from key/.code=\tikz@dv@handle@from@key{#1}{\tikz@dv@handle@c}{\tikz@dv@arg@c},
+  arg4 handle from key/.code=\tikz@dv@handle@from@key{#1}{\tikz@dv@handle@d}{\tikz@dv@arg@d},
+  arg5 handle from key/.code=\tikz@dv@handle@from@key{#1}{\tikz@dv@handle@e}{\tikz@dv@arg@e},
+  arg6 handle from key/.code=\tikz@dv@handle@from@key{#1}{\tikz@dv@handle@f}{\tikz@dv@arg@f},
+  arg7 handle from key/.code=\tikz@dv@handle@from@key{#1}{\tikz@dv@handle@g}{\tikz@dv@arg@g},
+  arg8 handle from key/.code=\tikz@dv@handle@from@key{#1}{\tikz@dv@handle@h}{\tikz@dv@arg@h}
+}%
+
+\def\tikz@dv@handle@from@key#1#2#3{%
+  \pgfkeysvalueof{#1}.get handle(#2)%
+  \def#3{#2}%
+}%
+
+
+
+
+
+\tikzdeclarecoordinatesystem{visualization}
+{%
+  \tikzset{/data point/.cd,#1}%
+  \pgfpointdvlocaldatapoint%
+}%
+
+
+
+
+
+
+
+
+\tikzdatavisualizationset{%
+  new axis base/.style={
+    new object={
+      class=scaling mapper,
+      store=/tikz/data visualization/#1/scaling mapper,
+      before creation={
+        \pgfkeysgetvalue{/tikz/data visualization/#1/scaling}\tikz@temp
+        \ifx\tikz@temp\pgfutil@empty%
+          \pgfkeysgetvalue{/tikz/data visualization/#1/scaling/default}\tikz@temp
+        \fi
+        \expandafter\tikz@dv@lib@parse@scaling\tikz@temp\pgf@stop%
+        \pgfkeyslet{/tikz/data visualization/#1/scaling}\tikz@temp
+      },
+      arg1 from key=/tikz/data visualization/#1/attribute,
+      arg2/.expanded=\pgfkeysvalueof{/tikz/data visualization/#1/attribute}/scaled,
+      arg3 from key=/tikz/data visualization/#1/scaling,
+      arg4 from key=/tikz/data visualization/#1/function
+    },
+    #1/attribute/.initial={#1},
+    #1/function/.initial=,
+    #1/scaling/.initial=,
+    #1/scaling/default/.initial=0 at 0 and 1 at 1,
+    #1/ticks at/.initial=,
+    #1/default ticks at/.initial=,
+    #1/major ticks/.initial=,
+    #1/minor ticks/.initial=,
+    #1/subminor ticks/.initial=,
+    #1/grid at/.initial=,
+    #1/default grid at/.initial=,
+    #1/major grid/.initial=,
+    #1/minor grid/.initial=,
+    #1/subminor grid/.initial=,
+    #1/label/.initial=,
+    #1/padding min/.initial=,
+    #1/padding max/.initial=,
+    #1/.code={
+      \let\tikz@temp\tikz@dv@axis%
+      \def\tikz@dv@axis{/tikz/data visualization/#1}%
+      \expandafter\tikz@do@axis@options\expandafter{\tikz@temp}{##1}%
+    },
+    #1/@compute at positions/.initial=\tikz@lib@dv@compute@at@linear,
+    axes list/.append={\tikz@lib@dv@do@axis{#1}}
+  },
+  all axes/.code={
+    \def\tikz@lib@dv@args{#1}%
+    \pgfkeysvalueof{/tikz/data visualization/axes list}%
+  },
+  styling/.style=,
+  style/.style={styling/.append style={#1}},
+  @node styling/.initial=,
+  node styling/.style={%
+    /utils/exec={\pgfkeysgetvalue{/tikz/data visualization/@node styling}\tikz@temp\expandafter\tikzset\expandafter{\tikz@temp}}},
+  node style/.style={/tikz/data visualization/@node styling/.append={,#1}},
+  low/.initial=0,
+  high/.initial=0,
+  padded/.style={low=padded min,high=padded max},
+  tick length/.style={low={-#1},high={#1}},
+  common/.initial=,
+  major/.initial=,
+  minor/.initial=,
+  subminor/.initial=,
+  @setup at setters/.style={
+    common/.code=\tikz@lib@dv@add@{common}{##1},
+    major/.code=\tikz@lib@dv@add@{major}{##1},
+    minor/.code=\tikz@lib@dv@add@{minor}{##1},
+    subminor/.code=\tikz@lib@dv@add@{subminor}{##1}
+  },
+  @setup at setters,
+  direction axis/.initial=,
+  tick text low even padding/.initial=0pt,
+  tick text high even padding/.initial=0pt,
+  tick text low odd padding/.initial=0pt,
+  tick text high odd padding/.initial=0pt,
+  tick text odd padding/.style={tick text low odd padding={-#1},tick text high odd padding={#1}},
+  tick text even padding/.style={tick text low even padding={-#1},tick text high even padding={#1}},
+  tick text padding/.style={tick text odd padding={#1},tick text even padding={#1}},
+  stack/.style={tick text even padding={#1}},
+  stack'/.style={tick text odd padding={#1}},
+  stack/.default=1em,
+  stack'/.default=1em,
+  tick text at low/.is if=tikz@dv@min@tick@node,
+  tick text at high/.is if=tikz@dv@max@tick@node,
+  no tick text/.style={tick text at low=false,tick text at high=false},
+  every major ticks/.style={style={line cap=round},tick length=2pt},
+  every minor ticks/.style={style={solid, help lines,thin,line cap=round},tick length=1.4pt},
+  every subminor ticks/.style={style={solid, help lines,line cap=round},tick length=0.8pt},
+  clean ticks/.style={node style={fill=white}},
+  every grid/.style={high=max,low=min},
+  every major grid/.style={style={solid, help lines,thin,black!25}},
+  every minor grid/.style={style={solid, help lines,black!25}},
+  every subminor grid/.style={style={solid, help lines,black!10}},
+  at default ticks/.code={%
+    \expandafter\pgfkeysalso\expandafter{\tikz@lib@dv@ticks@default@at}},
+  at ticks/.code={%
+    \expandafter\pgfkeysalso\expandafter{\tikz@lib@dv@ticks@default@at}%
+    \expandafter\pgfkeysalso\expandafter{\tikz@lib@dv@ticks@at}},
+}%
+
+\def\tikz@lib@dv@add@#1#2{\pgfkeysaddvalue{/tikz/data visualization/#1}{}{,#2}}%
+
+\def\tikz@dv@lib@parse@scaling#1 at#2and #3 at#4\pgf@stop{%
+  \pgfmathsetmacro{\tikz@dv@lib@min@at}{#2}
+  \pgfmathsetmacro{\tikz@dv@lib@max@at}{#4}
+  \edef\tikz@temp{#1 at \tikz@dv@lib@min@at and #3 at \tikz@dv@lib@max@at}%
+}%
+
+
+\tikzdatavisualizationset{
+  at/.code={\def\tikz@dv@at@list{#1}},
+  also at/.code={\expandafter\def\expandafter\tikz@dv@at@list\expandafter{\tikz@dv@at@list,#1}},
+  major at/.style={major={at={#1}}},
+  minor at/.style={minor={at={#1}}},
+  subminor at/.style={subminor={at={#1}}},
+  major also at/.style={major={also at={#1}}},
+  minor also at/.style={minor={also at={#1}}},
+  subminor also at/.style={subminor={also at={#1}}},
+  options at/.code={\expandafter\def\expandafter\tikz@dv@style@at@list\expandafter{\tikz@dv@style@at@list,{#1}}},
+  no tick text at/.style={options at={#1 as [no tick text]}}
+}%
+
+
+\def\tikz@lib@dv@do@axis#1{%
+  \def\tikz@marshal{#1=}
+  \expandafter\expandafter\expandafter\tikzdatavisualizationset%
+  \expandafter\expandafter\expandafter{\expandafter\tikz@marshal\expandafter{\tikz@lib@dv@args}}
+}%
+
+\def\tikz@do@axis@options#1#2{
+  \pgfkeys{/tikz/data visualization/axis options/.cd,#2}
+  \def\tikz@dv@axis{#1}
+}%
+\let\tikz@dv@axis\pgfutil@empty
+
+\tikzdatavisualizationset{
+  every ticks/.style={
+    node style={%
+      font=\pgfutil@font@footnotesize,
+      inner sep=1pt,
+      outer sep=.1666em,
+      rounded corners=1.5pt
+    }
+  },
+  every data set label/.style={
+    every ticks,
+    node style={
+      font=\pgfutil@font@small,
+    }
+  },
+  @color of visualizer labels/.style={text=black},
+  every label in legend/.style={
+    node style={
+      fill=none,
+    }
+  },
+  every axis label/.style={
+    node style={%
+      font=\pgfutil@font@small,
+    }
+  }
+}%
+
+
+\tikzset{
+  /tikz/data visualization/axis options/.cd,
+  attribute/.style={\tikz@dv@axis/attribute={#1}},
+  function/.style={\tikz@dv@axis/function={#1}},
+  scaling/.style={\tikz@dv@axis/scaling={#1}},
+  padding min/.style={\tikz@dv@axis/padding min={#1}},
+  padding max/.style={\tikz@dv@axis/padding max={#1}},
+  padding/.style={padding min={-#1},padding max={#1}},
+  label/.code={%
+    \def\pgf@temp{#1}%
+    \ifx\pgf@temp\tikz@lib@dv@auto@attribute%
+      \tikzdatavisualizationset{\tikz@dv@axis/label/.expanded=$\noexpand\mathit{\pgfkeysvalueof{\tikz@dv@axis/attribute}}$}%
+    \else
+      \tikzdatavisualizationset{\tikz@dv@axis/label={#1}}%
+    \fi
+  },
+  label/.default=\tikz@lib@dv@auto@attribute,
+  tick placement strategy/.style={\tikz@dv@axis/@compute at positions={#1}},
+  linear steps/.style={tick placement strategy=\tikz@lib@dv@compute@at@linear},
+  goto/.code={\tikz@dv@goto{\tikz@dv@axis}{#1}},
+  goto pos/.code={\tikz@dv@goto@pos{\tikz@dv@axis}{#1}},
+  anchor at min/.code={\tikz@lib@dv@special@at{\tikz@dv@axis}{\tikz@dv@min@anchor}},
+  anchor at max/.code={\tikz@lib@dv@special@at{\tikz@dv@axis}{\tikz@dv@max@anchor}},
+  visualize axis/.code=\expandafter\tikz@lib@dv@av\expandafter{\tikz@dv@axis}{#1},
+  ticks/.style={\tikz@dv@axis/ticks at/.append={,#1}},
+  ticks/.default=some,
+  visualize ticks/.code=\expandafter\tikz@lib@dv@tv\expandafter{\tikz@dv@axis}{#1},
+  grid/.style={\tikz@dv@axis/grid at/.append={,#1}},
+  grid/.default=at default ticks,
+  visualize grid/.code=\expandafter\tikz@lib@dv@gv\expandafter{\tikz@dv@axis}{#1},
+  ticks and grid/.style={\tikz@dv@axis/ticks at/.append={,#1},\tikz@dv@axis/grid at/.append={,#1}},
+  visualize label/.code=\expandafter\tikz@lib@dv@lv\expandafter{\tikz@dv@axis}{#1},
+}%
+
+\def\tikz@lib@dv@auto@attribute{\tikz@lib@dv@auto@attribute}%
+
+
+\tikzdatavisualizationset{
+  axis options/.cd,
+  include value/.style={%
+    /tikz/data visualization/before survey/.expanded={%
+      \noexpand\pgfkeysgetvalue{\tikz@dv@axis/scaling mapper}\noexpand\tikz@dv@axis@mapper%
+      \noexpand\foreach \noexpand\tikz@lib@dv@temp in {#1} {%
+        \noexpand\tikz@dv@axis@mapper.include in value(\noexpand\tikz@lib@dv@temp)%
+      }%
+    }%
+  },
+  min value/.style={
+    /tikz/data visualization/at end survey/.expanded={%
+      \noexpand\pgfkeysgetvalue{\tikz@dv@axis/scaling mapper}\noexpand\tikz@dv@axis@mapper%
+      \noexpand\tikz@lib@dv@set\noexpand\tikz@dv@axis@mapper{#1}{min}%
+    }
+  },
+  max value/.style={
+    /tikz/data visualization/at end survey/.expanded={%
+      \noexpand\pgfkeysgetvalue{\tikz@dv@axis/scaling mapper}\noexpand\tikz@dv@axis@mapper%
+      \noexpand\tikz@lib@dv@set\noexpand\tikz@dv@axis@mapper{#1}{max}%
+    }
+  },
+}%
+
+\def\tikz@lib@dv@set#1#2#3{%
+  \pgfdvmathenter{\pgf@dv@value}{#2}%
+  #1.get in range interval()%
+  \pgfdvinrangeinterval.let #3(\pgf@dv@value)%
+}%
+
+\tikzdatavisualizationset{
+  axis layer/.style=on background layer,
+  ticks layer/.style=on background layer,
+  ticks node layer/.style=,
+  grid layer/.style=on background layer,
+}%
+
+
+
+\def\tikz@lib@dv@av#1#2{
+  \tikzdatavisualizationset{
+    axes actions/.append={\tikz@lib@dv@show@axis{#1}{#2}}
+  }
+}%
+
+\def\tikz@lib@dv@show@axis#1#2{%
+  \scope[data visualization/axis layer,/tikz/data visualization/.cd,low=min,high=max,every axis/.try,#2]
+    \pgfkeysgetvalue{#1/scaling mapper}\tikz@dv@axis@mapper%
+    \tikzpointandanchordirection{\tikz@dv@axis@mapper.set in to(min)}{\tikz@dv@axis@mapper.set in to(max)}
+    \xdef\tikz@dv@axis@dir{\noexpand\pgfqpoint{\the\pgf@x}{\the\pgf@y}}
+    \path[draw,/tikz/data visualization/styling]
+    \pgfextra{
+      {
+        \tikz@dv@goto{#1}{\pgfkeysvalueof{/tikz/data visualization/low}}%
+        \pgfpathdvmoveto%
+      }
+      {
+        \tikz@dv@goto{#1}{\pgfkeysvalueof{/tikz/data visualization/high}}%
+        \pgfpathdvlineto%
+      }
+    };
+  \endscope
+}%
+
+\def\tikz@dv@goto#1#2{%
+  \edef\pgf@@temp{#2}%
+  \ifx\pgf@@temp\tikz@lib@dv@padded@min@text%
+    \pgfkeysvalueof{#1/scaling mapper}.set in to(min)%
+    \pgfkeysvalueof{#1/scaling mapper}.get out()%
+    \pgfkeysgetvalue{#1/padding min}\pgf@temp%
+    \pgfmathparse{\pgf@temp}%
+    \pgfkeyslet{/data point/\pgfdvout/offset}\pgfmathresult%
+  \else%
+    \ifx\pgf@@temp\tikz@lib@dv@padded@max@text%
+      \pgfkeysvalueof{#1/scaling mapper}.set in to(max)%
+      \pgfkeysvalueof{#1/scaling mapper}.get out()%
+      \pgfkeysgetvalue{#1/padding max}\pgf@temp%
+      \pgfmathparse{\pgf@temp}%
+      \pgfkeyslet{/data point/\pgfdvout/offset}\pgfmathresult%
+    \else%
+      \pgfkeysvalueof{#1/scaling mapper}.set in to(#2)%
+    \fi%
+  \fi%
+}%
+
+\def\tikz@dv@goto@pos#1#2{%
+  \pgfkeyssetvalue{/data point/\pgfkeysvalueof{#1/attribute}/out pos}{#2}%
+}%
+
+\def\tikz@lib@dv@padded@min@text{padded min}%
+\def\tikz@lib@dv@padded@max@text{padded max}%
+
+\def\tikz@lib@dv@special@at#1#2{%
+  \tikzpointandanchordirection{\pgfkeysvalueof{#1/scaling mapper}.set in to(min)}{\pgfkeysvalueof{#1/scaling mapper}.set in to(max)}
+  \tikzset{anchor/.expanded={#2}}
+}%
+
+
+
+\def\tikz@lib@dv@tv#1#2{
+  \tikzdatavisualizationset{
+    ticks actions/.append={\tikz@lib@dv@default@action{ticks}{#1}{#2}},
+    major ticks actions/.append={\tikz@lib@dv@show@ticks{major}{#1}{#2}},
+    minor ticks actions/.append={\tikz@lib@dv@show@ticks{minor}{#1}{#2}},
+    subminor ticks actions/.append={\tikz@lib@dv@show@ticks{subminor}{#1}{#2}}
+  }
+}%
+
+\def\tikz@lib@dv@default@action#1#2#3{%
+  \let\tikz@marshal\pgfutil@empty%
+  {%
+    \let\tikz@lib@dv@ticks@at\pgfutil@empty%
+    \pgfkeysgetvalue{#2/ticks at}\tikz@lib@dv@ticks@default@at%
+    \pgfkeysgetvalue{#2/#1 at}\tikz@lib@dv@settings%
+    \pgfkeysgetvalue{#2/scaling mapper}\tikz@lib@dv@mapper
+    \tikzdatavisualizationset{major/.code=,minor/.code=,subminor/.code=,common/.code=}
+    \expandafter\tikzdatavisualizationset\expandafter{\tikz@lib@dv@settings}%
+    \tikzdatavisualizationset{@setup at setters}%
+    \pgfkeysgetvalue{/tikz/data visualization/compute step}\tikz@temp@step%
+    \ifx\tikz@temp@step\pgfutil@empty%
+    \else%
+      \pgfkeysvalueof{#2/@compute at positions}%
+      \xdef\tikz@marshal{
+        major={\pgfkeysvalueof{/tikz/data visualization/major}},
+        minor={\pgfkeysvalueof{/tikz/data visualization/minor}},
+        subminor={\pgfkeysvalueof{/tikz/data visualization/subminor}}}
+    \fi
+  }%
+  \pgfkeyslet{#2/default #1 at}\tikz@marshal
+}%
+
+\def\tikz@lib@dv@show@ticks#1#2#3{%
+  \pgfkeysgetvalue{#2/default ticks at}\tikz@lib@dv@default@settings%
+  \ifx\tikz@lib@dv@default@settings\pgfutil@empty%
+    \pgfkeysgetvalue{#2/ticks at}\tikz@lib@dv@settings%
+  \else%
+    \pgfkeysgetvalue{#2/ticks at}\tikz@lib@dv@settings%
+    \expandafter\expandafter\expandafter\def%
+    \expandafter\expandafter\expandafter\tikz@lib@dv@settings%
+    \expandafter\expandafter\expandafter{\expandafter\tikz@lib@dv@default@settings\expandafter,\tikz@lib@dv@settings}
+  \fi%
+  \ifx\tikz@lib@dv@settings\pgfutil@empty%
+  \else
+    {%
+      \let\tikz@dv@at@list\pgfutil@empty%
+      \let\tikz@dv@style@at@list\pgfutil@empty%
+      \pgfkeysgetvalue{#2/scaling mapper}\tikz@lib@dv@mapper
+      \scope[/tikz/data visualization/.cd,every ticks/.try,every #1 ticks/.try,#3]%
+        \expandafter\tikzdatavisualizationset\expandafter{\tikz@lib@dv@settings}%
+        \pgfkeysgetvalue{/tikz/data visualization/common}\tikz@temp
+        \expandafter\tikzdatavisualizationset\expandafter{\tikz@temp}
+        \pgfkeysgetvalue{/tikz/data visualization/#1}\tikz@temp
+        \expandafter\tikzdatavisualizationset\expandafter{\tikz@temp}
+        \pgfkeysgetvalue{/tikz/data visualization/\pgfkeysvalueof{/tikz/data visualization/direction axis}/scaling mapper}\pgf@dv@tick@dir@mapper
+        \foreach \tikz@dv@tick@pos[count=\tikz@dv@tick@count] in \tikz@dv@at@list
+        {
+          \ifx\tikz@dv@tick@pos\pgfutil@empty
+            \c@pgf@counta=\tikz@dv@tick@count\relax%
+            \advance\c@pgf@counta by-1\relax%
+            \edef\tikz@dv@tick@count{\the\c@pgf@counta}%
+          \else
+            \expandafter\tikz@lib@dv@parse\tikz@dv@tick@pos\pgf@stop%
+            \expandafter\tikzdatavisualizationset\expandafter{\tikz@lib@dv@tick@opt}%
+            \tikz@lib@dv@mapper.set in to(\tikz@dv@tick@pos)%
+            \pgf@process{\pgfpointdvlocaldatapoint}
+            \xdef\pgf@dv@tick@origin{\noexpand\pgfqpoint{\the\pgf@x}{\the\pgf@y}}
+            \tikzpointandanchordirection{\pgf@dv@tick@dir@mapper.set in to(min)}{\pgf@dv@tick@dir@mapper.set in to(max)}
+            \xdef\pgf@dv@tick@dir{\noexpand\pgfqpoint{\the\pgf@x}{\the\pgf@y}}
+            \tikz@lib@handle@at@style%
+            \pgfkeysgetvalue{/tikz/data visualization/high}\tikz@dv@max@val%
+            \pgfkeysgetvalue{/tikz/data visualization/low}\tikz@dv@min@val%
+            \iftikz@dv@max@tick@node\pgfmathsetmacro\tikz@dv@max@val{%
+              \tikz@dv@max@val+(\pgfkeysvalueof{%
+                /tikz/data  visualization/tick text high
+                \ifodd\tikz@dv@tick@count odd \else even \fi padding}%
+              )}%
+            \fi%
+            \iftikz@dv@min@tick@node\pgfmathsetmacro\tikz@dv@min@val{%
+              \tikz@dv@min@val+(\pgfkeysvalueof{%
+                /tikz/data  visualization/tick text low
+                \ifodd\tikz@dv@tick@count odd \else even \fi padding}%
+              )}%
+            \fi%
+            \pgf@process{\pgfpointadd{\pgf@dv@tick@origin}{\pgfpointscale{\tikz@dv@max@val}{\pgf@dv@tick@dir}}}
+            \xdef\tikz@dv@max@tick{\the\pgf@x,\the\pgf@y}
+            \pgf@process{\pgfpointadd{\pgf@dv@tick@origin}{\pgfpointscale{\tikz@dv@min@val}{\pgf@dv@tick@dir}}}
+            \xdef\tikz@dv@min@tick{\the\pgf@x,\the\pgf@y}
+            \scope[data visualization/ticks layer]
+              \tikzdatavisualizationset{every \ifodd\tikz@dv@tick@count odd \else even \fi tick/.try}
+              \draw [/tikz/data visualization/styling] (\tikz@dv@min@tick) -- (\tikz@dv@max@tick);
+            \endscope
+            \iftikz@dv@min@tick@node
+              \scope[data visualization/ticks node layer]
+                \tikzdatavisualizationset{every \ifodd\tikz@dv@tick@count odd \else even \fi tick/.try}
+                \path [/tikz/data visualization/styling] (\tikz@dv@min@tick) \tikz@dv@handle@tick{\tikz@dv@min@anchor};
+              \endscope
+            \fi
+            \iftikz@dv@max@tick@node
+              \scope[data visualization/ticks node layer]
+                \tikzdatavisualizationset{every \ifodd\tikz@dv@tick@count odd \else even \fi tick/.try}
+                \path [/tikz/data visualization/styling] (\tikz@dv@max@tick)   \tikz@dv@handle@tick{\tikz@dv@max@anchor};
+              \endscope
+            \fi
+          \fi
+        }
+      \endscope
+    }
+  \fi
+}%
+
+\def\tikz@lib@dv@parse#1\pgf@stop{%
+  \pgfutil@in@{as}{#1}%
+  \ifpgfutil@in@%
+    \tikz@lib@dv@parse@as#1\pgf@stop%
+  \else%
+    \tikz@lib@dv@parse@as#1as\tikz@lib@dv@typeset\pgf@stop%
+  \fi%
+}%
+\def\tikz@lib@dv@parse@as#1as{%
+  \def\tikz@dv@tick@pos{#1}%
+  \pgfutil@ifnextchar[{\tikz@lib@dv@parse@as@opt}{\tikz@lib@dv@parse@as@opt[]}%
+}%
+\def\tikz@lib@dv@parse@as@opt[#1]{%
+  \def\tikz@lib@dv@tick@opt{#1}%
+  \pgfutil@ifnextchar\pgf@stop{\tikz@lib@dv@parse@as@text\tikz@lib@dv@typeset}{\tikz@lib@dv@parse@as@text}
+}%
+\def\tikz@lib@dv@parse@as@text#1\pgf@stop{%
+  \def\tikz@lib@dv@tick@text{#1}%
+}%
+
+\def\tikz@lib@dv@typeset{%
+  \pgfdvmathenter{\tikz@lib@dv@typesetnum}{\tikz@dv@tick@pos}%
+  \pgfdvmathexitbyscientificformat{\tikz@lib@dv@typesetnum}{\tikz@lib@dv@typesetnum}%
+  \pgfkeysvalueof{/tikz/data visualization/tick prefix}%
+  \pgfkeys{/tikz/data visualization/tick typesetter=\tikz@lib@dv@typesetnum}%
+  \pgfkeysvalueof{/tikz/data visualization/tick suffix}%
+}%
+
+\newif\iftikz@dv@min@tick@node
+\newif\iftikz@dv@max@tick@node
+
+\def\tikz@dv@handle@tick#1{%
+  \pgfextra{
+    \ifx\tikz@lib@dv@tick@text\pgfutil@empty%
+      \global\let\tikz@dv@tick@marshal=\pgfutil@empty%
+    \else
+      \def\tikz@dv@tick@marshal{node[anchor=#1,/tikz/data visualization/node styling]}%
+      \expandafter\pgfutil@g@addto@macro\expandafter\tikz@dv@tick@marshal\expandafter{\expandafter{\tikz@lib@dv@tick@text}}
+    \fi
+  \expandafter}%
+  \tikz@dv@tick@marshal
+}%
+
+
+\def\tikz@lib@handle@at@style{%
+  \ifx\tikz@dv@style@at@list\pgfutil@empty%
+  \else%
+    \let\tikz@dv@lib@this@at@style=\pgfutil@empty%
+    \pgfdvmathenter{\tikz@temp}{\tikz@dv@tick@pos}%
+    \pgfdvmathexitbyscientificformat{\tikz@dv@compare@to}{\tikz@temp}%
+    \foreach \tikz@dv@at@style in \tikz@dv@style@at@list {%
+      \ifx\tikz@dv@at@style\pgfutil@empty%
+      \else%
+        \expandafter\tikz@dv@lib@handle@one@at@style\tikz@dv@at@style\tikz@stop%
+      \fi%
+    }
+    \ifx\tikz@dv@lib@this@at@style\pgfutil@empty%
+    \else%
+      \expandafter\tikzdatavisualizationset\expandafter{\tikz@dv@lib@this@at@style}%
+    \fi%
+  \fi%
+}%
+
+\def\tikz@dv@lib@handle@one@at@style#1as#2[#3]#4\tikz@stop{%
+  \pgfdvmathenter{\tikz@lib@dv@at@math@var}{#1}%
+  \pgfdvmathexitbyscientificformat{\tikz@dv@temp}{\tikz@lib@dv@at@math@var}%
+  \ifx\tikz@dv@temp\tikz@dv@compare@to%
+    \expandafter\gdef\expandafter\tikz@dv@lib@this@at@style\expandafter{\tikz@dv@lib@this@at@style,#3}%
+  \fi%
+}%
+
+
+\def\tikzpointandanchordirection#1#2{%
+  \pgf@process{\pgfpointdvdirection{#1}{#2}}
+  {
+    \pgf@ya=\pgf@y
+    \pgf@y=-\pgf@x
+    \pgf@x=\pgf@ya
+    \tikz@auto@anchor
+    \xdef\tikz@dv@max@anchor{\tikz@anchor}
+    \tikz@auto@anchor@prime
+    \xdef\tikz@dv@min@anchor{\tikz@anchor}
+  }
+}%
+
+
+
+
+
+\def\tikz@lib@dv@gv#1#2{
+  \tikzdatavisualizationset{
+    grid actions/.append={\tikz@lib@dv@default@action{grid}{#1}{#2}},
+    major grid actions/.append={\tikz@lib@dv@show@grid{major}{#1}{#2}},
+    minor grid actions/.append={\tikz@lib@dv@show@grid{minor}{#1}{#2}},
+    subminor grid actions/.append={\tikz@lib@dv@show@grid{subminor}{#1}{#2}},
+  }
+}%
+
+\def\tikz@lib@dv@show@grid#1#2#3{%
+  \pgfkeysgetvalue{#2/default grid at}\tikz@lib@dv@default@settings%
+  \ifx\tikz@lib@dv@default@settings\pgfutil@empty%
+    \pgfkeysgetvalue{#2/grid at}\tikz@lib@dv@settings%
+  \else%
+    \pgfkeysgetvalue{#2/grid at}\tikz@lib@dv@settings%
+    \expandafter\expandafter\expandafter\def%
+    \expandafter\expandafter\expandafter\tikz@lib@dv@settings%
+    \expandafter\expandafter\expandafter{\expandafter\tikz@lib@dv@default@settings\expandafter,\tikz@lib@dv@settings}
+  \fi%
+  \ifx\tikz@lib@dv@settings\pgfutil@empty%
+  \else
+    {%
+      \let\tikz@dv@at@list\pgfutil@empty
+      \let\tikz@dv@style@at@list\pgfutil@empty
+      \pgfkeysgetvalue{#2/scaling mapper}\tikz@lib@dv@mapper
+      \let\tikz@lib@dv@ticks@default@at\pgfutil@empty%
+      \scope[data visualization/grid layer,/tikz/data visualization/.cd,every #1 grid/.try,every grid,#3]
+        \pgfkeysgetvalue{#2/ticks at}\tikz@lib@dv@ticks@at%
+        \expandafter\tikzdatavisualizationset\expandafter{\tikz@lib@dv@settings}%
+        \pgfkeysgetvalue{/tikz/data visualization/common}\tikz@temp
+        \expandafter\tikzdatavisualizationset\expandafter{\tikz@temp}
+        \pgfkeysgetvalue{/tikz/data visualization/#1}\tikz@temp
+        \expandafter\tikzdatavisualizationset\expandafter{\tikz@temp}
+        \edef\tikz@lib@dv@dir@axis{/tikz/data visualization/\pgfkeysvalueof{/tikz/data visualization/direction axis}}%
+        \foreach \tikz@dv@grid@pos in \tikz@dv@at@list
+        {
+          \ifx\tikz@dv@grid@pos\pgfutil@empty
+          \else
+            \expandafter\tikz@lib@dv@parse\tikz@dv@grid@pos\pgf@stop%
+            \expandafter\tikzdatavisualizationset\expandafter{\tikz@lib@dv@tick@opt}%
+            \tikz@lib@dv@mapper.set in to(\tikz@dv@tick@pos)%
+            \draw[/tikz/data visualization/styling]
+              \pgfextra{
+                \tikz@dv@goto{\tikz@lib@dv@dir@axis}{\pgfkeysvalueof{/tikz/data visualization/low}}%
+                \pgfpathdvmoveto%
+                \tikz@dv@goto{\tikz@lib@dv@dir@axis}{\pgfkeysvalueof{/tikz/data visualization/high}}%
+                \pgfpathdvlineto%
+              };
+          \fi
+        }
+      \endscope
+    }
+  \fi
+}%
+
+
+
+
+
+
+
+
+
+
+\def\tikz@lib@dv@lv#1#2{
+  \tikzdatavisualizationset{
+    label actions/.append={\tikz@lib@dv@show@label{#1}{#2}}
+  }
+}%
+
+\def\tikz@lib@dv@show@label#1#2{%
+  \pgfkeysgetvalue{#1/label}\tikz@dv@lib@label%
+  \ifx\tikz@dv@lib@label\pgfutil@empty%
+  \else
+    \scope[anchor=center,/tikz/data visualization/.cd,every axis label/.try,#2]
+      \expandafter\tikz@lib@dv@parse@node\tikz@dv@lib@label\pgf@stop
+    \endscope
+  \fi
+}%
+
+\def\tikz@lib@dv@parse@node{\pgfutil@ifnextchar[\tikz@lib@dv@parse@node@opt{\tikz@lib@dv@parse@node@opt[]}}%
+\def\tikz@lib@dv@parse@node@opt[#1]#2\pgf@stop{
+  \tikzdatavisualizationset{#1}
+  \pgftransformshift{\pgfpointdvlocaldatapoint}%
+  \node [/tikz/data visualization/node styling] {#2};
+}%
+
+
+
+
+\tikzdatavisualizationset{
+  compute step/.initial=,
+  step/.style={compute step=\def\tikz@lib@dv@step{#1}},
+  minor steps between steps/.initial=,
+  minor steps between steps/.default=9,
+  phase/.initial=0,
+  tick typesetter/.code=\pgfmathprintnumber{#1},
+  tick prefix/.initial=,
+  tick suffix/.initial=,
+  tick unit/.style={tick suffix={$\,\pgfutil@font@normalfont#1$}},%
+}%
+
+\def\tikz@lib@dv@compute@at@linear{%
+  \let\tikz@lib@dv@compute@about=\tikz@lib@dv@about@linear%
+  \let\tikz@lib@dv@step\relax%
+  \pgfkeysvalueof{/tikz/data visualization/compute step}
+  \ifx\tikz@lib@dv@step\relax%
+  \else%
+    \tikz@lib@dv@mapper.get in range interval()%
+    \pgfdvinrangeinterval.get min and max()%
+    \pgfkeysgetvalue{/tikz/data visualization/phase}\tikz@temp
+    \pgfdvmathenter{\tikz@dv@lib@phase}{\tikz@temp}
+    \pgfdvmathenter{\tikz@dv@lib@step}{\tikz@lib@dv@step}
+    \pgfdvmathifless{\pgfdvmathalwayszero}{\tikz@dv@lib@step}{%
+      \pgfdvmathsub{\tikz@dv@lib@temp}{\pgfdvmin}{\tikz@dv@lib@phase}%
+      \pgfdvmathdiv{\tikz@dv@lib@temp}{\tikz@dv@lib@temp}{\tikz@dv@lib@step}%
+      \pgfdvmathfloor{\tikz@dv@lib@temp}{\tikz@dv@lib@temp}%
+      \pgfdvmathmul{\tikz@lib@dv@current}{\tikz@dv@lib@temp}{\tikz@dv@lib@step}%
+      \pgfdvmathadd{\tikz@lib@dv@current}{\tikz@lib@dv@current}{\tikz@dv@lib@phase}%
+      \let\tikz@lib@dv@ats\pgfutil@empty%
+      \let\tikz@lib@dv@minor@ats\pgfutil@empty%
+      \tikz@lib@dv@mapper.get function(\tikz@temp)%
+      \ifx\tikz@temp\pgfutil@empty%
+        \pgfdvmathenter{\tikz@one@hundreth}{0.001}%
+        \pgfdvmathsub{\tikz@lib@temp}{\pgfdvmax}{\pgfdvmin}%
+        \pgfdvmathmul{\tikz@lib@dv@epsilon}{\tikz@lib@temp}{\tikz@one@hundreth}%
+      \else
+        \let\tikz@lib@dv@epsilon\pgfdvmathalwayszero
+      \fi
+      \pgfdvmathsub{\tikz@lib@dv@min@minus@epsilon}{\pgfdvmin}{\tikz@lib@dv@epsilon}%
+      \pgfdvmathadd{\tikz@lib@dv@max@plus@epsilon}{\pgfdvmax}{\tikz@lib@dv@epsilon}%
+      \pgfkeysgetvalue{/tikz/data visualization/minor steps between steps}\tikz@lib@dv@substeps%
+      \ifx\tikz@lib@dv@substeps\pgfutil@empty
+      \else
+        \pgfmathsetmacro\tikz@temp{\tikz@lib@dv@substeps+1}%
+        \pgfdvmathenter{\tikz@dv@lib@substeps}{\tikz@temp}%
+        \pgfdvmathdiv{\tikz@lib@dv@substep}{\tikz@dv@lib@step}{\tikz@dv@lib@substeps}%
+      \fi
+      \loop%
+        \ifx\tikz@lib@dv@substeps\pgfutil@empty%
+        \else%
+          \let\tikz@lib@dv@subcurrent=\tikz@lib@dv@current%
+          \pgfmathsetcount{\c@pgf@counta}{\tikz@lib@dv@substeps}%
+          \let\tikz@lib@dv@next=\tikz@lib@dv@subloop%
+          \tikz@lib@dv@subloop
+        \fi%
+        \pgfdvmathifless{\tikz@lib@dv@current}{\tikz@lib@dv@min@minus@epsilon}{}{%
+          \pgfdvmathexitbyserializing{\tikz@temp}{\tikz@lib@dv@current}%
+          \edef\tikz@lib@dv@ats{\tikz@lib@dv@ats,\tikz@temp}%
+        }
+        \pgfdvmathadd{\tikz@lib@dv@current}{\tikz@lib@dv@current}{\tikz@dv@lib@step}%
+        \pgfdvmathifless{\tikz@lib@dv@current}{\tikz@lib@dv@max@plus@epsilon}{\tikz@lib@dv@continuetrue}{\tikz@lib@dv@continuefalse}%
+      \iftikz@lib@dv@continue%
+      \repeat%
+      \tikzdatavisualizationset{major/.expanded={at={\tikz@lib@dv@ats}},minor/.expanded={at={\tikz@lib@dv@minor@ats}}}%
+    }{%
+      \pgfdvmathexitbyserializing{\tikz@temp}{\pgfdvmin}%
+      \tikzdatavisualizationset{major/.expanded={at={\tikz@temp}}}%
+    }%
+  \fi%
+}%
+\newif\iftikz@lib@dv@continue
+
+\def\tikz@lib@dv@subloop{
+  \pgfdvmathadd{\tikz@lib@dv@subcurrent}{\tikz@lib@dv@subcurrent}{\tikz@lib@dv@substep}%
+  \pgfdvmathifless{\tikz@lib@dv@subcurrent}{\pgfdvmin}{}{%
+    \pgfdvmathifless{\tikz@lib@dv@subcurrent}{\pgfdvmax}{%
+      \pgfdvmathexitbyserializing{\tikz@temp}{\tikz@lib@dv@subcurrent}%
+      \edef\tikz@lib@dv@minor@ats{\tikz@lib@dv@minor@ats,\tikz@temp}
+      }{}}
+  \advance\c@pgf@counta by-1\relax%
+  \ifnum\c@pgf@counta=0\relax%
+    \let\tikz@lib@dv@next=\relax
+  \fi
+  \tikz@lib@dv@next
+}%
+
+
+
+
+\tikzdatavisualizationset{
+  about/.style={compute step=\tikz@lib@dv@compute@about{#1}},
+  about strategy/.initial=,
+  standard about strategy/.style={about strategy={1.5/1.0,2.3/2.0,4/2.5,7/5,11/10}},
+  standard about strategy,
+  euro about strategy/.style={about strategy={1.5/1.0,3/2.0,7/5,11/10}},
+  decimal about strategy/.style={about strategy={3/1.0,11/10}},
+  half about strategy/.style={about strategy={2/1.0,7/5,11/10}},
+  quarter about strategy/.style={about strategy={1.8/1.0,4/2.5,7/5,11/10}},
+  int about strategy/.style={about strategy={1.5/1.0,2.5/2.0,3.5/3.0,4.5/4.0,7/5,11/10}},
+  none/.style={compute step=},
+  few/.style={about=3},
+  some/.style={about=5},
+  many/.style={about=10},
+}%
+
+\def\tikz@lib@dv@about@linear#1{%
+  \tikz@lib@dv@mapper.get in range interval()%
+  \pgfdvinrangeinterval.get min and max()%
+  \pgfdvmathsub{\tikz@lib@dv@diff}{\pgfdvmax}{\pgfdvmin}
+  \pgfdvmathenter{\tikz@lib@dv@about@val}{#1}%
+  \pgfdvmathdiv{\tikz@lib@dv@around}{\tikz@lib@dv@diff}{\tikz@lib@dv@about@val}%
+  \pgfmathfloattomacro{\tikz@lib@dv@around}{\tikz@lib@dv@flags}{\tikz@lib@dv@mant}{\tikz@lib@dv@exp}%
+  \pgf@xc=\tikz@lib@dv@mant pt %
+  \pgfkeysgetvalue{/tikz/data visualization/about strategy}\tikz@lib@dv@strat
+  \foreach \tikz@lib@dv@threshold/\tikz@lib@replace in \tikz@lib@dv@strat
+  {
+    \ifdim\pgf@xc<\tikz@lib@dv@threshold pt%
+      \global\pgf@xc=\tikz@lib@replace pt%
+      \breakforeach
+    \fi
+  }%
+  \ifdim\pgf@xc<10pt%
+    \pgfmathfloatcreate{\tikz@lib@dv@flags}{\pgf@sys@tonumber{\pgf@xc}}{\tikz@lib@dv@exp}%
+  \else
+    \begingroup
+    \c@pgf@countd=\tikz@lib@dv@exp
+    \advance\c@pgf@countd by1
+    \edef\tikz@lib@dv@exp{\the\c@pgf@countd}%
+    \pgfmath@smuggleone\tikz@lib@dv@exp
+    \endgroup
+    \divide\pgf@xc by 10\relax
+    \pgfmathfloatcreate{\tikz@lib@dv@flags}{\pgf@sys@tonumber{\pgf@xc}}{\tikz@lib@dv@exp}%
+  \fi
+  \pgfmathfloattofixed{\pgfmathresult}%
+  \let\tikz@lib@dv@step=\pgfmathresult
+}%
+
+
+
+
+
+
+\tikzset{
+  /tikz/data visualization/axis options/.cd,
+  exponential steps/.style={tick placement strategy=\tikz@lib@dv@compute@at@log},
+  logarithmic/.style={
+    \tikz@dv@axis/function=\pgfdvmathln{\pgfvalue}{\pgfvalue},
+    \tikz@dv@axis/scaling/default=1 at 0 and 10 at 1,
+    exponential steps
+  }
+}%
+
+\def\tikz@lib@dv@compute@at@log{%
+  \let\tikz@lib@dv@compute@about=\tikz@lib@dv@about@log%
+  \let\tikz@lib@dv@step\relax%
+  \pgfkeysvalueof{/tikz/data visualization/compute step}
+  \ifx\tikz@lib@dv@step\relax%
+  \else%
+    \tikz@lib@dv@mapper.get in range interval()%
+    \pgfdvinrangeinterval.get min and max()%
+    \pgfdvmathlog{\pgfdvminlog}{\pgfdvmin}%
+    \pgfdvmathlog{\pgfdvmaxlog}{\pgfdvmax}%
+    \pgfkeysgetvalue{/tikz/data visualization/phase}\tikz@temp
+    \pgfdvmathenter{\tikz@dv@lib@phase}{\tikz@temp}
+    \pgfdvmathenter{\tikz@dv@lib@step}{\tikz@lib@dv@step}
+    \pgfdvmathsub{\tikz@dv@lib@temp}{\pgfdvminlog}{\tikz@dv@lib@phase}%
+    \pgfdvmathdiv{\tikz@dv@lib@temp}{\tikz@dv@lib@temp}{\tikz@dv@lib@step}%
+    \pgfdvmathfloor{\tikz@dv@lib@temp}{\tikz@dv@lib@temp}%
+    \pgfdvmathmul{\tikz@lib@dv@current}{\tikz@dv@lib@temp}{\tikz@dv@lib@step}%
+    \pgfdvmathadd{\tikz@lib@dv@current}{\tikz@lib@dv@current}{\tikz@dv@lib@phase}%
+    \let\tikz@lib@dv@ats\pgfutil@empty%
+    \let\tikz@lib@dv@minor@ats\pgfutil@empty%
+    \pgfdvmathenter{\tikz@one@hundreth}{0.001}%
+    \pgfdvmathsub{\tikz@lib@temp}{\pgfdvmaxlog}{\pgfdvminlog}%
+    \pgfdvmathmul{\tikz@lib@dv@epsilon}{\tikz@lib@temp}{\tikz@one@hundreth}%
+    \pgfdvmathsub{\tikz@lib@dv@min@minus@epsilon}{\pgfdvminlog}{\tikz@lib@dv@epsilon}%
+    \pgfdvmathadd{\tikz@lib@dv@max@plus@epsilon}{\pgfdvmaxlog}{\tikz@lib@dv@epsilon}%
+    \pgfkeysgetvalue{/tikz/data visualization/minor steps between steps}\tikz@lib@dv@substeps%
+    \ifx\tikz@lib@dv@substeps\pgfutil@empty
+    \else
+      \pgfmathsetmacro\tikz@temp{\tikz@lib@dv@substeps+1}%
+      \pgfdvmathenter{\tikz@dv@lib@substeps}{\tikz@temp}%
+    \fi
+    \loop%
+      \ifx\tikz@lib@dv@substeps\pgfutil@empty%
+      \else%
+        \let\tikz@lib@dv@subcurrent=\tikz@lib@dv@current%
+        \pgfdvmathadd{\tikz@lib@dv@subcurrent@next}{\tikz@lib@dv@subcurrent}{\tikz@dv@lib@step}%
+        \pgfdvmathpowten{\tikz@lib@dv@subcurrent}{\tikz@lib@dv@subcurrent}%
+        \pgfdvmathpowten{\tikz@lib@dv@subcurrent@max}{\tikz@lib@dv@subcurrent@next}%
+        \pgfdvmathsub{\tikz@lib@dv@subcurrent@diff}{\tikz@lib@dv@subcurrent@max}{\tikz@lib@dv@subcurrent}%
+        \pgfdvmathdiv{\tikz@lib@dv@substep}{\tikz@lib@dv@subcurrent@diff}{\tikz@dv@lib@substeps}%
+        \pgfmathsetcount{\c@pgf@counta}{\tikz@lib@dv@substeps}%
+        \let\tikz@lib@dv@next=\tikz@lib@dv@subloop%
+        \tikz@lib@dv@subloop
+      \fi%
+      \pgfdvmathifless{\tikz@lib@dv@current}{\tikz@lib@dv@min@minus@epsilon}{}{%
+        \pgfdvmathpowten{\tikz@lib@dv@current@pow}{\tikz@lib@dv@current}%
+        \pgfdvmathexitbyserializing{\tikz@temp}{\tikz@lib@dv@current@pow}%
+        \edef\tikz@lib@dv@ats{\tikz@lib@dv@ats,\tikz@temp}%
+      }
+      \pgfdvmathadd{\tikz@lib@dv@current}{\tikz@lib@dv@current}{\tikz@dv@lib@step}%
+      \pgfdvmathifless{\tikz@lib@dv@current}{\tikz@lib@dv@max@plus@epsilon}{\tikz@lib@dv@continuetrue}{\tikz@lib@dv@continuefalse}%
+      \iftikz@lib@dv@continue%
+    \repeat%
+    \tikzdatavisualizationset{major/.expanded={at={\tikz@lib@dv@ats}},minor/.expanded={at={\tikz@lib@dv@minor@ats}}}%
+  \fi%
+}%
+
+
+\def\tikz@lib@dv@about@log#1{%
+  \tikz@lib@dv@mapper.get in range interval()%
+  \pgfdvinrangeinterval.get min and max()%
+  \pgfdvmathlog{\pgfdvmin}{\pgfdvmin}%
+  \pgfdvmathlog{\pgfdvmax}{\pgfdvmax}%
+  \pgfdvmathsub{\tikz@lib@dv@diff}{\pgfdvmax}{\pgfdvmin}
+  \pgfdvmathenter{\tikz@lib@dv@about@val}{#1}%
+  \pgfdvmathdiv{\tikz@lib@dv@around}{\tikz@lib@dv@diff}{\tikz@lib@dv@about@val}%
+  \pgfmathfloattomacro{\tikz@lib@dv@around}{\tikz@lib@dv@flags}{\tikz@lib@dv@mant}{\tikz@lib@dv@exp}
+  \ifdim\tikz@lib@dv@exp pt<0pt%
+    \pgfmathfloatcreate{1}{1.0}{0}%
+  \else
+    \pgf@xc=\tikz@lib@dv@mant pt\relax%
+    \ifdim\pgf@xc<2.5pt
+      \pgfmathfloatcreate{1}{1.0}{\tikz@lib@dv@exp}
+    \else\ifdim\pgf@xc<5.1pt
+      \pgfmathfloatcreate{1}{3.0}{\tikz@lib@dv@exp}
+    \else
+      \pgfmathfloatcreate{1}{6.0}{\tikz@lib@dv@exp}
+    \fi\fi
+  \fi%
+  \pgfmathfloattofixed{\pgfmathresult}
+  \let\tikz@lib@dv@step=\pgfmathresult
+}%
+
+
+
+
+
+
+
+
+\tikzdatavisualizationset{%
+  new Cartesian axis/.style={
+    new axis base={#1},
+    new object={
+      class=linear transformer,
+      store=/tikz/data visualization/#1/linear transformer,
+      arg1/.expanded=\pgfkeysvalueof{/tikz/data visualization/#1/attribute}/scaled,
+      arg2 from key=/tikz/data visualization/#1/unit vector,
+    },
+    #1/scaling/default/.initial=0 at 0 and 1 at 1cm,
+    #1/unit vector/.initial=\pgfqpoint{1pt}{0pt},
+  }
+}%
+
+\tikzset{
+  /tikz/data visualization/axis options/.cd,
+  unit vector/.code=\tikz@scan@one@point\tikz@lib@dv@uv#1,
+  length/.style={\tikz@dv@axis/scaling=min at 0 and max at {#1}},
+  unit length/.code={\tikz@dv@parse@unit@length{#1}},
+  power unit length/.style={\tikz@dv@axis/scaling=1 at 0 and 10 at {#1}}
+}%
+
+\def\tikz@lib@dv@uv#1{%
+  \pgfkeyssetvalue{\tikz@dv@axis/unit vector}{#1}
+}%
+
+\def\tikz@dv@parse@unit@length#1{
+  \pgfutil@in@{per}{#1}
+  \ifpgfutil@in@%
+    \tikz@dv@parse@unit@length@#1\pgf@stop%
+  \else%
+    \tikz@dv@parse@unit@length@#1per1units\pgf@stop%
+  \fi%
+}%
+\def\tikz@dv@parse@unit@length@#1per#2units\pgf@stop{
+  \pgfkeysalso{\tikz@dv@axis/scaling=0 at 0 and {#2} at {#1}}
+}%
+
+
+
+\tikzdatavisualizationset{
+  new visualizer/.style n args={3}{
+    #1/.code={
+      \def\tikz@visualizer{#1}%
+      \pgfkeys{/tikz/data visualization/visualizer options/.cd,##1}
+      \pgf@dv@do@adddata{\pgfkeysvalueof{/pgf/data visualization/obj}.add data(\pgfkeys{/data point/set={#1}})}%
+    },
+    /utils/exec={
+      \advance\tikzdvvisualizercounter by 1\relax
+      \edef\tikz@temp{/data point/set/#1/.initial=\the\tikzdvvisualizercounter}
+      \expandafter\tikzset\expandafter{\tikz@temp}
+    },
+    /data point/#1/execute at begin/.initial={
+      \pgfkeyssetvalue{/data point/set}{#1}
+      \scope[
+        #2,
+        /tikz/data visualization/every visualizer/.try,
+        /tikz/data visualization/visualizers/#1/signal,
+        /tikz/data visualization/visualizers/#1/styling/.try]
+    },
+    /data point/#1/execute at end/.initial={
+        \path; %
+      \endscope
+    },
+    /tikz/data visualization/visualizers/#1/signal/.code=\pgf@signalstyle.emit(),
+    /tikz/data visualization/visualizers/#1/styling/.style=,
+    /tikz/data visualization/visualizers/#1/label in legend options/.style={#3},
+  },
+  style sheet/.style={/data point/set/.style sheet={#1}},
+  /pgf/data/set/.style={/data point/set={#1}},
+}%
+
+\tikzdatavisualizationset{
+  new sub visualizer/.style n args={4}{
+    #4/#1/.code={
+      \def\tikz@visualizer{#4/#1}%
+      \pgfkeys{/tikz/data visualization/visualizer options/.cd,##1}
+    },
+    /data point/#4/#1/execute at begin/.initial={
+      \pgfkeyssetvalue{/data point/set}{#4}
+      \scope[
+        #2,
+        /tikz/data visualization/every visualizer/.try,
+        /tikz/data visualization/visualizers/#4/signal,
+        /tikz/data visualization/visualizers/#4/styling/.try,
+        /tikz/data visualization/visualizers/#4/#1/styling/.try]
+    },
+    /data point/#4/#1/execute at end/.initial={
+        \path; %
+      \endscope
+    },
+    /tikz/data visualization/visualizers/#4/#1/styling/.style=,
+    /tikz/data visualization/visualizers/#4/#1/label in legend options/.style={#3},
+  }
+}%
+
+
+\def\tikz@do@visualizer#1#2{%
+  \tikzdatavisualizationset{
+    #2={#1}
+  }
+}%
+
+\newcount\tikzdvvisualizercounter
+
+\newif\iftikz@dv@visualizer@label@inline
+
+\tikzdatavisualizationset{visualizer options/.cd,
+  @set/.style 2 args={
+    /tikz/data visualization/visualizers/\tikz@visualizer/styling/.append style={/utils/exec={\let\tikz@dv@plot@handler=#1}},
+    /tikz/data visualization/visualizers/\tikz@visualizer/label in legend options/.append style={#2}
+  },
+  no lines/.style={@set={\pgfplothandlerdiscard}{default label in legend mark}},
+  smooth line/.style={@set={\pgfplothandlercurveto}{default label in legend path}},
+  smooth cycle/.style={@set={\pgfplothandlerclosedcurve}{default label in legend closed path}},
+  straight line/.style={@set={\pgfplothandlerlineto}{default label in legend path}},
+  straight cycle/.style={@set={\pgfplothandlerpolygon}{default label in legend closed path}},
+  polygon/.style={straight cycle},%
+  gap line/.style={@set={\pgfplothandlergaplineto}{default label in legend path}},
+  gap cycle/.style={@set={\pgfplothandlergapcycle}{gap circular label in legend line}}
+}%
+
+
+
+
+\tikzdatavisualizationset{
+  new label visualizer/.style 2 args={
+    new object={
+      when=before visualization,
+      class=label visualizer,
+      before creation={
+        \begingroup
+        \def\tikz@visualizer{#1}%
+        \pgfkeys{/tikz/data visualization/visualizer label options/.cd,
+          #2}
+        \pgfkeysgetvalue{/tikz/data visualization/visualizer label options/text}\tikz@dv@temp@lab
+        \def\tikz@tempa{
+          \scope[
+          /utils/exec=\def\tikz@visualizer{#1},%
+          /tikz/data visualization/visualizer label options/.cd,
+          #2]
+          \tikzdatavisualizationset{every data set label/.try}
+          \path [
+            /data point/set={#1},/utils/exec=\pgf@signalstyle.emit(),
+            /tikz/data visualization/.cd,every label in data/.try]
+          (label visualizer coordinate') --
+          (label visualizer coordinate)
+          node [
+            auto,
+            at end,
+            /tikz/data visualization/node styling]
+        }
+        \expandafter\def\expandafter\tikz@tempb\expandafter{\expandafter{\tikz@dv@temp@lab};}%
+        \expandafter\expandafter\expandafter\gdef%
+        \expandafter\expandafter\expandafter\tikz@dv@label@code%
+        \expandafter\expandafter\expandafter{\expandafter\expandafter\expandafter\relax%
+          \expandafter\expandafter\expandafter{\expandafter\tikz@tempa\tikz@tempb\endscope}}
+        \global\let\tikz@dv@label@attribute=\tikz@dv@label@attribute
+        \global\let\tikz@dv@label@threshold=\tikz@dv@label@threshold
+        \endgroup
+      },
+      arg1/.expand once=\tikz@dv@label@attribute,
+      arg2=\tikz@dv@label@threshold,
+      arg3/.expand once=\tikz@dv@label@code,
+      arg4=\pgfdvvisualizerfilter{#1}
+    },
+    /utils/exec=\tikz@create@label@count{#1}
+  },
+  text colored/.style={node style={text=visualizer color}}
+}%
+
+\def\tikz@create@label@count#1{
+  \tikzdatavisualizationset{
+    new object={
+      when=before survey,
+      store=/tikz/data visualization/visualizers/#1/count/obj,
+      class=count,
+      arg1=set/#1/count,
+      after creation={\tikzdvobj.set filter(\pgfdvvisualizerfilter{#1})}
+    }
+  }
+}%
+
+\pgfkeys{
+  /tikz/data visualization/visualizer label options/.cd,
+  when/.code args={#1 is#2}{%
+    \def\tikz@dv@label@attribute{#1}%
+    \def\tikz@dv@label@threshold{#2}%
+  },
+  index/.code={%
+    \edef\tikz@dv@label@attribute{set/\tikz@visualizer/count}%
+    \def\tikz@dv@label@threshold{#1}%
+  },
+  pos/.code={%
+    \edef\tikz@dv@label@attribute{set/\tikz@visualizer/count}%
+    \pgfkeysvalueof{/tikz/data visualization/visualizers/\tikz@visualizer/count/obj}.get max(\tikz@lib@max)
+    \edef\tikz@dv@label@threshold{(#1*\tikz@lib@max)}%
+  },
+  auto/.code={%
+    \edef\tikz@dv@label@attribute{set/\tikz@visualizer/count}%
+    \pgfkeysvalueof{/tikz/data visualization/visualizers/\tikz@visualizer/count/obj}.get max(\tikz@lib@max)
+    \edef\tikz@dv@label@threshold{({(\pgfkeysvalueof{/data point/set/\tikz@visualizer}-0.5)/\the\tikzdvvisualizercounter*\tikz@lib@max})}
+  },
+  text/.initial=,
+  text'/.style={text={#1},node style=swap,/utils/exec=\def\tikz@lib@dv@pin@sign{-}},
+  node style/.style={/tikz/data visualization/node style={#1}},
+  text colored/.style=/tikz/data visualization/text colored,
+  pin angle/.store in=\tikz@lib@dv@pin@dir,
+  pin length/.style={node style={pin distance={#1}}},
+}%
+
+\let\tikz@lib@dv@pin@sign\pgfutil@empty
+
+\let\tikz@dv@label@attribute\pgfutil@empty
+\let\tikz@dv@label@threshold\pgfutil@empty
+\let\tikz@dv@label@code\pgfutil@empty
+
+
+
+
+
+\tikzdatavisualizationset{
+  new legend/.code={
+    \pgfkeysifdefined{/tikz/data visualization/#1/at}{}
+    {\tikzdatavisualizationset{
+    new object={
+      class=legend,
+      store=/tikz/data visualization/#1/obj,
+      arg1 from key=/tikz/data visualization/#1/@columns or rows,
+      arg2 from key=/tikz/data visualization/#1/@ideal,
+      arg3 from key=/tikz/data visualization/#1/max entries,
+      arg4 from key=/tikz/data visualization/#1/@strategy,
+      after creation={
+        \tikzdatavisualizationset{
+          legend actions/.append={
+            \pgfkeysgetvalue{/tikz/data visualization/#1/obj}\pgf@dv@legend%
+            {
+              \pgf@dv@legend.get arrangement(\pgf@dv@temp)%
+              \pgfkeysgetvalue{/tikz/data visualization/#1/at}\pgf@dv@at%
+              \pgfkeysgetvalue{/tikz/data visualization/#1/anchor}\pgf@dv@anchor%
+              \let\pgfdvnextcell=\pgfmatrixnextcell%
+              \let\pgfdvendrow=\pgfmatrixendrow%
+              \def\pgf@marshal{
+                \matrix[at/.expand once=\pgf@dv@at,matrix anchor/.expand
+                once=\pgf@dv@anchor,/tikz/data visualization/#1/matrix node styling]
+              }
+              \expandafter\pgf@marshal\expandafter{\pgf@dv@temp};
+            }
+          }
+        }
+      }
+    },
+    #1/@columns or rows/.initial=columns,
+    #1/@ideal/.initial=1,
+    #1/max entries/.initial=100,
+    #1/@strategy/.initial=down then right,
+    #1/anchor/.initial=west,
+    #1/at/.initial=(data visualization bounding box.east),
+    #1/matrix node styling/.style={row sep=0pt,column sep=.8em},
+    #1/.code={
+      \let\tikz@temp\tikz@dv@legend%
+      \def\tikz@dv@legend{/tikz/data visualization/#1}%
+      \expandafter\tikz@do@legend@options\expandafter{\tikz@temp}{##1}%
+    },
+    #1={every new legend}
+  }}},
+  new legend/.default=main legend,
+  legend/.style={
+    new legend,
+    main legend={#1}
+  }
+}%
+
+\def\tikz@do@legend@options#1#2{
+  \pgfkeys{/tikz/data visualization/legend options/.cd,#2}
+  \def\tikz@dv@legend{#1}
+}%
+\let\tikz@dv@legend\pgfutil@empty
+
+
+\tikzset{
+  /tikz/data visualization/legend options/.cd,
+  ideal number of columns/.style={\tikz@dv@legend/@columns or rows=columns,\tikz@dv@legend/@ideal={#1}},
+  ideal number of rows/.style={\tikz@dv@legend/@columns or rows=rows,\tikz@dv@legend/@ideal={#1}},
+  columns/.style={ideal number of columns={#1}},%
+  rows/.style={ideal number of rows={#1}},%
+  max rows/.style={\tikz@dv@legend/@columns or rows=columns,\tikz@dv@legend/max entries={#1}},
+  max columns/.style={\tikz@dv@legend/@columns or rows=rows,\tikz@dv@legend/max entries={#1}},
+  down then right/.style={\tikz@dv@legend/@strategy=down then right},
+  down then left/.style={\tikz@dv@legend/@strategy=down then left},
+  up then right/.style={\tikz@dv@legend/@strategy=up then right},
+  up then left/.style={\tikz@dv@legend/@strategy=up then left},
+  right then down/.style={\tikz@dv@legend/@strategy=right then down},
+  left then down/.style={\tikz@dv@legend/@strategy=left then down},
+  right then up/.style={\tikz@dv@legend/@strategy=right then up},
+  left then up/.style={\tikz@dv@legend/@strategy=left then up},
+  anchor/.style={\tikz@dv@legend/anchor={#1}},
+  at/.style={\tikz@dv@legend/at={#1}},
+  right/.style={east outside},
+  left/.style={west outside},
+  above/.style={north outside},
+  below/.style={south outside},
+  east outside/.style={
+    columns=1,
+    at={([xshift=.8em]data visualization bounding box.east)},
+    anchor=west,
+  },
+  north east outside/.style={
+    columns=1,
+    at={([xshift=.8em]data visualization bounding box.north east|-
+      data bounding box.north)},
+    anchor=north west,
+  },
+  south east outside/.style={
+    columns=1,
+    at={([xshift=.8em]data visualization bounding box.south east |-
+      data bounding box.south)},
+    anchor=south west,
+  },
+  west outside/.style={
+    columns=1,
+    label style=text left,
+    at={([xshift=-.8em]data visualization bounding box.west)},
+    anchor=east,
+  },
+  north west outside/.style={
+    columns=1,
+    label style=text left,
+    at={([xshift=-.8em]data visualization bounding box.north west |-
+      data bounding box.north)},
+    anchor=north east,
+  },
+  south west outside/.style={
+    columns=1,
+    label style=text left,
+    at={([xshift=-.8em]data visualization bounding box.south west |-
+      data bounding box.south)},
+    anchor=south east,
+  },
+  south outside/.style={
+    rows=1,
+    at={([yshift=-.5em]data visualization bounding box.south)},
+    anchor=north,
+  },
+  north outside/.style={
+    rows=1,
+    at={([yshift=.5em]data visualization bounding box.north)},
+    anchor=south,
+  },
+  every new legend/.style={east outside,label style=text right},
+  every legend inside/.style={
+    opaque=white,
+    label style={node style={font=\pgfutil@font@footnotesize}}
+  },
+  opaque/.style={
+    matrix node style={
+      inner sep=.333ex,
+      outer sep=.5ex,
+      rounded corners=3pt,
+      execute at begin cell={\tikzset{sharp corners}}, %
+      fill=#1
+    },
+  },
+  opaque/.default=white,
+  transparent/.style={matrix node style={fill=none}},
+  north east inside/.style={
+    columns=1,
+    at={([xshift=-.3em]data bounding box.north east)},
+    anchor=north east,
+    every legend inside
+  },
+  south west inside/.style={
+    columns=1,
+    at={([xshift=.3em]data bounding box.south west)},
+    anchor=south west,
+    every legend inside
+  },
+  north west inside/.style={
+    columns=1,
+    at={([xshift=.3em]data bounding box.north west)},
+    anchor=north west,
+    every legend inside
+  },
+  south east inside/.style={
+    columns=1,
+    at={([xshift=-.3em]data bounding box.south east)},
+    anchor=south east,
+    every legend inside
+  },
+  west inside/.style={
+    columns=1,
+    at={([xshift=.3em]data bounding box.west)},
+    anchor=west,
+    every legend inside
+  },
+  east inside/.style={
+    columns=1,
+    at={([xshift=.3em]data bounding box.east)},
+    anchor=east,
+    every legend inside
+  },
+  north inside/.style={
+    rows=1,
+    at={(data bounding box.north)},
+    anchor=north,
+    every legend inside
+  },
+  south inside/.style={
+    rows=1,
+    at={(data bounding box.south)},
+    anchor=south,
+    every legend inside
+  },
+  at values/.style={
+    at={(visualization cs:#1)},
+    anchor=center,
+    every legend inside
+  },
+  right of/.style={
+    at={(visualization cs:#1)},
+    anchor=west,
+    every legend inside
+  },
+  left of/.style={
+    at={(visualization cs:#1)},
+    anchor=east,
+    every legend inside
+  },
+  above of/.style={
+    at={(visualization cs:#1)},
+    anchor=south,
+    every legend inside
+  },
+  below of/.style={
+    at={(visualization cs:#1)},
+    anchor=north,
+    every legend inside
+  },
+  above right of/.style={
+    at={(visualization cs:#1)},
+    anchor=south west,
+    every legend inside
+  },
+  above left of/.style={
+    at={(visualization cs:#1)},
+    anchor=south east,
+    every legend inside
+  },
+  below right of/.style={
+    at={(visualization cs:#1)},
+    anchor=north west,
+    every legend inside
+  },
+  below left of/.style={
+    at={(visualization cs:#1)},
+    anchor=north east,
+    every legend inside
+  },
+  label style/.style={
+    matrix node style={/tikz/data visualization/every label in legend/.append style={#1}}
+  },
+  matrix node style/.style={\tikz@dv@legend/matrix node styling/.append style={#1}},
+}%
+
+
+\tikzdatavisualizationset{
+  new legend entry/.code={
+    \begingroup
+      \pgfkeys{/tikz/data visualization/legend entry options/.cd,#1}
+      \pgfkeysgetvalue{/tikz/data visualization/legend entry options/legend}\tikz@dv@temp@legend
+      \global\let\tikz@dv@temp@legend\tikz@dv@temp@legend
+    \endgroup
+    \tikzdatavisualizationset{new legend/.expanded=\tikz@dv@temp@legend}%
+    \expandafter\tikz@dv@add@legend@entry\expandafter{\tikz@dv@temp@legend}{#1}
+  }
+}%
+
+\def\tikz@dv@add@legend@entry#1#2{
+  \tikz@main@dv.at start survey({
+      \pgfkeysgetvalue{/tikz/data visualization/#1/obj}\pgf@temp
+      \pgf@temp.add entry(\tikz@dv@render@legend@entry{legend=#1,#2})
+    })
+}%
+
+\def\tikz@dv@render@legend@entry#1{
+  \pgfkeys{/tikz/data visualization/.cd,every data set label}
+  \pgfkeys{/tikz/data visualization/legend entry options/.cd,
+    /tikz/data visualization/every label in legend,#1}%
+  \pgfkeysgetvalue{/tikz/data visualization/legend entry options/text}\tikz@dv@temp@lab
+  \pgfkeysgetvalue{/tikz/data visualization/@node styling}\tikz@dv@temp@style
+  \pgfkeysgetvalue{/tikz/data visualization/legend entry options/setup}\tikz@dv@temp@setup
+  \pgfkeysgetvalue{/tikz/data visualization/legend entry options/visualizer in legend styling}\tikz@dv@temp@visual@styling
+  \scope[/utils/exec=\expandafter\pgfkeysalso\expandafter{\tikz@dv@temp@setup},
+         /utils/exec=\pgf@signalstyle.emit()]
+    \node[/tikz/data visualization/node styling,
+          /utils/exec=\expandafter\pgfkeysalso\expandafter{\tikz@dv@temp@style}]
+    {\tikz@dv@pre@height\tikz@dv@temp@lab\tikz@dv@post@height};
+    \scope[/utils/exec=\expandafter\pgfkeysalso\expandafter{\tikz@dv@temp@visual@styling}]
+      \iftikz@lib@dv@text@only
+      \else
+        \pgfkeysvalueof{/tikz/data visualization/legend entry options/visualizer in legend}
+      \fi
+    \endscope
+  \endscope
+}%
+
+\def\tikz@dv@pre@height{\hbox{\vrule height .75em width0pt}}%
+\def\tikz@dv@post@height{\hbox{\vrule depth .25em width0pt}}%
+
+
+
+\pgfkeys{
+  /tikz/data visualization/legend entry options/.cd,
+  text/.initial=,
+  node style/.style={/tikz/data visualization/node style={#1}},
+  legend/.initial=main legend,
+  setup/.initial=,
+  visualizer in legend/.initial=,
+  visualizer in legend styling/.initial=,
+  visualizer in legend style/.style={visualizer in legend styling/.append={,#1}},
+  text right/.style={
+    node style={anchor=mid west,inner ysep=1pt,inner xsep=0pt,reset cm,xshift=.333em},
+    visualizer in legend style={reset cm},
+  },
+  text left/.style={
+    node style={anchor=mid east,inner ysep=1pt,inner xsep=0pt,reset
+      cm,xshift=-.333em,align=right},
+    visualizer in legend style={reset cm,xscale=-1},
+  },
+  text only/.style={
+    node style={anchor=mid west,inner ysep=1pt,inner xsep=0pt,reset cm,text=visualizer color},
+    /utils/exec=\tikz@lib@dv@text@onlytrue
+  },
+  text colored/.style=/tikz/data visualization/text colored,
+}%
+\let\tikz@lib@dv@pin@dir\pgfutil@empty
+\newif\iftikz@lib@dv@text@only
+
+\pgfkeys{
+  /tikz/data visualization/visualizer options/.cd,
+  label in legend/.code={\expandafter\tikz@dv@new@label@in@legend@for@visualizer\expandafter{\tikz@visualizer}{#1}},
+  label in data/.code=\tikzdatavisualizationset{new label visualizer/.expand once=\expandafter{\tikz@visualizer}{auto,#1}},
+  pin in data/.style={label in data={%
+      node style={%
+        /utils/exec={
+          \ifx\tikz@lib@dv@pin@dir\pgfutil@empty
+            \pgf@process{\pgfpointnormalised{%
+                \pgfpointdiff%
+                {\pgfpointanchor{label visualizer coordinate}{center}}%
+                {\pgfpointanchor{label visualizer coordinate'}{center}}}}%
+            \pgf@x=-\pgf@x\relax%
+            \edef\tikz@lib@dv@temp@rot{\noexpand\pgfqpoint{\the\pgf@y}{\the\pgf@x}}%
+            \tikz@addtransform{\pgftransformshift{\pgfpointscale{\tikz@lib@dv@pin@sign\tikz@pin@distance}{\tikz@lib@dv@temp@rot}}}
+          \else%
+            \tikz@addtransform{\pgftransformshift{\pgfpointpolar{\tikz@lib@dv@pin@dir}{\tikz@lib@dv@pin@sign\tikz@pin@distance}}}
+          \fi%
+        },
+        append after command={
+          \bgroup
+            [current point is local=true]
+            (\tikzlastnode) edge [solid, every pin edge] (label visualizer coordinate)
+          \egroup%
+      }},
+      ,#1}},
+  style/.style={/tikz/data visualization/visualizers/\tikz@visualizer/styling/.append style={,#1}},
+  label in legend options/.style={/tikz/data visualization/visualizers/\tikz@visualizer/label in legend options/.append style={,#1}},
+  ignore style sheets/.style={/tikz/data visualization/visualizers/\tikz@visualizer/signal/.code=,/utils/exec=\advance\tikzdvvisualizercounter by -1\relax},
+}%
+
+\def\tikz@dv@new@label@in@legend@for@visualizer#1#2{
+  \tikzdatavisualizationset{
+    new legend entry={
+      visualizer in legend style={/tikz/data visualization/visualizers/#1/styling/.try},
+      /tikz/data visualization/every label in legend/.try,
+      /tikz/.cd,
+      every label/.try,
+      /tikz/data visualization/legend entry options/.cd,
+      setup={/data point/set={#1}},
+      /tikz/data visualization/visualizers/#1/label in legend options/.try,
+      #2,
+    }
+  }
+}%
+
+\def\tikz@dv@legend@entry@as@example{
+  \pgfkeysgetvalue{/data point/set}{\tikz@visualizer}
+  \pgfkeysvalueof{/data point/\tikz@visualizer/execute at begin}
+  \tikz@dv@plot@handler
+  \pgfplotstreamstart
+  \pgfkeysgetvalue{/tikz/data visualization/legend entry options/label in legend line coordinates}{\tikz@dv@temp}
+  \foreach \coordinate in \tikz@dv@temp
+  { \pgfplotstreampoint{\expandafter\tikz@scan@one@point\expandafter\pgfutil@firstofone\coordinate} }
+  \pgfplotstreamend
+  \pgfkeysvalueof{/data point/\tikz@visualizer/execute at end}
+  \pgfkeysvalueof{/data point/\tikz@visualizer/execute at begin}
+  \tikz@dv@plot@mark@maker
+  \pgfplotstreamstart
+  \pgfkeysgetvalue{/tikz/data visualization/legend entry options/label in legend mark coordinates}{\tikz@dv@temp}
+  \foreach \coordinate in \tikz@dv@temp
+  { \pgfplotstreampoint{\expandafter\tikz@scan@one@point\expandafter\pgfutil@firstofone\coordinate} }
+  \pgfplotstreamend
+  \pgfkeysvalueof{/data point/\tikz@visualizer/execute at end}
+}%
+
+
+\tikzdatavisualizationset{
+  legend entry options/.cd,
+  label in legend line coordinates/.initial=,
+  label in legend rectangle coordinates/.initial={(-1ex,-.5ex),(-1ex,0.968ex),(0ex,0.968ex),(0ex,-.5ex)},
+  label in legend mark coordinates/.initial=,
+  label in legend one mark/.style={
+    label in legend line coordinates={},
+    label in legend mark coordinates={(0,0)},
+  },
+  label in legend three marks/.style={
+    label in legend line coordinates={},
+    label in legend mark coordinates={(-3ex,-.3ex),(-1.5ex,.3ex),(0,0)},
+  },
+  straight label in legend line/.style={
+    label in legend line coordinates={(-2em,0),(-1.5em,0),(-.5em,0),(0,0)},
+    label in legend mark coordinates={(-1.5em,0),(-.5em,0)},
+  },
+  zig zag label in legend line/.style={
+    label in legend line coordinates={(-2em,0),(-1.5em,.3ex),(-.5em,-.3ex),(0,0)},
+    label in legend mark coordinates={(-1.5em,.3ex),(-.5em,-.3ex)},
+  },
+  circular label in legend line/.style={
+    label in legend line coordinates={%
+      ([xshift=-1em]0:.9em and .35ex),%
+      ([xshift=-1em]45:.9em and .35ex),%
+      ([xshift=-1em]90:.9em and .35ex),%
+      ([xshift=-1em]135:.9em and .35ex),%
+      ([xshift=-1em]180:.9em and .35ex),%
+      ([xshift=-1em]225:.9em and .35ex),%
+      ([xshift=-1em]270:.9em and .35ex),%
+      ([xshift=-1em]315:.9em and .35ex)},%
+    label in legend mark coordinates={([xshift=-1em]120:.9em and .35ex),([xshift=-1em]-60:.9em and .35ex)},
+  },
+  gap circular label in legend line/.style={
+    label in legend line coordinates={%
+      ([xshift=-1em,yshift=.2ex]90:1.4ex and 0.9ex),%
+      ([xshift=-1em,yshift=.2ex]162:1.4ex and 0.9ex),%
+      ([xshift=-1em,yshift=.2ex]234:1.4ex and 0.9ex),%
+      ([xshift=-1em,yshift=.2ex]306:1.4ex and 0.9ex),%
+      ([xshift=-1em,yshift=.2ex]18:1.4ex and 0.9ex)},
+    label in legend mark coordinates={
+      ([xshift=-1em,yshift=.2ex]90:1.4ex and 0.9ex),%
+      ([xshift=-1em,yshift=.2ex]162:1.4ex and 0.9ex),%
+      ([xshift=-1em,yshift=.2ex]234:1.4ex and 0.9ex),%
+      ([xshift=-1em,yshift=.2ex]306:1.4ex and 0.9ex),%
+      ([xshift=-1em,yshift=.2ex]18:1.4ex and 0.9ex)}
+  },
+  default label in legend path/.style={zig zag label in legend line},
+  default label in legend closed path/.style={circular label in legend line},
+  default label in legend mark/.style={label in legend one mark},
+}%
+
+
+\def\tikz@dv@legend@entry@visualizer@visualizer{
+}%
+
+
+
+
+\tikzdatavisualizationset{
+  visualize as line/.style={
+    new object={
+      when=after survey,
+      store=/tikz/data visualization/visualizers/#1,
+      class=plot handler visualizer,
+      arg1=#1,
+      arg2={\tikz@dv@plot@handler,\tikz@dv@plot@mark@maker}
+    },
+    new visualizer={#1}{%
+      every path/.style={draw},
+      style={every mark/.append style={color=visualizer color}},
+      mark size=2pt,
+      semithick,
+      color=visualizer color,
+      mark=none,
+      /tikz/data visualization/every visualize as line/.try,
+    }{visualizer in legend=\tikz@dv@legend@entry@as@example},
+    #1={straight line}
+  },
+  visualize as line/.default=line,
+  visualize as smooth line/.style={
+    visualize as line={#1},
+    #1={smooth line}
+  },
+  visualize as smooth line/.default=line,
+  visualize as smooth cycle/.style={
+    visualize as smooth line={#1},
+    #1={smooth cycle}
+  },
+  visualize as smooth cycle/.default=line,
+  visualize as scatter/.style={
+    new object={
+      when=after survey,
+      store=/tikz/data visualization/visualizers/#1,
+      class=plot handler visualizer,
+      arg1=#1,
+      arg2={\tikz@dv@plot@mark@maker}
+    },
+    new visualizer={#1}{%
+      mark=x,
+      mark size=2pt,
+      style={every mark/.append style={color=visualizer color}},
+      /tikz/data visualization/every visualize as scatter/.try,
+    }{visualizer in legend=\tikz@dv@legend@entry@as@example},
+    #1={no lines}
+  },
+  visualize as scatter/.default=scatter
+}%
+
+\def\tikz@dv@plot@mark@maker{
+  \let\tikz@options=\pgfutil@empty%
+  \let\tikz@transform=\pgfutil@empty%
+  \tikzset{solid,shift only,every mark}%
+  \tikz@options%
+  \ifx\tikz@plot@mark\pgfutil@empty%
+    \pgfplothandlerdiscard
+  \else
+    \pgfplothandlermark{\tikz@transform\pgfuseplotmark{\tikz@plot@mark}}
+  \fi
+}%
+
+
+
+
+
+\tikzdatavisualizationset{
+  visualize as rectangles/.style={
+    new object={
+      when=before survey,
+      store=/tikz/data visualization/visualizers/#1,
+      class=rectangle visualizer,
+      arg1=#1
+    },
+    /data point/#1/attribute 1/.initial=x,
+    /data point/#1/attribute 2/.initial=y,
+    new visualizer={#1}{%
+      every path/.style={draw},
+      semithick,
+      color=visualizer color,
+      /tikz/data visualization/every visualize as rectangles/.try,
+    }{visualizer in legend=\tikz@dv@legend@entry@as@rectangle},
+    #1={}
+  },
+  visualize as rectangles/.default=rectangles,
+  visualizer options/.cd,
+  attribute 1/.style={/data point/\tikz@visualizer/attribute 1={#1}},
+  attribute 2/.style={/data point/\tikz@visualizer/attribute 2={#1}},
+}%
+
+
+
+\def\tikz@dv@legend@entry@as@rectangle{
+  \pgfkeysgetvalue{/data point/set}{\tikz@visualizer}
+  \pgfkeysvalueof{/data point/\tikz@visualizer/execute at begin}
+  \pgfplothandlerpolygon
+  \pgfplotstreamstart
+  \pgfkeysgetvalue{/tikz/data visualization/legend entry options/label in legend rectangle coordinates}{\tikz@dv@temp}
+  \foreach \coordinate in \tikz@dv@temp
+  { \pgfplotstreampoint{\expandafter\tikz@scan@one@point\expandafter\pgfutil@firstofone\coordinate} }
+  \pgfplotstreamend
+  \pgfkeysvalueof{/data point/\tikz@visualizer/execute at end}
+}%
+
+
+
+
+
+
+\pgfkeysdef{/handlers/.style sheet}{%
+  \edef\pgf@marshal{
+    \noexpand \pgfoonew \noexpand\tikz@dv@temp=new style attribute(\pgfkeyscurrentpath,#1)
+    \noexpand \tikz@dv@temp.default connects()
+  }
+  \pgf@marshal
+}%
+
+\tikzset{
+  visualizer color/.code=\colorlet{visualizer color}{#1},
+  visualizer color=black
+}%
+
+
+\pgfdvdeclarestylesheet{vary thickness}
+{
+  default style/.style={line width={0.3pt+(#1)*0.2pt}}
+}%
+
+\pgfdvdeclarestylesheet{vary dashing}
+{
+  default style/.style=solid,
+  1/.style=solid,
+  2/.style={dash pattern=on 5\pgflinewidth off 2\pgflinewidth},
+  3/.style={dash pattern=on 1.5\pgflinewidth off 1.5\pgflinewidth},
+  4/.style={dash pattern=on 5\pgflinewidth off 1.5\pgflinewidth on 1.5\pgflinewidth off 1.5\pgflinewidth},
+  5/.style={dash pattern=on 10\pgflinewidth off 3\pgflinewidth},
+  6/.style={dash pattern=on 10\pgflinewidth off 2\pgflinewidth on 2\pgflinewidth off 2\pgflinewidth},
+  7/.style={dash pattern=on 8\pgflinewidth off 2\pgflinewidth on
+    1.5\pgflinewidth off 1.5\pgflinewidth on 1.5\pgflinewidth off
+    1.5\pgflinewidth on 1.5\pgflinewidth off 1.5\pgflinewidth}
+}%
+
+\pgfdvdeclarestylesheet{vary thickness and dashing}
+{
+  default style/.style=thin,
+  1/.style=thin,
+  2/.style=thick,
+  3/.style={
+    dash pattern=on 5\pgflinewidth off 2\pgflinewidth,
+    thin
+  },
+  4/.style={
+    dash pattern=on 5\pgflinewidth off 2\pgflinewidth,
+    thick,
+  },
+  5/.style={
+    dash pattern=on 1.5\pgflinewidth off 1.5\pgflinewidth,
+    thin
+  },
+  6/.style={
+    dash pattern=on 1.5\pgflinewidth off 1.5\pgflinewidth,
+    thick
+  },
+  7/.style={
+    dash pattern=on 5\pgflinewidth off 1.5\pgflinewidth on
+    1.5\pgflinewidth off 1.5\pgflinewidth,
+    thin
+  },
+  8/.style={
+    dash pattern=on 5\pgflinewidth off 1.5\pgflinewidth on
+    1.5\pgflinewidth off 1.5\pgflinewidth,
+    thick
+  },
+  9/.style={
+    dash pattern=on 10\pgflinewidth off 3\pgflinewidth,
+    thin
+  },
+  10/.style={
+    dash pattern=on 10\pgflinewidth off 3\pgflinewidth,
+    thick
+  },
+  11/.style={
+    dash pattern=on 10\pgflinewidth off 2\pgflinewidth on
+    2\pgflinewidth off 2\pgflinewidth,
+    thin
+  },
+  12/.style={
+    dash pattern=on 10\pgflinewidth off 2\pgflinewidth on
+    2\pgflinewidth off 2\pgflinewidth,
+    thick
+  },
+  13/.style={
+    dash pattern=on 8\pgflinewidth off 2\pgflinewidth on
+    1.5\pgflinewidth off 1.5\pgflinewidth on 1.5\pgflinewidth off
+    1.5\pgflinewidth on 1.5\pgflinewidth off 1.5\pgflinewidth,
+    thin
+  },
+  14/.style={
+    dash pattern=on 8\pgflinewidth off 2\pgflinewidth on
+    1.5\pgflinewidth off 1.5\pgflinewidth on 1.5\pgflinewidth off
+    1.5\pgflinewidth on 1.5\pgflinewidth off 1.5\pgflinewidth,
+    thick
+  }
+}%
+
+
+\pgfdvdeclarestylesheet{strong colors}
+{
+  default style/.style={visualizer color=black},
+  1/.style={visualizer color=black},
+  2/.style={visualizer color=red!80!black},
+  3/.style={visualizer color=blue!80!black},
+  4/.style={visualizer color=green!60!black},
+  5/.style={visualizer color=orange!80!black},
+  6/.style={visualizer color=black!60}
+}%
+
+
+\pgfdvdeclarestylesheet{cross marks}
+{
+  default style/.style={mark=x,every mark/.append style=thin,mark size=2pt},
+  1/.style={mark=x,every mark/.append style=thin,mark size=2pt},
+  2/.style={mark=+,every mark/.append style=thin,mark size=2pt},
+  3/.style={mark=Mercedes star,every mark/.append style=thin,mark size=2pt},
+  4/.style={mark=Mercedes star flipped,every mark/.append style=thin,mark size=2pt},
+  5/.style={mark=star,every mark/.append style=thin,mark size=2pt},
+  6/.style={mark=10-pointed star,every mark/.append style={line width=.3pt,mark size=1.8pt}}
+}%
+
+
+\pgfdvdeclarestylesheet{* mark}
+{
+  default style/.style={mark=*,every mark/.append style=thin,mark size=1.4pt},
+}%
+
+\pgfdvdeclarestylesheet{dot mark}
+{
+  default style/.style={mark=*,every mark/.append style=thin,mark size=0.6pt},
+}%
+
+
+\pgfdvdeclarestylesheet{o mark}
+{
+  default style/.style={mark=o,every mark/.append style=thin,mark size=1.4pt},
+}%
+
+
+
+
+\def\tikzdvdeclarestylesheetcolorseries#1#2#3#4{%
+  \definecolorseries{tikzdvcolorseries#1}{#2}{step}[#2]{#3}{#4}%
+  \resetcolorseries{tikzdvcolorseries#1}%
+  \pgfdvdeclarestylesheet{#1}
+  {
+    default style/.style={
+      /utils/exec=\colorlet{tikz@dv@temp}[rgb]{tikzdvcolorseries#1!![##1]},
+      visualizer color=tikz@dv@temp
+    }
+  }%
+}%
+
+\tikzdvdeclarestylesheetcolorseries{vary hue}{hsb}{.4,0.9,0.8}{.213,0,0}%
+\tikzdvdeclarestylesheetcolorseries{shades of blue}{hsb}{.65,1.4,1}{0,-.4,-.0}%
+\tikzdvdeclarestylesheetcolorseries{shades of red}{hsb}{0,1.4,1}{0,-.4,-.0}%
+\tikzdvdeclarestylesheetcolorseries{gray scale}{hsb}{0,0,-.34}{0,0,.34}%
+
+
+
+
+
+
+
+
+\tikzdatavisualizationset{
+  xy Cartesian/.style={
+    new Cartesian axis=x axis,
+    x axis={attribute=x,unit vector={(1pt,0cm)}},
+    new Cartesian axis=y axis,
+    y axis={attribute=y,unit vector={(0cm,1pt)}}
+  },
+  Xy axes/.style={x axis={#1},y axis={#1}},
+  uv Cartesian/.style={
+    new Cartesian axis=u axis,
+    u axis={attribute=u,unit vector={(1pt,0cm)}},
+    new Cartesian axis=v axis,
+    v axis={attribute=v,unit vector={(0cm,1pt)}}
+  },
+  uv axes/.style={u axis={#1},v axis={#1}},
+}%
+
+\tikzdatavisualizationset{
+  xyz Cartesian cabinet/.style={
+    xy Cartesian,
+    new Cartesian axis=z axis,
+    z axis={attribute=z,unit vector={(-0.353553pt,-0.353553pt)}}
+  },
+  xyz axes/.style={x axis={#1},y axis={#1},z axis={#1}},
+  uvw Cartesian cabinet/.style={
+    uv Cartesian,
+    new Cartesian axis=w axis,
+    w axis={attribute=w,unit vector={(-0.353553pt,-0.353553pt)}}
+  }
+  uvw axes/.style={u axis={#1},v axis={#1},w axis={#1}},
+}%
+
+
+
+
+\tikzdatavisualizationset{
+  new axis system/.style n args={4}{
+    #1/.style={
+      #2,
+      #1/.cd,
+      #3,
+      /tikz/data visualization/every #1/.try,
+      ##1,
+      /tikz/data visualization/.cd,
+      #4,
+    }
+  }
+}%
+
+
+
+\tikzdatavisualizationset{
+  new axis system={school book axes}{%
+    xy Cartesian,
+    x axis={
+      include value=0,
+      scaling=0 at 0 and \pgfkeysvalueof{/tikz/data visualization/school book axes/unit} at 1cm,
+      visualize axis={y axis={goto=0},style=->,padded},
+      visualize ticks={common={y axis={goto=0},direction axis=y axis},
+        major={tick text at low,
+          options at=0 as [{style={draw=none},no tick text}]
+        }},
+      visualize grid={common={direction axis=y axis,padded}},
+      ticks={step=\pgfkeysvalueof{/tikz/data visualization/school book axes/unit}},
+      padding=0.75em
+    },
+    y axis={
+      include value=0,
+      scaling=0 at 0 and \pgfkeysvalueof{/tikz/data visualization/school book axes/unit} at 1cm,
+      visualize axis={x axis={goto=0},style=->,padded},
+      visualize ticks={
+        common={x axis={goto=0},direction axis=x axis},
+        major={tick text at low,options at=0 as [{high=0,low=0,style={draw=none},node style={anchor=north east}}]}
+      },
+      visualize grid={common={direction axis=x axis,padded}},
+      ticks={step=\pgfkeysvalueof{/tikz/data visualization/school book axes/unit}},
+      padding=0.75em
+    }
+  }{%
+    standard labels
+  }{%
+    @make labels
+  },
+  school book axes/.cd,
+  standard labels/.style={
+    /tikz/data visualization/@make labels/.style={
+      x axis={
+        visualize label={
+          x axis={goto=padded max, anchor at max},
+          y axis={goto=0}
+        }
+      },
+      y axis={
+        visualize label={
+          y axis={goto=padded max, anchor at max},
+          x axis={goto=0}
+        }
+      }
+    }
+  },
+  unit/.initial=1,
+}%
+
+
+
+
+
+\tikzdatavisualizationset{
+  new axis system={scientific axes}{%
+    xy Cartesian,
+    every axis/.append style={style={draw=black!50}},
+    every ticks/.append style={style={draw=black!50}},
+    x axis={
+      length=\pgfkeysvalueof{/tikz/data visualization/scientific axes/width},
+      ticks
+    },
+    y axis={
+      length=\pgfkeysvalueof{/tikz/data visualization/scientific axes/height},
+      ticks
+    }
+  }{%
+    standard labels,
+    outer ticks,
+  }{%
+    @make axes,
+    @make labels
+  },
+  scientific axes/.cd,
+  width/.initial=5cm,
+  height/.initial=0.618*\pgfkeysvalueof{/tikz/data visualization/scientific axes/width},%
+  outer ticks/.style={
+    /tikz/data visualization/@make axes/.style={
+      x axis={
+        visualize ticks={common={y axis={goto=padded min},direction axis=y axis,high=0pt},major={tick text at low}},
+        visualize ticks={common={y axis={goto=padded max},direction axis=y axis,low=0pt}},
+        visualize axis={y axis={goto=padded min},padded},
+        visualize axis={y axis={goto=padded max},padded},
+        visualize grid={common={direction axis=y axis,padded}},
+      },
+      y axis={
+        visualize ticks={common={x axis={goto=padded min},direction axis=x axis,high=0pt},major={tick text at low}},
+        visualize ticks={common={x axis={goto=padded max},direction axis=x axis,low=0pt}},
+        visualize axis={x axis={goto=padded min},padded},
+        visualize axis={x axis={goto=padded max},padded},
+        visualize grid={common={direction axis=x axis,padded}},
+      }
+    }
+  },
+  inner ticks/.style={
+    /tikz/data visualization/@make axes/.style={
+      x axis={
+        visualize ticks={common={y axis={goto=padded min},direction axis=y axis,low=0pt},major={tick text at low}},
+        visualize ticks={common={y axis={goto=padded max},direction axis=y axis,high=0pt}},
+        visualize axis={y axis={goto=padded min},padded},
+        visualize axis={y axis={goto=padded max},padded},
+        visualize grid={common={direction axis=y axis,padded}},
+      },
+      y axis={
+        visualize ticks={common={x axis={goto=padded min},direction axis=x axis,low=0pt},major={tick text at low}},
+        visualize ticks={common={x axis={goto=padded max},direction axis=x axis,high=0pt}},
+        visualize axis={x axis={goto=padded min},padded},
+        visualize axis={x axis={goto=padded max},padded},
+        visualize grid={common={direction axis=x axis,padded}},
+      }
+    }
+  },
+  clean/.style={
+    /tikz/data visualization/@make axes/.style={
+      x axis={
+        visualize ticks={common={y axis={goto=padded min},direction axis=y axis,high=0pt},major={tick text at low}},
+        visualize axis={y axis={goto=padded min}},
+        visualize axis={y axis={goto=min}, style={black!25, line cap=rect}},
+        visualize axis={y axis={goto=max}, style={black!25, line cap=rect}},
+        visualize grid={common={direction axis=y axis}},
+        padding=.5em,
+      },
+      y axis={
+        visualize ticks={common={x axis={goto=padded min},direction axis=x axis,high=0pt},major={tick text at low}},
+        visualize axis={x axis={goto=padded min}},
+        visualize axis={x axis={goto=min}, style={black!25, line cap=rect}},
+        visualize axis={x axis={goto=max}, style={black!25, line cap=rect}},
+        visualize grid={common={direction axis=x axis}},
+        padding=.5em
+      },
+    }
+  },
+  standard labels/.style={
+    /tikz/data visualization/@make labels/.style={
+      x axis={
+        visualize label={
+          x axis={goto pos=.5},
+          node style={
+            at={(0,0 |- data visualization bounding box.south)},
+            below
+          }
+        }
+      },
+      y axis={
+        visualize label={
+          y axis={goto pos=.5},
+          node style={
+            at={(0,0 -| data visualization bounding box.west)},
+            rotate=90,
+            above}
+        }
+      }
+    }
+  },
+  upright labels/.style={
+    /tikz/data visualization/@make labels/.style={
+      x axis={
+        visualize label={
+          x axis={goto pos=.5},
+          node style={
+            at={(0,0 |- data visualization bounding box.south)},
+            below
+          }
+        }
+      },
+      y axis={
+        visualize label={
+          y axis={goto pos=.5},
+          node style={
+            at={(0,0 -| data visualization bounding box.west)},
+            left
+          }
+        }
+      }
+    }
+  },
+  end labels/.style={
+    /tikz/data visualization/@make labels/.style={
+      x axis={
+        visualize label={
+          y axis={goto=padded min},
+          node style={
+            at={(0,0 -| data visualization bounding box.east)},
+            right
+          }
+        }
+      },
+      y axis={
+        visualize label={
+          x axis={goto=padded min},
+          node style={
+            at={(0,0 |- data visualization bounding box.north)},
+            above
+          }
+        }
+      }
+    }
+  }
+}%
+
+
+
+\endinput

preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/datavisualization/tikzlibrarydatavisualization.formats.functions.code.tex

@@ -0,0 +1,8 @@
+
+\ProvidesFileRCS{tikzlibrarydatavisualization.formats.functions.code.tex}
+
+\usetikzlibrary{datavisualization}%
+\usepgflibrary{datavisualization.formats.functions}%
+
+
+\endinput

preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/datavisualization/tikzlibrarydatavisualization.polar.code.tex

@@ -0,0 +1,527 @@
+
+\ProvidesFileRCS{tikzlibrarydatavisualization.polar.code.tex}
+
+\usetikzlibrary{datavisualization}%
+\usepgflibrary{datavisualization.polar}%
+
+
+\tikzdatavisualizationset{%
+  new polar axes/.style 2 args={
+    new axis base=#1,
+    #1={attribute=angle},
+    new axis base=#2,
+    #2={attribute=radius},
+    #2/scaling/default=0 at 0 and 1 at 1cm,
+    new object={
+      store=/tikz/data visualization/#1/polar transformer,
+      class=polar transformer,
+      arg1/.expanded=\pgfkeysvalueof{/tikz/data visualization/angle axis/attribute}/scaled,
+      arg2/.expanded=\pgfkeysvalueof{/tikz/data visualization/radius axis/attribute}/scaled,
+      arg3 from key=/tikz/data visualization/#1/unit vector 0 degrees,
+      arg4 from key=/tikz/data visualization/#1/unit vector 90 degrees
+    },
+    /tikz/data visualization/#1/unit vector 0 degrees/.initial=\pgfqpoint{1pt}{0pt},
+    /tikz/data visualization/#1/unit vector 90 degrees/.initial=\pgfqpoint{0pt}{1pt},
+  },
+  new polar axes/.default={angle axis}{radius axis}
+}%
+\def\tikz@lib@dv@polar@a#1{
+  \pgfkeyssetvalue{\tikz@dv@axis/unit vector 0 degrees}{#1}
+}%
+\def\tikz@lib@dv@polar@b#1{
+  \pgfkeyssetvalue{\tikz@dv@axis/unit vector 90 degrees}{#1}
+}%
+
+
+
+
+\tikzset{
+  /tikz/data visualization/axis options/.cd,
+  unit vectors/.code 2 args={
+    \tikz@scan@one@point\tikz@lib@dv@polar@a#1
+    \tikz@scan@one@point\tikz@lib@dv@polar@b#2
+  },
+  degrees/.style={\tikz@dv@axis/scaling=0 at 0 and 1 at 1},
+  radians/.style={\tikz@dv@axis/scaling=0 at 0 and 0.03141592653589793 at 1.8},
+}%
+
+
+
+\tikzdatavisualizationset{
+  new axis system={scientific polar axes}{%
+    new polar axes,
+    angle axis={attribute=angle},
+    radius axis={attribute=radius},
+    every axis/.append style={style={draw=black!50}},
+    every ticks/.append style={style={draw=black!50}},
+  }{%
+    0 to 360,%
+    outer ticks,
+  }{%
+    @make axes,
+    scientific polar axes/@setup axes,
+    /utils/exec={
+      \edef\pgf@marshal{\noexpand\tikzdatavisualizationset{\pgfkeysvalueof{/tikz/data visualization/@which visualize radius axis}/.list={\pgfkeysvalueof{/tikz/data visualization/\pgfkeysvalueof{/tikz/data visualization/@which radius axes at}}}}}
+      \pgf@marshal
+    },
+    @make labels
+  },
+  @which radius axes at/.initial=@inner radius axes at,
+  @which visualize radius axis/.initial=@visualize radius axis,
+  @inner radius axes at/.initial=,
+  @clean radius axes at/.initial=,
+  @visualize radius axis/.style 2 args={
+    radius axis={
+      visualize axis={angle axis={goto=#1},high=padded max,low=0},
+      visualize ticks={
+        common={angle axis={goto=#1}, direction axis=angle axis},
+        major={tick text at #2,
+          options at=0 as [{style={draw=none},no tick text}]
+        }
+      }
+    }
+  },
+  @visualize clean radius axis/.style n args={5}{
+    radius axis={
+      visualize axis={angle
+        axis={goto=#1},high=max,low=0,style={black!25,line cap=rect}},
+      visualize axis={angle
+        axis={goto=#1},high=max,low=0,style={line cap=rect,#4}},
+      visualize ticks={
+        style={#4},
+        common={angle axis={goto=#1}, direction axis=angle axis, #3=0},
+        major={tick text at #2,#5}
+      }
+    }
+  },
+  @visualize zero/.style={@inner visualize zero={#1}},
+  @clean visualize zero/.style={},
+  @inner visualize zero/.style={
+    radius axis={
+      visualize ticks={
+        common={angle axis={goto=0}, direction axis=angle axis},
+        major={tick text at low,low=0,high=0,at=0 as
+          [{style={draw=none},node style={anchor=#1}}]
+        }
+      }
+    }
+  },
+  @degrees/.style={
+    angle axis={degrees, ticks={step=15, tick suffix=$^\circ$, major={
+          options at=360 as [{style={draw=none},no tick text}],
+          options at=-180 as [{style={draw=none},no tick text}]}}}
+  },
+  @rad/.style={
+    angle axis={radians, ticks={
+        step=(pi/12),
+        node style={
+          /pgf/number format/frac,
+          /pgf/number format/frac shift={1}
+        },
+        tick typesetter/.code={%
+          \pgfmathsetmacro{\tikz@lib@dv@pol}{round(####1*3.819718634205488)/12}%
+          \pgfmathapproxequalto{\tikz@lib@dv@pol}{0}%
+          \ifdim\pgfmathresult pt=1.0pt%
+            $0$%
+          \else%
+            \pgfmathapproxequalto{\tikz@lib@dv@pol}{1}%
+            \ifdim\pgfmathresult pt=1.0pt%
+              $\pi$%
+            \else
+              \pgfmathapproxequalto{\tikz@lib@dv@pol}{-1}%
+              \ifdim\pgfmathresult pt=1.0pt%
+                $-\pi$%
+              \else%
+                \pgfmathprintnumber{\tikz@lib@dv@pol}$\pi$%
+              \fi%
+            \fi%
+          \fi%
+        },
+        major={
+          options at=6.2831985e0 as [{style={draw=none},no tick text}],
+          options at=6.2831192e0 as [{style={draw=none},no tick text}],
+          options at=6.2830794e0 as [{style={draw=none},no tick text}],
+          options at=6.2828787e0 as [{style={draw=none},no tick text}],
+          options at=6.2831598e0 as [{style={draw=none},no tick text}],
+          options at=-3.1415991e0 as [{style={draw=none},no tick text}],
+          options at=-3.1415802e0 as [{style={draw=none},no tick text}],
+          options at=-3.1415602e0 as [{style={draw=none},no tick text}],
+          options at=-3.14153961e0 as [{style={draw=none},no tick text}],
+          options at=-3.1414406e0 as [{style={draw=none},no tick text}],
+        }
+      }
+    }
+  },
+  @make labels/.style={},
+}%
+
+\tikzdatavisualizationset{
+  scientific polar axes/.cd,
+  outer ticks/.style={
+    /tikz/data visualization/@make axes/.style={
+      radius axis={
+        min value=0,
+        length=\pgfkeysvalueof{/tikz/data visualization/scientific polar axes/radius},
+        padding=0em,
+        ticks={few},
+        visualize grid={common={direction axis=angle axis,low=min,high=max}},
+      },
+      angle axis={
+        visualize axis={radius axis={goto=padded max},low=min,high=max},
+        visualize ticks={common={radius axis={goto=padded max},direction
+            axis=radius axis},common={low=0},major={tick text at high}},
+        visualize grid={common={direction axis=radius axis},low=0,high=padded max},
+      }
+    },
+    /tikz/data visualization/@which radius axes at=@inner radius axes at,
+    /tikz/data visualization/@which visualize radius axis=@visualize radius axis,
+    /tikz/data visualization/@visualize zero/.style={@inner visualize zero={##1}},
+  },
+  inner ticks/.style={
+    /tikz/data visualization/@make axes/.style={
+      radius axis={
+        min value=0,
+        length=\pgfkeysvalueof{/tikz/data visualization/scientific polar axes/radius},
+        padding=0em,
+        ticks={few},
+        visualize grid={common={direction axis=angle axis,low=min,high=max}},
+      },
+      angle axis={
+        visualize axis={radius axis={goto=padded max},low=min,high=max},
+        visualize ticks={common={radius axis={goto=padded max},direction
+            axis=radius axis},common={high=0},major={tick text at high}},
+        visualize grid={common={direction axis=radius axis},low=0,high=padded max},
+      }
+    },
+    /tikz/data visualization/@which radius axes at=@inner radius axes at,
+    /tikz/data visualization/@which visualize radius axis=@visualize radius axis,
+    /tikz/data visualization/@visualize zero/.style={@inner visualize zero={##1}},
+  },
+  clean/.style={
+    /tikz/data visualization/@make axes/.style={
+      radius axis={
+        min value=0,
+        length=\pgfkeysvalueof{/tikz/data visualization/scientific polar axes/radius},
+        padding=.5em,
+        ticks={few},
+        visualize grid={common={direction axis=angle axis,low=min,high=max}},
+      },
+      angle axis={
+        padding=.5em,
+        visualize axis={radius axis={goto=max}, style={black!25, line cap=rect},low=min,high=max},
+        visualize axis={radius axis={goto=padded max}, style={line cap=rect}, low=min,high=max},
+        visualize ticks={common={radius axis={goto=padded max}, direction axis=radius axis},common={low=0},major={tick text at high}},
+        visualize grid={common={direction axis=radius axis},low=0,high=max},
+      }
+    },
+    /tikz/data visualization/@which radius axes at=@clean radius axes at,
+    /tikz/data visualization/@which visualize radius axis=@visualize clean radius axis,
+    /tikz/data visualization/@visualize zero/.style={@clean visualize zero={##1}},
+  },
+  radius/.initial=3.25cm,
+  0 to pi half/.style={
+    @setup axes/.style={
+      angle axis={min value=0, max value=1.570796326794897},
+      @rad,
+      @visualize zero=north east,
+      @inner radius axes at={{0}{low},{1.570796326794897}{high}},
+      @clean radius axes at={%
+        {0}{low}{high}{yshift=\pgfkeysvalueof{/tikz/data visualization/angle axis/padding min}}{},%
+        {1.570796326794897}{high}{low}{xshift=-\pgfkeysvalueof{/tikz/data visualization/angle axis/padding max}}{}
+      }
+    }
+  },
+  0 to 90/.style={
+    @setup axes/.style={
+      angle axis={min value=0, max value=90},
+      @degrees,
+      @visualize zero=north east,
+      @inner radius axes at={{0}{low},{90}{high}},
+      @clean radius axes at={%
+        {0}{low}{high}{yshift=\pgfkeysvalueof{/tikz/data visualization/angle axis/padding min}}{},%
+        {90}{high}{low}{xshift=-\pgfkeysvalueof{/tikz/data visualization/angle axis/padding max}}{}
+      }
+    }
+  },
+  quadrant/.style={
+    @setup axes/.style={
+      angle axis={scaling=min at 0 and max at 90, ticks},
+      @visualize zero=north east,
+      @inner radius axes at={{min}{low},{max}{high}},
+      @clean radius axes at={%
+        {min}{low}{high}{yshift=\pgfkeysvalueof{/tikz/data visualization/angle axis/padding min}}{},%
+        {max}{high}{low}{xshift=-\pgfkeysvalueof{/tikz/data visualization/angle axis/padding max}}{}
+      }
+    }
+  },
+  quadrant clockwise/.style={
+    @setup axes/.style={
+      angle axis={scaling=min at 90 and max at 0, ticks},
+      @visualize zero=north east,
+      @inner radius axes at={{min}{low},{max}{high}},
+      @clean radius axes at={%
+        {max}{high}{low}{yshift=\pgfkeysvalueof{/tikz/data visualization/angle axis/padding min}}{},%
+        {min}{low}{high}{xshift=-\pgfkeysvalueof{/tikz/data visualization/angle axis/padding max}}{}
+      }
+    }
+  },
+  -pi half to 0/.style={
+    @setup axes/.style={
+      angle axis={min value=-1.570796326794897, max value=0},
+      @rad,
+      @visualize zero=south east,
+      @inner radius axes at={{-1.570796326794897}{low},{0}{high}},
+      @clean radius axes at={%
+        {-1.570796326794897}{low}{high}{xshift=\pgfkeysvalueof{/tikz/data visualization/angle axis/padding min}}{},%
+        {0}{high}{low}{yshift=\pgfkeysvalueof{/tikz/data visualization/angle axis/padding max}}{}
+      }
+    }
+  },
+  -90 to 0/.style={
+    @setup axes/.style={
+      angle axis={min value=-90, max value=0},
+      @degrees,
+      @visualize zero=south east,
+      @inner radius axes at={{-90}{low},{0}{high}},
+      @clean radius axes at={%
+        {-90}{low}{high}{xshift=\pgfkeysvalueof{/tikz/data visualization/angle axis/padding min}}{},%
+        {0}{high}{low}{yshift=\pgfkeysvalueof{/tikz/data visualization/angle axis/padding max}}{}
+      }
+    }
+  },
+  fourth quadrant/.style={
+    @setup axes/.style={
+      angle axis={scaling=min at -90 and max at 0, ticks},
+      @visualize zero=south east,
+      @inner radius axes at={{min}{low},{max}{high}},
+      @clean radius axes at={%
+        {min}{low}{high}{xshift=\pgfkeysvalueof{/tikz/data visualization/angle axis/padding min}}{},%
+        {max}{high}{low}{yshift=\pgfkeysvalueof{/tikz/data visualization/angle axis/padding max}}{}
+      }
+    }
+  },
+  fourth quadrant clockwise/.style={
+    @setup axes/.style={
+      angle axis={scaling=min at 0 and max at -90, ticks},
+      @visualize zero=south east,
+      @inner radius axes at={{min}{low},{max}{high}},
+      @clean radius axes at={%
+        {max}{high}{low}{xshift=\pgfkeysvalueof{/tikz/data visualization/angle axis/padding min}}{},%
+        {min}{low}{high}{yshift=\pgfkeysvalueof{/tikz/data visualization/angle axis/padding max}}{}
+      }
+    }
+  },
+  0 to pi/.style={
+    @setup axes/.style={
+      angle axis={min value=0, max value=3.141592653589793},
+      @rad,
+      @visualize zero=north,
+      @inner radius axes at={{0}{low},{1.570796326794897}{high},{3.141592653589793}{high}},
+      @clean radius axes at={%
+        {0}{low}{high}{yshift=\pgfkeysvalueof{/tikz/data visualization/angle axis/padding min}}{},%
+        {3.141592653589793}{high}{low}{yshift=-\pgfkeysvalueof{/tikz/data
+            visualization/angle axis/padding max}}{options at=0 as
+          [{style={draw=none}, no tick text}]}
+      }
+    }
+  },
+  0 to 180/.style={
+    @setup axes/.style={
+      angle axis={min value=0, max value=180},
+      @degrees,
+      @visualize zero=north,
+      @inner radius axes at={{0}{low},{90}{high},{180}{high}},
+      @clean radius axes at={%
+        {0}{low}{high}{yshift=\pgfkeysvalueof{/tikz/data visualization/angle axis/padding min}}{},%
+        {180}{high}{low}{yshift=-\pgfkeysvalueof{/tikz/data
+            visualization/angle axis/padding max}}{options at=0 as
+          [{style={draw=none}, no tick text}]}
+      }
+    }
+  },
+  upper half/.style={
+    @setup axes/.style={
+      angle axis={scaling=min at 0 and max at 180, ticks},
+      @visualize zero=north,
+      @inner radius axes at={{min}{low},{max}{high}},
+      @clean radius axes at={%
+        {min}{low}{high}{yshift=\pgfkeysvalueof{/tikz/data visualization/angle axis/padding min}}{},%
+        {max}{high}{low}{yshift=-\pgfkeysvalueof{/tikz/data
+            visualization/angle axis/padding max}}{options at=0 as
+          [{style={draw=none}, no tick text}]}
+      }
+    }
+  },
+  upper half clockwise/.style={
+    @setup axes/.style={
+      angle axis={scaling=min at 180 and max at 0, ticks},
+      @visualize zero=north,
+      @inner radius axes at={{min}{low},{max}{high}},
+      @clean radius axes at={%
+        {min}{low}{high}{yshift=\pgfkeysvalueof{/tikz/data visualization/angle axis/padding min}}{},%
+        {max}{high}{low}{yshift=-\pgfkeysvalueof{/tikz/data
+            visualization/angle axis/padding max}}{options at=0 as
+          [{style={draw=none}, no tick text}]}
+      }
+    }
+  },
+  lower half/.style={
+    @setup axes/.style={
+      angle axis={scaling=min at -180 and max at 0, ticks},
+      @visualize zero=south,
+      @inner radius axes at={{min}{low},{max}{high}},
+      @clean radius axes at={%
+        {min}{low}{high}{yshift=-\pgfkeysvalueof{/tikz/data visualization/angle axis/padding min}}{},%
+        {max}{high}{low}{yshift=\pgfkeysvalueof{/tikz/data
+            visualization/angle axis/padding max}}{options at=0 as
+          [{style={draw=none}, no tick text}]}
+      }
+    }
+  },
+  lower half clockwise/.style={
+    @setup axes/.style={
+      angle axis={scaling=min at 0 and max at -180, ticks},
+      @visualize zero=south,
+      @inner radius axes at={{min}{low},{max}{high}},
+      @clean radius axes at={%
+        {min}{low}{high}{yshift=-\pgfkeysvalueof{/tikz/data visualization/angle axis/padding min}}{},%
+        {max}{high}{low}{yshift=\pgfkeysvalueof{/tikz/data
+            visualization/angle axis/padding max}}{options at=0 as
+          [{style={draw=none}, no tick text}]}
+      }
+    }
+  },
+  -pi half to pi half/.style={
+    @setup axes/.style={
+      @rad,
+      angle axis={min value=-1.570796326794897, max value=1.570796326794897},
+      @visualize zero=east,
+      @inner radius axes at={{0}{low},{1.570796326794897}{low},{-1.570796326794897}{high}},
+      @clean radius axes at={%
+        {-1.570796326794897}{low}{high}{xshift=\pgfkeysvalueof{/tikz/data visualization/angle axis/padding min}}{},%
+        {1.570796326794897}{high}{low}{xshift=-\pgfkeysvalueof{/tikz/data
+            visualization/angle axis/padding max}}{options at=0 as
+          [{style={draw=none}, no tick text}]}
+      }
+    }
+  },
+  -90 to 90/.style={
+    @setup axes/.style={
+      angle axis={min value=-90, max value=90},
+      @degrees,
+      @visualize zero=east,
+      @inner radius axes at={{-90}{low},{0}{low},{90}{high}},
+      @clean radius axes at={%
+        {-90}{low}{high}{xshift=\pgfkeysvalueof{/tikz/data visualization/angle axis/padding min}}{},%
+        {90}{high}{low}{xshift=-\pgfkeysvalueof{/tikz/data
+            visualization/angle axis/padding max}}{options at=0 as
+          [{style={draw=none}, no tick text}]}
+      }
+    }
+  },
+  right half/.style={
+    @setup axes/.style={
+      angle axis={scaling=min at -90 and max at 90, ticks},
+      @visualize zero=east,
+      @inner radius axes at={{min}{low},{max}{high}},
+      @clean radius axes at={%
+        {min}{low}{high}{xshift=\pgfkeysvalueof{/tikz/data visualization/angle axis/padding min}}{},%
+        {max}{high}{low}{xshift=-\pgfkeysvalueof{/tikz/data
+            visualization/angle axis/padding max}}{options at=0 as
+          [{style={draw=none}, no tick text}]}
+      }
+    }
+  },
+  right half clockwise/.style={
+    @setup axes/.style={
+      angle axis={scaling=min at 90 and max at -90, ticks},
+      @visualize zero=east,
+      @inner radius axes at={{min}{low},{max}{high}},
+      @clean radius axes at={%
+        {min}{low}{high}{xshift=\pgfkeysvalueof{/tikz/data visualization/angle axis/padding min}}{},%
+        {max}{high}{low}{xshift=-\pgfkeysvalueof{/tikz/data
+            visualization/angle axis/padding max}}{options at=0 as
+          [{style={draw=none}, no tick text}]}
+      }
+    }
+  },
+  left half/.style={
+    @setup axes/.style={
+      angle axis={scaling=min at 90 and max at 270, ticks},
+      @visualize zero=west,
+      @inner radius axes at={{min}{low},{max}{high}},
+      @clean radius axes at={%
+        {min}{low}{high}{xshift=-\pgfkeysvalueof{/tikz/data visualization/angle axis/padding min}}{},%
+        {max}{high}{low}{xshift=\pgfkeysvalueof{/tikz/data
+            visualization/angle axis/padding max}}{options at=0 as
+          [{style={draw=none}, no tick text}]}
+      }
+    }
+  },
+  left half clockwise/.style={
+    @setup axes/.style={
+      angle axis={scaling=min at 270 and max at 90, ticks},
+      @visualize zero=west,
+      @inner radius axes at={{min}{low},{max}{high}},
+      @clean radius axes at={%
+        {min}{low}{high}{xshift=-\pgfkeysvalueof{/tikz/data visualization/angle axis/padding min}}{},%
+        {max}{high}{low}{xshift=\pgfkeysvalueof{/tikz/data
+            visualization/angle axis/padding max}}{options at=0 as
+          [{style={draw=none}, no tick text}]}
+      }
+    }
+  },
+  0 to 2pi/.style={
+    @setup axes/.style={
+      angle axis={min value=0, max value=6.283185307179586},
+      @rad,
+      @visualize zero=north east,
+      @inner radius axes at={{0}{low},{1.570796326794897}{high},{3.141592653589793}{high},{4.71238898038469}{low}},
+      @clean radius axes at={{0}{low}{high}{}{}}
+    }
+  },
+  -pi to pi/.style={
+    @setup axes/.style={
+      angle axis={min value=-3.141592653589793, max value=3.141592653589793},
+      @rad,
+      @visualize zero=north east,
+      @inner radius axes at={{0}{low},{1.570796326794897}{high},{3.141592653589793}{high},{-1.57079632679489}{low}},
+      @clean radius axes at={{0}{low}{high}{}{}}
+    }
+  },
+  0 to 360/.style={
+    @setup axes/.style={
+      angle axis={min value=0, max value=360},
+      @degrees,
+      @visualize zero=north east,
+      @inner radius axes at={{0}{low},{90}{high},{180}{high},{270}{low}},
+      @clean radius axes at={{0}{low}{high}{}{}}
+    }
+  },
+  -180 to 180/.style={
+    @setup axes/.style={
+      angle axis={min value=-180, max value=180},
+      @degrees,
+      @visualize zero=north east,
+      @inner radius axes at={{0}{low},{90}{high},{180}{high},{-90}{low}},
+      @clean radius axes at={{0}{low}{high}{}{}}
+    }
+  },
+}%
+
+
+
+
+
+\tikzset{
+  /tikz/data visualization/axis options/.cd,
+  percent/.style={\tikz@dv@axis/scaling=0 at 0 and 1 at 3.6},
+  full circle/.style={\tikz@dv@axis/scaling=min at 0 and max at 360},
+  half circle/.style={\tikz@dv@axis/scaling=min at 0 and max at 180},
+  quarter circle/.style={\tikz@dv@axis/scaling=min at 0 and max at 90}
+}%
+
+
+
+
+\endinput

preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/datavisualization/tikzlibrarydatavisualization.sparklines.code.tex

@@ -0,0 +1,26 @@
+
+\ProvidesFileRCS{tikzlibrarydatavisualization.sparklines.code.tex}
+
+\usetikzlibrary{datavisualization}%
+
+
+
+
+
+\tikzdatavisualizationset{
+  spark line/.style={
+    xy Cartesian,
+    x axis={
+      unit length={1pt}
+    },
+    y axis={
+      scaling={min at -0.2em and max at 0.8em}
+    },
+    new line plot,
+    every spark line plot/.try
+  }
+}%
+
+
+
+\endinput

preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/graphs/tikzlibrarygraphs.code.tex

@@ -0,0 +1,2275 @@
+
+\ProvidesFileRCS{tikzlibrarygraphs.code.tex}
+
+
+
+\def\tikzgraphsset{\pgfqkeys{/tikz/graphs}}%
+
+\tikzgraphsset{
+  new ->/.code n args={4}{%
+    \path [->,every new ->/.try]
+      (#1\tikzgraphleftanchor)
+      edge[#3] #4
+      (#2\tikzgraphrightanchor);},
+  new --/.code n args={4}{
+      \path [-,every new --/.try]
+      (#1\tikzgraphleftanchor)
+      edge[#3] #4
+      (#2\tikzgraphrightanchor);},
+  new <->/.code n args={4}{
+    \path [<->,every new <->/.try]
+      (#1\tikzgraphleftanchor)
+      edge[#3] #4
+      (#2\tikzgraphrightanchor);},
+  new -!-/.code n args={4}{},
+  new <-/.code n args={4}{%
+    \path [<-,every new <-/.try]
+      (#1\tikzgraphleftanchor)
+      edge[#3] #4
+      (#2\tikzgraphrightanchor);
+  }
+}%
+
+
+\def\tikz@lib@graph@store@anchor#1#2{%
+  \def\tikz@temp{#1}%
+  \ifx\tikz@temp\pgfutil@empty%
+    \let#2\tikz@temp%
+  \else%
+    \def\tikz@temp{.#1}%
+    \let#2\tikz@temp%
+  \fi%
+}%
+
+\tikzgraphsset{
+  default edge kind/.initial=--,
+  --/.style={default edge kind=--},
+  ->/.style={default edge kind=->},
+  <-/.style={default edge kind=<-},
+  <->/.style={default edge kind=<->},
+  -!-/.style={default edge kind=-!-},
+  default edge operator/.initial=matching and star,
+  left anchor/.code=\tikz@lib@graph@store@anchor{#1}{\tikzgraphleftanchor},
+  right anchor/.code=\tikz@lib@graph@store@anchor{#1}{\tikzgraphrightanchor},
+  left anchor=,
+  right anchor=
+}%
+
+
+
+\tikzgraphsset{
+  use existing nodes/.is if=tikz@lib@graph@all
+}%
+
+\tikzset{
+  new set/.code={
+    \expandafter\global\expandafter\let\csname tikz@lg@node@set #1\endcsname\pgfutil@empty%
+  },
+  set/.code={
+    \tikz@fig@mustbenamed%
+    \ifcsname tikz@lg@node@set #1\endcsname\else
+      \tikzerror{Undefined set `#1'}%
+    \fi
+    \expandafter\def\expandafter\tikz@alias\expandafter{\tikz@alias%
+      \expandafter\def\expandafter\pgf@temp\expandafter{\csname tikz@lg@node@set #1\endcsname}%
+      \expandafter\expandafter\expandafter\pgfutil@g@addto@macro\expandafter\pgf@temp\expandafter{\expandafter\tikz@lg@do\expandafter{\tikz@fig@name}}%
+    }%
+  },%
+}%
+
+\newif\iftikz@lib@graph@all
+
+
+\tikzgraphsset{
+  simple/.code={
+    \iftikz@lib@graph@simple%
+    \else
+      \tikz@lib@graph@simpletrue%
+      \pgfkeysalso{operator=\tikz@lib@graph@simple@done}%
+    \fi%
+  },
+  multi/.code={
+    \tikz@lib@graph@simplefalse%
+  }
+}%
+
+\newif\iftikz@lib@graph@simple
+
+\def\tikz@lib@graph@set@simple@edge#1#2#3#4#5{%
+  \ifcsname tikz@lg@e@#3@#2\endcsname%
+    \expandafter\global\expandafter\let\csname tikz@lg@e@#3@#2\endcsname\relax%
+  \fi%
+  \expandafter\gdef\csname tikz@lg@e@#2@#3\endcsname{\tikz@lib@graph@make@simple@edge{#1}{#2}{#3}{#4}{#5}}%
+}%
+
+\def\tikz@lib@graph@make@simple@edge#1#2#3#4#5{%
+  \pgfqkeys{/tikz/graphs}{new #1={#2}{#3}{#4}{#5}}%
+}%
+
+
+\def\tikz@lib@graph@simple@done{%
+  \tikz@lib@graph@pack@node@list%
+  {%
+    \let\tikz@lg@do\tikz@lib@graph@simple@node%
+    \tikz@lib@graph@node@list
+  }%
+}%
+
+\def\tikz@lib@graph@simple@node#1{%
+  {%
+    \def\tikz@lib@graph@simple@from@node{#1}%
+    \let\tikz@lg@do\tikz@lib@graph@simple@other@node%
+    \tikz@lib@graph@node@list%
+  }%
+}%
+
+\def\tikz@lib@graph@simple@other@node#1{%
+  \ifcsname tikz@lg@e@\tikz@lib@graph@simple@from@node @#1\endcsname%
+    \csname tikz@lg@e@\tikz@lib@graph@simple@from@node @#1\endcsname%
+    \expandafter\global\expandafter\let\csname tikz@lg@e@\tikz@lib@graph@simple@from@node @#1\endcsname\relax%
+  \fi%
+}%
+
+
+
+\tikzgraphsset{
+  @nodes styling/.style=,
+  nodes/.style={/tikz/graphs/@nodes styling/.append style={,#1}},
+  @edges styling/.initial=,
+  edges/.style={/tikz/graphs/@edges styling/.append={,#1}},
+  edge/.style={edges={#1}},
+  @edges node/.initial=,
+  edge node/.style={/tikz/graphs/@edges node/.append={#1}},
+  edge label/.style={/tikz/graphs/@edges node/.append={node[auto]{#1}}},
+  edge label'/.style={/tikz/graphs/@edges node/.append={node[auto,swap]{#1}}},
+  @operators/.initial=,
+  operator/.style={/tikz/graphs/@operators/.append={#1}},
+  @extra group options/.style=,
+}%
+
+
+\def\tikzgraphinvokeoperator#1{%
+  {%
+    \pgfkeyslet{/tikz/graphs/@operators}\pgfutil@empty%
+    \pgfkeys{/tikz/graphs/.cd,#1}%
+    \pgfkeysgetvalue{/tikz/graphs/@operators}\tikz@lib@graph@temp%
+    \global\let\tikz@lib@graph@temp\tikz@lib@graph@temp%
+  }%
+  \tikz@lib@graph@temp%
+  \global\let\tikz@lib@graph@temp\relax%
+}%
+
+
+
+\def\tikz@lib@graph@parser{%
+  \pgfutil@ifnextchar[{\tikz@lib@graph@parser@}{\tikz@lib@graph@parser@[]}%
+}%
+
+\def\tikz@lib@graph@parser@[#1]{%
+  \setbox\tikz@whichbox=\hbox\bgroup%
+    \unhbox\tikz@whichbox%
+    \hbox\bgroup
+      \bgroup%
+        \pgfinterruptpath%
+          \scope[graphs/.cd,@graph drawing setup/.try,@operators=,every graph/.try,#1]%
+            \begingroup%
+            \iftikz@graph@quick%
+              \expandafter\tikz@lib@graphs@parse@quick@graph%
+            \else%
+              \expandafter\tikz@lib@graphs@normal@main%
+            \fi%
+}%
+
+\long\def\tikz@lib@graphs@normal@main#1{%
+              \pgfkeysgetvalue{/tikz/graphs/@operators}\tikz@lib@graph@outer@operators%
+              \let\tikz@lib@graph@options\pgfutil@empty%
+              \let\tikz@lib@graph@node@list\pgfutil@empty%
+              \pgfkeyssetvalue{/tikz/graphs/placement/depth}{0}%
+              \pgfkeyssetvalue{/tikz/graphs/placement/width}{0}%
+              \pgfkeyssetvalue{/tikz/graphs/placement/level}{0}%
+              \tikz@lib@graph@start@hint@group%
+                \tikz@lib@graph@parse@group{#1}%
+              \tikz@lib@graph@end@hint@group
+              \tikz@lib@graph@outer@operators%
+              \let\tikz@lg@do=\tikz@lib@graph@cleanup%
+              \tikz@lib@graph@node@list%
+              \tikz@lib@graph@main@done%
+}%
+
+\def\tikz@lib@graph@main@done{%
+            \endgroup%
+          \endscope%
+        \endpgfinterruptpath%
+      \egroup
+    \egroup%
+  \egroup%
+  \tikz@lib@graph@parser@done%
+}%
+
+
+
+
+
+\def\tikz@lib@graph@start@hint@group{%
+  \pgfkeyssetvalue{/tikz/graphs/placement/local depth}{0}%
+  \pgfkeyssetvalue{/tikz/graphs/placement/local width}{0}%
+  \pgfkeyssetvalue{/tikz/graphs/placement/chain count}{0}%
+  \pgfkeyssetvalue{/tikz/graphs/placement/element count}{0}%
+}%
+
+\def\tikz@lib@graph@end@hint@group{%
+  \xdef\tikz@lib@graph@group@depth{\pgfkeysvalueof{/tikz/graphs/placement/local depth}}
+  \xdef\tikz@lib@graph@group@width{\pgfkeysvalueof{/tikz/graphs/placement/local width}}
+}%
+
+\def\tikz@lib@graph@hint@aftergroup{%
+  \pgfkeysgetvalue{/tikz/graphs/placement/width}\tikz@temp@h%
+  \pgfkeysgetvalue{/tikz/graphs/placement/local width}\tikz@temp@lh%
+  \pgfkeysgetvalue{/tikz/graphs/placement/local depth}\tikz@temp@lw%
+  \pgfmathsetmacro\tikz@temp@h{\tikz@lib@graph@group@width+\tikz@temp@h}
+  \pgfmathsetmacro\tikz@temp@lh{\tikz@lib@graph@group@width+\tikz@temp@lh}
+  \pgfmathsetmacro\tikz@temp@lw{max(\tikz@lib@graph@group@depth,\tikz@temp@lw)}
+  \pgfkeyslet{/tikz/graphs/placement/width}\tikz@temp@h%
+  \pgfkeyslet{/tikz/graphs/placement/local width}\tikz@temp@lh%
+  \pgfkeyslet{/tikz/graphs/placement/local depth}\tikz@temp@lw%
+  \pgfkeysgetvalue{/tikz/graphs/placement/element count}\tikz@temp%
+  \c@pgf@counta=\tikz@temp\relax%
+  \advance\c@pgf@counta by1\relax%
+  \edef\tikz@temp{\the\c@pgf@counta}%
+  \pgfkeyslet{/tikz/graphs/placement/element count}\tikz@temp%
+}%
+
+\def\tikz@lib@graph@placement@update{%
+  \pgfkeys{/tikz/graphs/placement/logical node depth/.expand once=\tikz@lib@graph@name}
+  \let\tikz@lib@graph@node@depth\pgfmathresult
+  \pgfkeys{/tikz/graphs/placement/logical node width/.expand once=\tikz@lib@graph@name}
+  \let\tikz@lib@graph@node@width\pgfmathresult
+  \pgfkeysgetvalue{/tikz/graphs/placement/width}\tikz@temp@h%
+  \pgfkeysgetvalue{/tikz/graphs/placement/local width}\tikz@temp@lh%
+  \pgfkeysgetvalue{/tikz/graphs/placement/local depth}\tikz@temp@lw%
+  \pgfmathsetmacro\tikz@temp@h{\tikz@lib@graph@node@width+\tikz@temp@h}
+  \pgfmathsetmacro\tikz@temp@lh{\tikz@lib@graph@node@width+\tikz@temp@lh}
+  \pgfmathsetmacro\tikz@temp@lw{max(\tikz@lib@graph@node@depth,\tikz@temp@lw)}
+  \pgfkeyslet{/tikz/graphs/placement/width}\tikz@temp@h%
+  \pgfkeyslet{/tikz/graphs/placement/local width}\tikz@temp@lh%
+  \pgfkeyslet{/tikz/graphs/placement/local depth}\tikz@temp@lw%
+  \pgfkeysgetvalue{/tikz/graphs/placement/element count}\tikz@temp%
+  \c@pgf@counta=\tikz@temp\relax%
+  \advance\c@pgf@counta by1\relax%
+  \edef\tikz@temp{\the\c@pgf@counta}%
+  \pgfkeyslet{/tikz/graphs/placement/element count}\tikz@temp%
+}%
+
+\def\tikz@lib@graph@placement@after@chain@update{%
+  \pgfkeysgetvalue{/tikz/graphs/placement/depth}\tikz@temp@w%
+  \pgfkeysgetvalue{/tikz/graphs/placement/local width}\tikz@temp@lh%
+  \pgfkeysgetvalue{/tikz/graphs/placement/local depth}\tikz@temp@lw%
+  \pgfmathsetmacro\tikz@temp@w{\tikz@lib@graph@chain@depth+\tikz@temp@w}%
+  \pgfmathsetmacro\tikz@temp@lw{\tikz@lib@graph@chain@depth+\tikz@temp@lw}%
+  \pgfmathsetmacro\tikz@temp@lh{max(\tikz@lib@graph@chain@width,\tikz@temp@lh)}%
+  \pgfkeyslet{/tikz/graphs/placement/depth}\tikz@temp@w%
+  \pgfkeyslet{/tikz/graphs/placement/local width}\tikz@temp@lh%
+  \pgfkeyslet{/tikz/graphs/placement/local depth}\tikz@temp@lw%
+  \pgfkeysgetvalue{/tikz/graphs/placement/chain count}\tikz@temp%
+  \c@pgf@counta=\tikz@temp\relax%
+  \advance\c@pgf@counta by1\relax%
+  \edef\tikz@temp{\the\c@pgf@counta}%
+  \pgfkeyslet{/tikz/graphs/placement/chain count}\tikz@temp%
+}%
+
+
+
+\long\def\tikz@lib@graph@parse@group#1{
+  \let\tikz@lib@graph@group@qa\pgfutil@empty%
+  \let\tikz@lib@graph@group@q\pgfutil@empty%
+  \let\tikz@lib@graph@group@c\pgfutil@empty%
+  \let\tikz@lib@graph@group@cont\pgfutil@empty%
+  \let\tikz@lib@graph@group@conta\pgfutil@empty%
+  \tikz@lib@graph@group@check#1\par\pgf@stop@eogroup%
+}%
+
+
+
+\def\tikz@lib@graph@group@check{%
+  \pgfutil@ifnextchar[\tikz@lib@graph@group@opt{\tikz@lib@graph@group@opt[]}%
+}%
+
+\def\tikz@lib@graph@group@opt[#1]{%
+  \let\tikz@lib@graph@parse@extras\pgfutil@empty%
+  \tikzgraphsset{
+    @operators=,
+    every group/.try,
+    @extra group options,
+    @extra group options/.style=,%
+    #1}%
+  \expandafter\tikz@lib@graph@par\tikz@lib@graph@parse@extras%
+}%
+
+\tikzgraphsset{
+  parse/.code={\expandafter\def\expandafter\tikz@lib@graph@parse@extras\expandafter{\tikz@lib@graph@parse@extras#1}},
+}%
+
+
+
+
+\def\tikz@lib@graph@par{%
+  \pgfutil@ifnextchar\bgroup{\tikz@lib@graph@par@@}{\tikz@lib@graph@par@}%
+}%
+\long\def\tikz@lib@graph@par@#1\par{%
+  \pgfutil@ifnextchar\pgf@stop@eogroup{%
+    \expandafter\tikz@lib@graph@quotes\tikz@lib@graph@group@c#1"}{%
+    \expandafter\def\expandafter\tikz@lib@graph@group@c\expandafter{\tikz@lib@graph@group@c#1}%
+    \tikz@lib@graph@par%
+  }%
+}%
+\long\def\tikz@lib@graph@par@@#1{%
+  \expandafter\def\expandafter\tikz@lib@graph@group@c\expandafter{\tikz@lib@graph@group@c{#1}}%
+  \tikz@lib@graph@par
+}%
+
+
+
+\def\tikz@lib@graph@quotes{%
+  \pgfutil@ifnextchar\bgroup{\tikz@lib@graph@quotes@@}{\tikz@lib@graph@quotes@}%
+}%
+\def\tikz@lib@graph@quotes@#1"{%
+  \pgfutil@ifnextchar\pgf@stop@eogroup{%
+    \tikz@lib@graph@passon{#1}%
+  }{%
+    \expandafter\def\expandafter\tikz@lib@graph@group@q\expandafter{\tikz@lib@graph@group@q#1"}%
+    \tikz@lib@graph@quotes@cont%
+  }%
+}%
+
+\def\tikz@lib@graph@quotes@cont#1"#2"{%
+  \pgfutil@ifnextchar\pgf@stop@eogroup{%
+    \tikz@lib@graph@passon{{#1}"#2}}{%
+    \expandafter\def\expandafter\tikz@lib@graph@group@q\expandafter{\tikz@lib@graph@group@q{#1}"#2"}%
+    \tikz@lib@graph@quotes@cont}%
+}%
+
+\def\tikz@lib@graph@quotes@@#1{%
+  \expandafter\def\expandafter\tikz@lib@graph@group@q\expandafter{\tikz@lib@graph@group@q{#1}}%
+  \tikz@lib@graph@quotes%
+}%
+
+
+
+{%
+  \catcode`\"=13\relax
+
+  \gdef\tikz@lib@graph@passon#1{\expandafter\tikz@lib@graph@quotesactive\tikz@lib@graph@group@q#1"}%
+
+  \gdef\tikz@lib@graph@quotesactive{%
+    \pgfutil@ifnextchar\bgroup{\tikz@lib@graph@quotesactive@@}{\tikz@lib@graph@quotesactive@}%
+  }%
+  \gdef\tikz@lib@graph@quotesactive@#1"{%
+    \pgfutil@ifnextchar\pgf@stop@eogroup{%
+      \expandafter\tikz@lib@graph@encloser\tikz@lib@graph@group@qa#1[%
+    }{%
+      \expandafter\def\expandafter\tikz@lib@graph@group@qa\expandafter{\tikz@lib@graph@group@qa#1"}%
+      \tikz@lib@graph@quotesactive@cont%
+    }%
+  }%
+
+  \gdef\tikz@lib@graph@quotesactive@cont#1"#2"{%
+    \pgfutil@ifnextchar\pgf@stop@eogroup{%
+      \expandafter\tikz@lib@graph@encloser\tikz@lib@graph@group@qa{#1}"#2[}{%
+      \expandafter\def\expandafter\tikz@lib@graph@group@qa\expandafter{\tikz@lib@graph@group@qa{#1}"#2"}%
+      \tikz@lib@graph@quotesactive@cont}%
+  }%
+
+  \gdef\tikz@lib@graph@quotesactive@@#1{%
+    \expandafter\def\expandafter\tikz@lib@graph@group@qa\expandafter{\tikz@lib@graph@group@qa{#1}}%
+    \tikz@lib@graph@quotesactive%
+  }%
+}%
+
+
+
+
+\def\tikz@lib@graph@encloser{%
+  \pgfutil@ifnextchar\bgroup{\tikz@lib@graph@encloser@@}{\tikz@lib@graph@encloser@}%
+}%
+\def\tikz@lib@graph@encloser@#1[{%
+  \pgfutil@ifnextchar\pgf@stop@eogroup{%
+    \expandafter\tikz@lib@graph@semi\tikz@lib@graph@group@cont#1;%
+  }{%
+    \expandafter\def\expandafter\tikz@lib@graph@group@cont\expandafter{\tikz@lib@graph@group@cont#1[}%
+    \tikz@lib@graph@encloser@cont%
+  }%
+}%
+
+\def\tikz@lib@graph@encloser@cont#1]#2[{%
+  \pgfutil@ifnextchar\pgf@stop@eogroup{%
+    \expandafter\tikz@lib@graph@semi\tikz@lib@graph@group@cont{#1}]#2;}{%
+    \expandafter\def\expandafter\tikz@lib@graph@group@cont\expandafter{\tikz@lib@graph@group@cont{#1}]#2[}%
+    \tikz@lib@graph@encloser@cont}%
+}%
+
+\def\tikz@lib@graph@encloser@@#1{%
+  \expandafter\def\expandafter\tikz@lib@graph@group@cont\expandafter{\tikz@lib@graph@group@cont{#1}}%
+  \tikz@lib@graph@encloser%
+}%
+
+
+
+
+
+\def\tikz@lib@graph@semi{%
+  \pgfutil@ifnextchar\bgroup{\tikz@lib@graph@semi@@}{\tikz@lib@graph@semi@}%
+}%
+\def\tikz@lib@graph@semi@#1;{%
+  \pgfutil@ifnextchar\pgf@stop@eogroup{%
+    \expandafter\tikz@lib@graph@main@parser\tikz@lib@graph@group@conta#1,}{%
+    \expandafter\def\expandafter\tikz@lib@graph@group@conta\expandafter{\tikz@lib@graph@group@conta#1,}%
+    \tikz@lib@graph@semi%
+  }%
+}%
+\def\tikz@lib@graph@semi@@#1{%
+  \expandafter\def\expandafter\tikz@lib@graph@group@conta\expandafter{\tikz@lib@graph@group@conta{#1}}%
+  \tikz@lib@graph@semi%
+}%
+
+
+
+\def\tikz@lib@graph@main@parser{%
+  \begingroup%
+    \pgfkeyssetvalue{/tikz/graphs/placement/local depth}{0}%
+    \pgfkeyssetvalue{/tikz/graphs/placement/local width}{0}%
+    \let\tikz@lib@graph@stored@actions\pgfutil@empty%
+    \let\tikz@lib@graph@node@list\pgfutil@empty%
+    \tikz@lib@graph@main@parser@start%
+}%
+\def\tikz@lib@graph@main@parser@start{%
+  \pgfutil@ifnextchar\bgroup{\tikz@lib@graph@protect@group}{\tikz@lib@graph@main@parser@cont}%
+}%
+
+\def\tikz@lib@graph@protect@group#1{%
+  \pgfutil@ifnextchar\relax{\tikz@lib@graph@main@parser@cont{{#1}}}{\tikz@lib@graph@main@parser@cont{{#1}}}%
+}%
+
+\def\tikz@lib@graph@main@parser@cont{\tikz@lib@graph@check@quotes\tikz@lib@graph@main@parser@cont@normal}%
+\def\tikz@lib@graph@main@parser@cont@normal#1,{%
+  \tikz@lib@graph@parse@one#1-\pgf@stop@eodashes%
+}%
+
+\def\tikz@lib@graph@parse@one{%
+  \pgfutil@ifnextchar\bgroup\tikz@lib@graph@scope\tikz@lib@graph@node%
+}%
+
+
+
+
+\def\tikz@lib@graph@check@quotes#1{%
+  \let\tikz@lib@graph@cont@quote#1%
+  \pgfutil@ifnextchar"{\begingroup\pgfkeys@temptoks{}\pgfutil@empty\tikz@lib@graph@quote@parser}{\tikz@lib@graph@check@quotes@active}%
+}%
+{%
+  \catcode`\"=13\relax
+  \gdef\tikz@lib@graph@check@quotes@active{%
+    \pgfutil@ifnextchar"{\begingroup\pgfkeys@temptoks{}\pgfutil@empty\tikz@lib@graph@quote@parser@active}{\tikz@lib@graph@cont@quote}%
+  }%
+  \gdef\tikz@lib@graph@quote@parser@active"#1"{%
+    \pgfkeys@temptoks\expandafter{\the\pgfkeys@temptoks #1}%
+    \pgfutil@ifnextchar"{\pgfkeys@temptoks\expandafter{\the\pgfkeys@temptoks "}\tikz@lib@graph@quote@parser@active}{\tikz@lib@graph@quote@parser@done}%
+  }%
+}%
+
+\def\tikz@lib@graph@quote@parser"#1"{%
+  \pgfkeys@temptoks\expandafter{\the\pgfkeys@temptoks #1}%
+  \pgfutil@ifnextchar"{\pgfkeys@temptoks\expandafter{\the\pgfkeys@temptoks "}\tikz@lib@graph@quote@parser}{\tikz@lib@graph@quote@parser@done}%
+}%
+
+\def\tikz@lib@graph@quote@parser@done{%
+  {\expandafter\scantokens\expandafter{%
+    \expandafter\expandafter\expandafter\tikzlibgraphactivations\expandafter\expandafter\expandafter\tikzlibgraphdoedef\expandafter{\the\pgfkeys@temptoks}%
+  }}%
+  {\expandafter\scantokens\expandafter{\expandafter\tikzlibgraphactivationsbrace\expandafter\xdef\expandafter\tikzlibgraphreplaced\expandafter<\tikzlibgraphreplaced>\catcode`\}=2\relax}}%
+  \edef\tikzlibgraphreplaced{\expandafter\detokenize\expandafter{\tikzlibgraphreplaced}}
+  \pgfutil@ifnextchar/\tikz@lib@graph@quotes@slash\tikz@lib@graph@quotes@no@slash%
+}%
+\def\tikz@lib@graph@quotes@no@slash{%
+  \expandafter\expandafter\expandafter\def\expandafter\expandafter\expandafter%
+  \tikz@smuggle\expandafter\expandafter\expandafter{\expandafter\tikzlibgraphreplaced\expandafter/\expandafter{\the\pgfkeys@temptoks}}%
+  \expandafter\endgroup\expandafter\tikz@lib@graph@cont@quote\tikz@smuggle%
+}%
+\def\tikz@lib@graph@quotes@slash/{%
+  \pgfutil@ifnextchar/%
+  {\tikz@lib@graph@quotes@no@slash/}{\expandafter\endgroup\expandafter\tikz@lib@graph@cont@quote\tikzlibgraphreplaced/}%
+}%
+\def\tikzlibgraphdoedef{\xdef\tikzlibgraphreplaced}%
+
+\def\tikz@lib@prepare@active#1#2#3{%
+  {%
+    \catcode`#1=13\relax%
+    \scantokens{\gdef\tikzlibgraphactivator{\def#2{@#3@}}}%
+  }%
+  \pgfutil@g@addto@macro\tikzlibgraphactivations{\catcode`#1=13\relax}%
+  \expandafter\pgfutil@g@addto@macro\expandafter\tikzlibgraphactivations\expandafter{\tikzlibgraphactivator}%
+}%
+
+\let\tikzlibgraphactivations\pgfutil@empty
+
+
+\outer\def\tikz@lib@outer@test{\tabalign}%
+\ifx\+\tikz@lib@outer@test
+  \def\+{\tabalign}
+\fi
+
+\tikz@lib@prepare@active{\$}{$}{DOLLAR SIGN}%
+\tikz@lib@prepare@active{\&}{&}{AMPERSAND}%
+\tikz@lib@prepare@active{\^}{^}{CIRCUMFLEX ACCENT}%
+\tikz@lib@prepare@active{\~}{~}{TILDE}%
+\tikz@lib@prepare@active{\_}{_}{LOW LINE}%
+\tikz@lib@prepare@active{\|}{|}{VERTICAL LINE}%
+\tikz@lib@prepare@active{\[}{[}{LEFT SQUARE BRACKET}%
+\tikz@lib@prepare@active{\]}{]}{RIGHT SQUARE BRACKET}%
+\tikz@lib@prepare@active{\(}{(}{LEFT PARENTHESIS}%
+\tikz@lib@prepare@active{\)}{)}{RIGHT PARENTHESIS}%
+\tikz@lib@prepare@active{\/}{/}{SOLIDUS}%
+\tikz@lib@prepare@active{\.}{.}{FULL STOP}%
+\tikz@lib@prepare@active{\-}{-}{HYPHEN MINUS}%
+\tikz@lib@prepare@active{\,}{,}{COMMA}%
+\tikz@lib@prepare@active{\+}{+}{PLUS SIGN}%
+\tikz@lib@prepare@active{\*}{*}{ASTERISK}%
+\tikz@lib@prepare@active{\'}{'}{APOSTROPHE}%
+\tikz@lib@prepare@active{\!}{!}{EXCLAMATION MARK}%
+\tikz@lib@prepare@active{\"}{"}{QUOTATION MARK}%
+\tikz@lib@prepare@active{\:}{:}{COLON}%
+\tikz@lib@prepare@active{\;}{;}{SEMINCOLON}%
+\tikz@lib@prepare@active{\<}{<}{LESS THAN SIGN}%
+\tikz@lib@prepare@active{\=}{=}{EQUALS SIGN}%
+\tikz@lib@prepare@active{\>}{>}{GREATER THAN SIGN}%
+\tikz@lib@prepare@active{\?}{?}{QUESTION MARK}%
+\tikz@lib@prepare@active{\`}{`}{GRAVE ACCENT}%
+{\catcode`\%=11\catcode`\#=11
+\tikz@lib@prepare@active{\%}{%}{PERCENT SIGN}
+\tikz@lib@prepare@active{\#}{#}{NUMBER SIGN}
+}
+
+\pgfutil@g@addto@macro\tikzlibgraphactivations{\catcode`\\=13\relax}%
+{%
+  \catcode`\|=0\relax
+  \catcode`\\=13\relax
+  |pgfutil@g@addto@macro|tikzlibgraphactivations{|def\{@REVERSE SOLIDUS@}}%
+}%
+{%
+  \gdef\tikzlibgraphscommercialat{@COMMERCIAL AT@}%
+  \let\g=\pgfutil@g@addto@macro
+  \catcode`\@=13\relax
+  \g\tikzlibgraphactivations{\catcode`\@=13\relax\let@=\tikzlibgraphscommercialat}%
+}%
+
+\def\tikzlibgraphactivationsbrace{%
+  \catcode`\{=13\relax%
+  \catcode`\}=13\relax%
+  \catcode`\<=1\relax%
+  \catcode`\>=2\relax%
+}%
+{%
+  \catcode`\{=13\relax%
+  \catcode`\}=13\relax%
+  \catcode`\<=1\relax%
+  \catcode`\>=2\relax%
+  \pgfutil@g@addto@macro\tikzlibgraphactivationsbrace<\def{<@LEFT CURLY BRACE@>> %
+  \pgfutil@g@addto@macro\tikzlibgraphactivationsbrace<\def}<@RIGHT CURLY BRACE@>> %
+>%
+
+
+
+\def\tikz@lib@graph@node{\tikz@lib@graph@check@quotes\tikz@lib@graph@node@normal}%
+
+\def\tikz@lib@graph@node@normal{%
+  \pgfutil@ifnextchar({\tikz@lib@graph@node@dressed}{\tikz@lib@graph@node@naked}%
+}%
+
+\def\tikz@lib@graph@node@dressed(#1){%
+  \tikz@lib@graph@node@naked{(#1)}%
+}%
+
+\def\tikz@lib@graph@node@naked#1-{%
+  \tikz@lib@graph@@node#1<\pgf@stop%
+}%
+
+\def\tikz@lib@graph@@node#1<#2\pgf@stop%
+{
+  \tikz@lib@graph@grab@name#1\pgf@stop%
+  \tikz@lib@graph@stored@actions%
+  \pgfutil@ifnextchar\pgf@stop@eodashes{%
+    \tikz@lib@graph@graph@done%
+  }{%
+    \def\pgf@test{#2}%
+    \ifx\pgf@test\pgfutil@empty%
+      \expandafter\tikz@lib@graph@no@back@arrow%
+    \else%
+      \expandafter\tikz@lib@graph@back@arrow%
+    \fi%
+  }%
+}%
+
+\def\tikz@lib@graph@no@back@arrow{%
+  \pgfutil@ifnextchar>\tikz@lib@graph@forward@arrow{%
+    \pgfutil@ifnextchar-\tikz@lib@graph@undirected@arrow{%
+      \pgfutil@ifnextchar!\tikz@lib@graph@no@arrow{%
+        \tikzerror{One of the arrow types <-, --, ->, -!- or <-> expected}%
+        \tikz@lib@graph@undirected@arrow%
+      }%
+    }%
+  }%
+}%
+
+\def\tikz@lib@graph@undirected@arrow-{%
+  \def\tikz@lib@graph@arrow@type{--}%
+  \tikz@lib@graph@after@arrow%
+}%
+
+\def\tikz@lib@graph@forward@arrow>{%
+  \def\tikz@lib@graph@arrow@type{->}%
+  \tikz@lib@graph@after@arrow%
+}%
+
+\def\tikz@lib@graph@bi@arrow>{%
+  \def\tikz@lib@graph@arrow@type{<->}%
+  \tikz@lib@graph@after@arrow%
+}%
+
+\def\tikz@lib@graph@no@arrow!-{%
+  \def\tikz@lib@graph@arrow@type{-!-}%
+  \tikz@lib@graph@after@arrow%
+}%
+
+\def\tikz@lib@graph@back@arrow{%
+  \pgfutil@ifnextchar>{\tikz@lib@graph@bi@arrow}{%
+    \def\tikz@lib@graph@arrow@type{<-}%
+    \tikz@lib@graph@after@arrow%
+  }%
+}%
+
+\def\tikz@lib@graph@after@arrow{%
+  \pgfutil@ifnextchar[{\tikz@lib@graph@after@arrow@opt}{\tikz@lib@graph@after@arrow@opt[]}%
+}%
+
+\def\tikz@lib@graph@after@arrow@opt[#1]{%
+  \tikzgraphinvokeoperator{recolor source by=source''}
+  \tikzgraphinvokeoperator{recolor target by=target'}
+  \expandafter\def\expandafter\tikz@lib@graph@stored@actions\expandafter{%
+    \expandafter\tikz@lib@graph@joiner\expandafter{\tikz@lib@graph@arrow@type}{#1}}%
+  \tikzgdeventgroupcallback{descendants}%
+  \tikz@lib@graph@parse@one%
+}%
+
+\def\tikz@lib@graph@joiner#1#2{%
+  \tikzgraphinvokeoperator{recolor source by=source'}
+  \tikzgraphinvokeoperator{recolor source'' by=source}
+  {%
+    \tikz@enable@edge@quotes%
+    \pgfkeyssetvalue{/tikz/graphs/default edge kind}{#1}%
+    \pgfkeys{/tikz/graphs/.cd,@operators=,%
+      /tikz/graphs/.unknown/.code=\tikz@lib@graph@unknown@edge@option{##1},#2}%
+    \pgfkeysgetvalue{/tikz/graphs/@operators}\pgf@temp%
+    \ifx\pgf@temp\pgfutil@empty%
+      \edef\pgf@temp{\noexpand\pgfkeys{/tikz/graphs/.cd,\pgfkeysvalueof{/tikz/graphs/default edge operator}}}%
+      \pgf@temp%
+      \pgfkeysgetvalue{/tikz/graphs/@operators}\pgf@temp%
+    \fi%
+    \pgf@temp%
+  }%
+  \tikzgraphinvokeoperator{not source',not target'}
+}%
+
+\def\tikz@lib@graph@unknown@edge@option#1{%
+  \def\tikz@temp{/tikz/graphs/@edges styling/.append=}
+  \expandafter\expandafter\expandafter\pgfkeys%
+  \expandafter\expandafter\expandafter{\expandafter\tikz@temp\expandafter{\expandafter,\pgfkeyscurrentname={#1}}}
+}%
+
+\def\tikz@lib@graph@graph@done\pgf@stop@eodashes{%
+    \xdef\tikz@lib@graph@chain@depth{\pgfkeysvalueof{/tikz/graphs/placement/local depth}}
+    \xdef\tikz@lib@graph@chain@width{\pgfkeysvalueof{/tikz/graphs/placement/local width}}
+    \expandafter%
+  \endgroup%
+  \expandafter\expandafter\expandafter\def%
+  \expandafter\expandafter\expandafter\tikz@lib@graph@node@list%
+  \expandafter\expandafter\expandafter{\expandafter\tikz@lib@graph@node@list\tikz@lib@graph@node@list}%
+  \tikz@lib@graph@placement@after@chain@update
+  \pgfutil@ifnextchar\pgf@stop@eogroup%
+  \tikz@lib@graph@graph@group@done%
+  \tikz@lib@graph@main@parser%
+}%
+
+\def\tikz@lib@graph@graph@group@done\pgf@stop@eogroup{%
+  \pgfkeysvalueof{/tikz/graphs/@operators}%
+}%
+
+
+
+\def\tikz@lib@graph@grab@name{%
+  \pgfutil@ifnextchar\foreach\tikz@lib@graph@do@foreach\tikz@lib@graph@parse@node@text%
+}%
+
+\def\tikz@lib@graph@do@foreach\foreach#1in{%
+  \pgfutil@ifnextchar\bgroup{\tikz@lib@graph@do@foreach@normal{#1}}{\def\tikz@temp{#1}\tikz@lib@graph@do@foreach@macro}%
+}%
+\def\tikz@lib@graph@do@foreach@macro#1{%
+  \expandafter\expandafter\expandafter\tikz@lib@graph@do@foreach@normal\expandafter\tikz@temp\expandafter{#1}%
+}%
+
+\def\tikz@lib@graph@do@foreach@normal#1#2#3\pgf@stop{%
+  \begingroup
+    \let\tikz@lib@graph@node@list@saved\pgfutil@empty%
+    \xdef\tikz@lib@graph@saved@placement{%
+      {\pgfkeysvalueof{/tikz/graphs/placement/local depth}}%
+      {\pgfkeysvalueof{/tikz/graphs/placement/local width}}%
+      {\pgfkeysvalueof{/tikz/graphs/placement/chain count}}%
+      {\pgfkeysvalueof{/tikz/graphs/placement/element count}}%
+      {\pgfkeysvalueof{/tikz/graphs/placement/width}}%
+      {\pgfkeysvalueof{/tikz/graphs/placement/depth}}%
+    }%
+    \foreach #1 in {#2}%
+    {%
+      \let\tikz@lib@graph@node@list\tikz@lib@graph@node@list@saved%
+      \expandafter\tikz@lib@graph@setup@placement\tikz@lib@graph@saved@placement%
+      \tikz@lib@graph@parse@group{#3}%
+      \xdef\tikz@lib@graph@saved@placement{%
+        {\pgfkeysvalueof{/tikz/graphs/placement/local depth}}%
+        {\pgfkeysvalueof{/tikz/graphs/placement/local width}}%
+        {\pgfkeysvalueof{/tikz/graphs/placement/chain count}}%
+        {\pgfkeysvalueof{/tikz/graphs/placement/element count}}%
+        {\pgfkeysvalueof{/tikz/graphs/placement/width}}%
+        {\pgfkeysvalueof{/tikz/graphs/placement/depth}}%
+      }%
+      \global\let\tikz@lib@graph@node@list@saved\tikz@lib@graph@node@list%
+    }%
+    \expandafter%
+  \endgroup%
+  \expandafter\expandafter\expandafter\def%
+  \expandafter\expandafter\expandafter\tikz@lib@graph@node@list%
+  \expandafter\expandafter\expandafter{\expandafter\tikz@lib@graph@node@list\tikz@lib@graph@node@list@saved}%
+  \expandafter\tikz@lib@graph@setup@placement\tikz@lib@graph@saved@placement%
+}%
+
+\def\tikz@lib@graph@setup@placement#1#2#3#4#5#6{%
+  \pgfkeyssetvalue{/tikz/graphs/placement/local depth}{#1}%
+  \pgfkeyssetvalue{/tikz/graphs/placement/local width}{#2}%
+  \pgfkeyssetvalue{/tikz/graphs/placement/chain count}{#3}%
+  \pgfkeyssetvalue{/tikz/graphs/placement/element count}{#4}%
+  \pgfkeyssetvalue{/tikz/graphs/placement/width}{#5}%
+  \pgfkeyssetvalue{/tikz/graphs/placement/depth}{#6}%
+}%
+
+\def\tikz@lib@graph@parse@node@text#1\pgf@stop{%
+  \pgfutil@in@{//}{#1 }
+  \ifpgfutil@in@%
+    \tikz@lib@parse@layout@node#1\pgf@stop%
+  \else%
+    \tikz@lib@graph@fake@nodefalse
+    \let\tikz@lib@graph@node@parsed\tikz@lib@graph@node@opt@normal%
+    \def\tikz@lib@graph@empty@node@parsed{\tikzgdeventcallback{node}{}}%
+    \tikz@lib@parse@normal@node#1[\pgf@stop%
+  \fi%
+}%
+
+\newif\iftikzgraphsautonumbernodes
+\newcount\tikz@lib@auto@number
+
+\def\tikz@lib@do@autonumber{%
+  \ifx\tikz@lib@graph@name@only\pgfutil@empty%
+  \else%
+    \edef\tikz@lib@graph@name@only{\tikz@lib@graph@name@only\tikz@lib@auto@sep\the\tikz@lib@auto@number}%
+    \global\advance\tikz@lib@auto@number by1\relax%
+  \fi%
+}%
+
+
+\def\tikz@lib@parse@normal@node#1[{
+  \pgfutil@in@{/}{#1}%
+  \ifpgfutil@in@%
+    \tikz@lib@parse@node@with@slash#1\pgf@stop%
+  \else
+    \pgfutil@in@{__}{#1}%
+    \ifpgfutil@in@%
+      \tikz@lib@parse@node@with@doubleunder#1\pgf@stop%
+    \else
+      \edef\pgf@marshal{\noexpand\pgfkeys@spdef\noexpand\tikz@lib@graph@name@only{#1}}%
+      \pgf@marshal%
+      \let\tikz@lib@graph@node@text\tikz@lib@graph@name@only%
+      \edef\tikz@lib@graph@name{\tikz@lib@graph@path\tikz@lib@graph@name@only}%
+    \fi%
+  \fi%
+  \tikz@lib@graph@handle@node@cont%
+}%
+
+\def\tikz@lib@parse@node@with@slash#1/{
+  \pgfkeys@spdef\tikz@lib@graph@name@only{#1}%
+  \ifx\tikz@lib@graph@name@only\pgfutil@empty%
+    \global\advance\tikz@fig@count by1\relax
+    \edef\tikz@lib@graph@name@only{tikz@f@\the\tikz@fig@count}%
+  \fi%
+  \edef\tikz@lib@graph@name{\tikz@lib@graph@path\tikz@lib@graph@name@only}%
+  \pgfutil@ifnextchar"\tikz@lg@slash@quote{\pgfutil@ifnextchar\tikz@active@quotes@token\tikz@lg@slash@quote@active\tikz@lg@slash@cont}
+}%
+\def\tikz@lg@slash@quote"#1"#2\pgf@stop{%
+  \iftikz@handle@active@nodes%
+    \def\tikz@lib@graph@node@text{\scantokens{#1}}%
+  \else
+    \def\tikz@lib@graph@node@text{#1}%
+  \fi%
+}%
+{\catcode`\"=13\relax
+  \gdef\tikz@lg@slash@quote@active"#1"#2\pgf@stop{%
+  \iftikz@handle@active@nodes%
+    \def\tikz@lib@graph@node@text{\scantokens{#1}}%
+  \else
+    \def\tikz@lib@graph@node@text{#1}%
+  \fi%
+  }%
+}%
+\def\tikz@lg@slash@cont#1\pgf@stop{%
+  \iftikz@handle@active@nodes%
+    \def\tikz@lib@graph@node@text{\scantokens{#1}}%
+  \else
+    \def\tikz@lib@graph@node@text{#1}%
+  \fi%
+}%
+
+\def\tikz@lib@parse@node@with@doubleunder#1__{\tikz@lib@parse@node@with@slash{#1}/}%
+
+\def\tikz@lg@find@fresh@name{%
+  \edef\tikz@lib@graph@name@only{\tikz@lib@graph@name@only'}%
+  \edef\tikz@lib@graph@name{\tikz@lib@graph@path\tikz@lib@graph@name@only}%
+  \tikz@lg@if@local@node{\tikz@lib@graph@name}{\tikz@lg@find@fresh@name}{}%
+}%
+
+
+
+\def\tikz@lib@graph@handle@node@cont{%
+  \iftikzgraphsautonumbernodes%
+    \tikz@lib@do@autonumber%
+  \fi%
+  \iftikz@lib@graph@fresh@node%
+    \tikz@lg@if@local@node{\tikz@lib@graph@name}{\tikz@lg@find@fresh@name}{}%
+  \fi%
+  \let\tikzgraphnodeas\tikzgraphnodeas@default%
+  \pgfutil@ifnextchar\pgf@stop{%
+    \ifx\tikz@lib@graph@name@only\pgfutil@empty%
+      \expandafter\tikz@lib@graph@node@empty@done%
+    \else
+      \expandafter\tikz@lib@graph@node@opt\expandafter[\expandafter]\expandafter[%
+    \fi%
+  }{\tikz@lib@graph@node@opt[}%
+}%
+
+\def\tikzgraphnodeas@default{%
+  \tikz@lib@graph@typesetter%
+}%
+
+\let\tikz@lib@graph@empty@node@parsed\relax%
+
+\def\tikz@lib@graph@node@opt[#1]#2[\pgf@stop{%
+  \tikz@lib@graph@node@parsed{#1}%
+}%
+
+\def\tikz@lib@graph@node@empty@done\pgf@stop{\tikz@lib@graph@empty@node@parsed}%
+
+
+\def\tikz@lib@parse@layout@node#1//{%
+  \pgf@lib@graph@empty@layout@nodefalse%
+  \let\tikz@lib@graph@node@parsed\tikz@lib@layout@node@parsed%
+  \let\tikz@lib@graph@empty@node@parsed\tikz@lib@graph@empty@layout@node@parsed
+  \tikz@lib@parse@normal@node#1[\pgf@stop%
+}%
+
+\newif\ifpgf@lib@graph@empty@layout@node
+
+\def\tikz@lib@layout@node@parsed{%
+  \tikz@lib@layout@parse@rest%
+}%
+
+\def\tikz@lib@graph@empty@layout@node@parsed{%
+  \pgf@lib@graph@empty@layout@nodetrue
+  \tikz@lib@layout@parse@rest{}%
+}%
+
+\def\tikz@lib@layout@parse@rest#1{%
+  \def\tikz@lib@layout@node@options{#1}%
+  \pgfutil@ifnextchar[{\tikz@lib@layout@node@opt}{\tikz@lib@layout@node@opt[]}%
+}%
+
+\def\tikz@lib@layout@node@parsed#1{%
+  \def\tikz@lib@layout@node@options{#1}%
+  \pgfutil@ifnextchar[{\tikz@lib@layout@node@opt}{\tikz@lib@layout@node@opt[]}%
+}%
+
+\def\tikz@lib@layout@node@opt[#1]{%
+  \def\tikz@lib@layout@options{#1}%
+  \pgfutil@ifnextchar\bgroup{\tikz@lib@layout@start}{\tikzerror{Opening brace at beginning of sublayout expected}}%
+}%
+
+
+
+\def\tikz@lib@graph@node@opt@normal#1{%
+  \expandafter\tikz@lib@graph@test@use@list\tikz@lib@graph@name@only\pgf@stop
+  \iftikz@lib@graph@use@list%
+    \let\tikz@lg@temp\pgfutil@empty%
+    \foreach \tikz@lg@node@name in \tikz@lib@graph@use@list {\expandafter\tikz@lib@graph@handle@use\expandafter{\tikz@lg@node@name}}
+    \expandafter\expandafter\expandafter\def%
+    \expandafter\expandafter\expandafter\tikz@lib@graph@node@list%
+    \expandafter\expandafter\expandafter{%
+      \expandafter\tikz@lib@graph@node@list\tikz@lg@temp}%
+    \let\tikz@lg@do\tikz@lib@graph@do@use%
+    \tikz@lg@temp%
+  \else%
+    \edef\tikz@lib@graph@name{\tikz@lib@graph@path\tikz@lib@graph@name@only}%
+    \expandafter\ifx\csname tikz@lib@graph@def@\tikz@lib@graph@name@only\endcsname\relax%
+      \pgfkeysgetvalue{/tikz/graphs/placement/level}\tikz@temp%
+      \c@pgf@counta=\tikz@temp\relax%
+      \advance\c@pgf@counta by1\relax%
+      \edef\tikz@temp{\the\c@pgf@counta}%
+      \pgfkeyslet{/tikz/graphs/placement/level}\tikz@temp%
+      \tikzgraphsset{
+        level/.try=\pgfkeysvalueof{/tikz/graphs/placement/level},
+        level \pgfkeysvalueof{/tikz/graphs/placement/level}/.try
+      }
+      {%
+        \edef\tikz@lib@graph@node@list{\noexpand\tikz@lg@do{\tikz@lib@graph@name}}%
+        \global\tikz@lib@graph@node@createdfalse%
+        \pgfkeyslet{/tikz/graphs/@operators}\pgfutil@empty%
+        \tikz@lib@activate@source@target@edge@syntax%
+        \tikz@lg@if@local@node{\tikz@lib@graph@name}%
+        {\tikz@lg@local@node@handle{#1}}%
+        {%
+          \tikz@lg@init@color{\tikz@lib@graph@name}{\tikz@lgc@all@true\tikz@lgc@source@true\tikz@lgc@target@true}%
+          \iftikz@lib@graph@all%
+            \tikzgraphsset{#1}\pgfkeysvalueof{/tikz/graphs/@operators}%
+          \else%
+            \pgfkeys{/tikz/graphs/placement/place}%
+            \let\tikzgraphnodetext\tikz@lib@graph@node@text%
+            \let\tikzgraphnodename\tikz@lib@graph@name@only%
+            \let\tikzgraphnodepath\tikz@lib@graph@path%
+            \let\tikzgraphnodefullname\tikz@lib@graph@name%
+            \iftikz@lib@graph@fake@node%
+              {%
+                \pgfkeys{
+                  /tikz/graphs/.cd,%
+                  .unknown/.code=,
+                  /tikz/graphs/@nodes styling,%
+                  #1}%
+                \pgfkeysgetvalue{/tikz/graphs/@operators}\tikz@lib@graph@op@save%
+                \global\let\tikz@lib@graph@op@save\tikz@lib@graph@op@save%
+              }%
+            \else%
+              \node [%
+                name=\tikz@lib@graph@name,%
+                execute at end node={%
+                  \pgfkeysgetvalue{/tikz/graphs/@operators}\tikz@lib@graph@op@save%
+                  \global\let\tikz@lib@graph@op@save\tikz@lib@graph@op@save%
+                },%
+                graphs/redirect unknown to tikz,
+                /tikz/graphs/.cd,%
+                /tikz/graphs/@nodes styling,%
+                #1]%
+                {%
+                  \tikzgraphnodeas%
+                };%
+            \fi%
+            \tikz@lib@graph@op@save\global\let\tikz@lib@graph@op@save\relax%
+            \global\tikz@lib@graph@node@createdtrue%
+          \fi
+        }%
+      }%
+      \iftikz@lib@graph@node@created\tikz@lib@graph@placement@update\fi%
+      \expandafter\expandafter\expandafter\def%
+      \expandafter\expandafter\expandafter\tikz@lib@graph@node@list%
+      \expandafter\expandafter\expandafter{%
+        \expandafter\tikz@lib@graph@node@list\expandafter\tikz@lg@do\expandafter{\tikz@lib@graph@name}}%
+      \iftikz@lib@graph@trie\tikzgraphsset{name=\tikz@lib@graph@name@only}\fi%
+    \else
+      \tikz@lib@graph@handle@graph{#1}%
+    \fi
+  \fi%
+}%
+
+\newif\iftikz@lib@graph@fake@node
+
+\newif\iftikz@lib@graph@use@list
+\def\tikz@lib@graph@test@use@list{%
+  \pgfutil@ifnextchar({\tikz@lib@graph@use@list@grap}{\tikz@lib@graph@test@use@list@done}%
+}%
+
+\def\tikz@lib@graph@test@use@list@done#1\pgf@stop{\tikz@lib@graph@use@listfalse}%
+\def\tikz@lib@graph@use@list@grap(#1)\pgf@stop{\def\tikz@lib@graph@use@list{#1}\tikz@lib@graph@use@listtrue}%
+
+
+
+\def\tikz@lib@layout@start#1#2\pgf@stop{%
+  \tikz@lib@ensure@gd@loaded%
+  \tikz@lib@graph@fake@nodefalse%
+  \ifpgf@lib@graph@empty@layout@node%
+  \else%
+    \ifx\tikz@lib@graph@name\pgfutil@empty%
+      \tikzerror{Internal error: Node has no name, but it should!}%
+    \else
+      \tikz@lib@graph@fake@nodetrue%
+      \expandafter\tikz@lib@graph@node@opt@normal\expandafter{\tikz@lib@layout@node@options}%
+    \fi%
+  \fi%
+  \edef\tikz@lib@graph@name{\tikz@lib@graph@path\tikz@lib@graph@name@only}%
+  \expandafter\expandafter\expandafter\def%
+  \expandafter\expandafter\expandafter\tikz@lib@layout@node@options\expandafter\expandafter\expandafter{\expandafter\tikz@lib@layout@startup@node@options\tikz@lib@layout@node@options,}%
+  \begingroup
+    \iftikz@lib@graph@fake@node%
+      \expandafter\expandafter\expandafter%
+      \expandafter\expandafter\expandafter\expandafter\tikz@lib@make@subgraph@node%
+      \expandafter\expandafter\expandafter%
+      \expandafter\expandafter\expandafter\expandafter{%
+        \expandafter\expandafter\expandafter\tikz@lib@graph@name%
+        \expandafter\expandafter\expandafter}%
+      \expandafter\expandafter\expandafter{%
+        \expandafter\tikz@lib@graph@node@text\expandafter}\expandafter{\tikz@lib@layout@node@options}
+    \fi%
+  \expandafter\expandafter\expandafter\scope\expandafter\expandafter\expandafter[\expandafter\tikz@lib@layout@node@options@prefix\tikz@lib@layout@options]
+    \tikzgdeventgroupcallback{array}%
+    \let\tikz@lib@graph@node@list\pgfutil@empty%
+    \tikz@lib@graph@start@hint@group%
+      \tikz@lib@graph@parse@group{#1}%
+    \tikz@lib@graph@end@hint@group%
+    \def\tikz@lg@old@col{\tikz@lgc@source@true}%
+    \let\tikz@lg@new@col\pgfutil@empty%
+    \let\tikz@lg@do\tikz@lg@change@color%
+    \tikz@lib@graph@node@list%
+    \def\tikz@lg@old@col{\tikz@lgc@target@true}%
+    \tikz@lib@graph@node@list%
+    \expandafter%
+  \endscope\expandafter%
+  \endgroup%
+  \expandafter\expandafter\expandafter\def%
+  \expandafter\expandafter\expandafter\tikz@lib@graph@node@list%
+  \expandafter\expandafter\expandafter{\expandafter\tikz@lib@graph@node@list\tikz@lib@graph@node@list}%
+  \tikz@lib@graph@hint@aftergroup%
+}%
+\def\tikz@lib@make@subgraph@node#1#2#3{%
+  \pgfgdsubgraphnode{#1}{#3}{\pgfgdsubgraphnodecontents{#2}}%
+}%
+\def\tikz@lib@layout@startup@node@options{%
+  /utils/exec=\tikzlibignorecomparisonsINTERNAL,
+  /tikz/graphs/.cd,%
+  redirect unknown to tikz,%
+  anchor=base,%
+  /tikz/every subgraph node/.try,%
+}%
+\def\tikzlibignorecomparisonsINTERNAL{%
+  \pgfkeys{/handlers/first char syntax=true}
+  \pgfkeyssetvalue{/handlers/first char syntax/\expandafter\meaning\string>}{\pgfutil@gobble}%
+  \pgfkeyssetvalue{/handlers/first char syntax/\expandafter\meaning\string<}{\pgfutil@gobble}%
+}%
+\def\tikz@lib@layout@node@options@prefix{graphs/.cd,}%
+
+\ifx\tikz@lib@ensure@gd@loaded\pgfutil@undefined%
+\def\tikz@lib@ensure@gd@loaded{\tikzerror{You must say \string\usetikzlibrary{graphdrawing} to use the (sub)layout syntax}}%
+\fi
+
+\def\tikz@lg@local@node@handle#1{%
+  \tikzgraphsset{source,target,.unknown/.code=,#1}%
+  \tikzgdlatenodeoptionacallback{\tikz@pp@name\tikz@lib@graph@name}%
+  \node also[graphs/redirect unknown to tikz,/tikz/graphs/.cd,#1](\tikz@lib@graph@name);%
+  \pgfkeysvalueof{/tikz/graphs/@operators}%
+}%
+
+\tikzgraphsset{redirect unknown to tikz/.style={
+    /tikz/graphs/.unknown/.code={%
+      \let\tikz@key\pgfkeyscurrentname%
+      \pgfkeys{tikz/.cd,\tikz@key={##1},/tikz/graphs/.cd}%
+    }}
+}%
+
+\def\tikz@lib@activate@source@target@edge@syntax{%
+  \pgfkeys{/handlers/first char syntax=true}
+  \pgfkeyssetvalue{/handlers/first char syntax/\expandafter\meaning\string>}{\tikz@lg@parse@more}%
+  \pgfkeyssetvalue{/handlers/first char syntax/\expandafter\meaning\string<}{\tikz@lg@parse@less}%
+}%
+
+\def\tikz@lg@parse@less#1{\tikz@lg@parse@less@#1\pgf@stop}%
+\def\tikz@lg@parse@less@<{\pgfutil@ifnextchar"{\tikz@lg@parse@quote{source}}{\tikz@lg@parse@noquote{source}}}%
+\def\tikz@lg@parse@more#1{\tikz@lg@parse@more@#1\pgf@stop}%
+\def\tikz@lg@parse@more@>{\pgfutil@ifnextchar"{\tikz@lg@parse@quote{target}}{\tikz@lg@parse@noquote{target}}}%
+
+\def\tikz@lg@parse@noquote#1#2\pgf@stop{{\tikzgraphsset{#1 edge style={#2}}}}%
+\def\tikz@lg@parse@quote#1#2\pgf@stop{%
+  {\tikzgraphsset{/tikz/node quotes mean={#1 edge node={node [every edge quotes,##2]{##1}}},/utils/exec=\tikz@enable@node@quotes,#2}}%
+}%
+
+\tikzgraphsset{
+  clear >/.style=target edge clear,
+  clear </.style=source edge clear
+}%
+
+
+
+\def\tikz@lib@graph@x{0}%
+\def\tikz@lib@graph@y{0}%
+
+\tikzgraphsset{
+  x/.code=\def\tikz@lib@graph@x{#1}\tikz@lib@graphs@check@at,
+  y/.code=\def\tikz@lib@graph@y{#1}\tikz@lib@graphs@check@at
+}%
+\def\tikz@lib@graphs@check@at{%
+  \expandafter\expandafter\expandafter\def%
+  \expandafter\expandafter\expandafter\tikz@temp%
+  \expandafter\expandafter\expandafter{%
+    \expandafter\expandafter\expandafter(%
+    \expandafter\expandafter\expandafter{\expandafter\tikz@lib@graph@x\expandafter}%
+    \expandafter,\expandafter{\tikz@lib@graph@y})}%
+  \pgfqkeys{/tikz}{at/.expand once=\tikz@temp}%
+}%
+
+
+\newif\iftikz@lib@graph@trie
+\tikzgraphsset{
+  trie/.is if=tikz@lib@graph@trie,
+  put node text on incoming
+  edges/.style={nodes={/utils/exec=\tikz@lg@make@edge@node{target}{#1}}},
+  put node text on outgoing
+  edges/.style={nodes={/utils/exec=\tikz@lg@make@edge@node{source}{#1}}},
+  edge quotes/.style={/tikz/every edge quotes/.style={#1}},
+  edge quotes center/.style={edge quotes={anchor=center}},
+  edge quotes mid/.style={edge quotes={anchor=mid}}
+}%
+
+\def\tikz@lg@make@edge@node#1#2{%
+  \def\pgf@marshal{node[#2]}%
+  \expandafter\expandafter\expandafter\def\expandafter\expandafter\expandafter\pgf@marshal\expandafter\expandafter\expandafter{\expandafter\pgf@marshal\expandafter{\tikzgraphnodetext}}%
+  \pgfkeysalso{#1 edge node/.expand once=\pgf@marshal,as=}%
+}%
+
+\newif\iftikz@lib@graph@fresh@node
+\tikzgraphsset{fresh nodes/.is if=tikz@lib@graph@fresh@node}%
+
+\tikzgraphsset{number nodes/.code=%
+  \pgfmathsetcount\tikz@lib@auto@number{#1}%
+  \tikzgraphsautonumbernodestrue,%
+  number nodes/.default=1,%
+  number nodes sep/.code=\def\tikz@lib@auto@sep{#1}
+}%
+\def\tikz@lib@auto@sep{\space}%
+
+\newif\iftikz@lib@graph@node@created
+
+\def\tikz@lib@graph@handle@use#1{%
+  \expandafter\let\expandafter\pgf@temp\csname tikz@lg@node@set #1\endcsname
+  \ifx\pgf@temp\relax
+    \pgfutil@g@addto@macro\tikz@lg@temp{\tikz@lg@do{#1}}
+  \else%
+    \expandafter\pgfutil@g@addto@macro\expandafter\tikz@lg@temp\expandafter{\pgf@temp}
+  \fi
+}%
+
+\def\tikz@lib@graph@do@use#1{%
+  \tikz@lg@init@color{#1}{\tikz@lgc@all@true\tikz@lgc@source@true\tikz@lgc@target@true}%
+}%
+
+\tikzgraphsset{
+  typeset/.store in=\tikz@lib@graph@typesetter,
+  math nodes/.style={/tikz/graphs/typeset=$\tikzgraphnodetext$},
+  empty nodes/.style={/tikz/graphs/typeset=},
+  typeset=\tikzgraphnodetext
+}%
+
+
+\def\tikz@lib@graph@scope#1{
+  \begingroup%
+    \tikzgdeventgroupcallback{array}%
+    \let\tikz@lib@graph@node@list\pgfutil@empty%
+    \tikz@lib@graph@start@hint@group%
+      \tikz@lib@graph@parse@group{#1}%
+    \tikz@lib@graph@end@hint@group%
+    \expandafter%
+  \endgroup%
+  \expandafter\expandafter\expandafter\def%
+  \expandafter\expandafter\expandafter\tikz@lib@graph@node@list%
+  \expandafter\expandafter\expandafter{\expandafter\tikz@lib@graph@node@list\tikz@lib@graph@node@list}%
+  \tikz@lib@graph@hint@aftergroup%
+  \tikz@lib@graph@stored@actions%
+  \pgfutil@ifnextchar-{\tikz@lib@graph@scope@minus}{%
+    \pgfutil@ifnextchar<{\tikz@lib@graph@scope@less}{%
+      \tikzerror{One of the arrow types <-, --, ->, -!-, or <-> expected}%
+    }%
+  }%
+}%
+
+\def\tikz@lib@graph@scope@minus-{
+  \pgfutil@ifnextchar>\tikz@lib@graph@forward@arrow{%
+    \pgfutil@ifnextchar-\tikz@lib@graph@undirected@arrow{%
+      \pgfutil@ifnextchar!\tikz@lib@graph@no@arrow{%
+        \pgfutil@ifnextchar\pgf@stop@eodashes\tikz@lib@graph@graph@done{%
+          \tikzerror{One of the arrow types <-, --, ->, -!-, or <-> expected}%
+          \tikz@lib@graph@undirected@arrow%
+        }%
+      }%
+    }%
+  }%
+}%
+
+\def\tikz@lib@graph@scope@less<-{\tikz@lib@graph@back@arrow}%
+
+
+
+
+
+\tikzgraphsset{
+  declare/.code 2 args={\expandafter\def\csname tikz@lib@graph@def@#1\endcsname{\tikz@lib@graph@do@graph{#2}}}%
+}%
+
+\def\tikz@lib@graph@handle@graph#1{%
+  \begingroup%
+    \let\tikz@lib@graph@node@list\pgfutil@empty%
+    \tikzgraphsset{@extra group options/.style={#1}}%
+    \tikz@lib@graph@start@hint@group%
+      \csname tikz@lib@graph@def@\tikz@lib@graph@name@only\endcsname%
+    \tikz@lib@graph@end@hint@group%
+    \expandafter%
+  \endgroup%
+  \expandafter\expandafter\expandafter\def%
+  \expandafter\expandafter\expandafter\tikz@lib@graph@node@list%
+  \expandafter\expandafter\expandafter{\expandafter\tikz@lib@graph@node@list\tikz@lib@graph@node@list}%
+  \tikz@lib@graph@hint@aftergroup%
+}%
+
+\def\tikz@lib@graph@do@graph#1{%
+  \tikz@lib@graph@parse@group{#1}%
+}%
+
+\let\tikz@lib@graph@path\pgfutil@empty
+
+\tikzgraphsset{
+  name separator/.store in=\tikz@lib@graph@name@separator,
+  name separator=\space,
+  name/.code={%
+    \edef\tikz@lib@graph@path{\tikz@lib@graph@path#1\tikz@lib@graph@name@separator}%
+  }%
+}%
+
+
+\def\tikz@lg@newif{\csname newif\endcsname}%
+\tikzgraphsset{
+  as/.code=\def\tikzgraphnodeas{#1},%
+  color class/.style={%
+    /utils/exec=\expandafter\tikz@lg@newif\csname iftikz@lgc@#1@\endcsname,
+    #1/.style={operator={%
+      \edef\tikz@lg@col{\expandafter\noexpand\csname tikz@lgc@#1@true\endcsname}%
+      \let\tikz@lg@do\tikz@lg@colorize%
+      \tikz@lib@graph@node@list%
+    }},
+    not #1/.style={operator={%
+      \edef\tikz@lg@old@col{\expandafter\noexpand\csname tikz@lgc@#1@true\endcsname}%
+      \let\tikz@lg@new@col\pgfutil@empty%
+      \let\tikz@lg@do\tikz@lg@change@color%
+      \tikz@lib@graph@node@list%
+    }},
+    recolor #1 by/.style={operator={%
+      \edef\tikz@lg@old@col{\expandafter\noexpand\csname tikz@lgc@#1@true\endcsname}%
+      \edef\tikz@lg@new@col{\expandafter\noexpand\csname tikz@lgc@##1@true\endcsname}%
+      \let\tikz@lg@do\tikz@lg@change@color%
+      \tikz@lib@graph@node@list%
+    }},
+    !#1/.style=not #1,
+  },
+  color class=source,
+  color class=source',
+  color class=source'',
+  color class=target,
+  color class=target',
+  color class=all
+}%
+
+\def\tikz@lg@init@color#1#2{%
+  \expandafter\gdef\csname tikz@lgc@#1\endcsname{#2}%
+}%
+
+\def\tikz@lib@graph@cleanup#1{%
+  \expandafter\global\expandafter\let\csname tikz@lgc@#1\endcsname\relax%
+  \ifcsname tikz@lgca@@#1\endcsname\expandafter\global\expandafter\let\csname tikz@lgca@@#1\endcsname\relax\fi%
+  \ifcsname tikz@lgcb@@#1\endcsname\expandafter\global\expandafter\let\csname tikz@lgcb@@#1\endcsname\relax\fi%
+}%
+
+\def\tikz@lg@colorize#1{%
+  \expandafter\let\expandafter\pgf@temp\csname tikz@lgc@#1\endcsname%
+  \expandafter\expandafter\expandafter\def%
+  \expandafter\expandafter\expandafter\pgf@temp%
+  \expandafter\expandafter\expandafter{%
+    \expandafter\tikz@lg@col\pgf@temp}%
+  \expandafter\global\expandafter\let\csname tikz@lgc@#1\endcsname\pgf@temp%
+}%
+
+\def\tikz@lg@change@color#1{%
+  \def\tikz@lg@temp@save{#1}%
+  \let\tikz@lg@collect\pgfutil@empty%
+  \expandafter\let\expandafter\pgf@temp\csname tikz@lgc@#1\endcsname%
+  \expandafter\tikz@lg@change@check\pgf@temp\pgf@stop%
+}%
+\def\tikz@lg@change@check#1{%
+  \ifx#1\pgf@stop%
+    \tikz@lg@change@write@back%
+  \else%
+    \def\pgf@temp{#1}%
+    \ifx\pgf@temp\tikz@lg@old@col%
+      \expandafter\tikz@lg@change@add\expandafter{\tikz@lg@new@col}%
+    \else%
+      \tikz@lg@change@add{#1}%
+    \fi%
+    \expandafter\tikz@lg@change@check
+  \fi%
+}%
+\def\tikz@lg@change@add#1{%
+  \expandafter\def\expandafter\tikz@lg@collect\expandafter{\tikz@lg@collect#1}%
+}%
+
+\def\tikz@lg@change@write@back{%
+  \expandafter\global\expandafter\let\csname tikz@lgc@\tikz@lg@temp@save\endcsname\tikz@lg@collect%
+}%
+
+
+
+\def\tikz@lg@if@has@color#1#2#3#4{%
+  {%
+    \csname tikz@lgc@#1\endcsname%
+    \expandafter\let\expandafter\pgf@temp\csname iftikz@lgc@#2@\endcsname%
+    \ifx\pgf@temp\relax%
+      \tikz@lib@reset@temp%
+    \fi%
+    \pgf@temp%
+      \global\tikz@color@testtrue%
+    \else%
+      \global\tikz@color@testfalse%
+    \fi%
+  }%
+  \iftikz@color@test#3\else#4\fi%
+}%
+\newif\iftikz@color@test
+
+\def\tikz@lg@if@local@node#1#2#3{\expandafter\ifx\csname tikz@lgc@#1\endcsname\relax#3\else#2\fi}%
+
+\def\tikz@lib@reset@temp{\let\pgf@temp\iffalse}%
+
+\def\tikz@lib@annotate@#1#2#3#4{%
+  \expandafter\ifx\csname tikz@lgc#1@@#2\endcsname\relax%
+    \expandafter\gdef\csname tikz@lgc#1@@#2\endcsname{{#3}{#4}}%
+  \else%
+    \expandafter\expandafter\expandafter\tikz@lib@annotate@read\csname tikz@lgc#1@@#2\endcsname{#3}{#4}%
+    \expandafter\global\expandafter\let\csname tikz@lgc#1@@#2\endcsname\pgf@temp%
+  \fi%
+}%
+\def\tikz@lib@annotate@read#1#2#3#4{\def\pgf@temp{{#1,#3}{#2#4}}}%
+
+\tikzgraphsset{
+  source edge style/.code=\tikz@lib@annotate@{a}{\tikz@lib@graph@name}{#1}{},
+  source edge node/.code=\tikz@lib@annotate@{a}{\tikz@lib@graph@name}{}{#1},
+  source edge clear/.code={
+    \expandafter\global\expandafter\let\csname tikz@lgca@@\tikz@lib@graph@name\endcsname\relax%
+  },
+  target edge style/.code=\tikz@lib@annotate@{b}{\tikz@lib@graph@name}{#1}{},
+  target edge node/.code=\tikz@lib@annotate@{b}{\tikz@lib@graph@name}{}{#1},
+  target edge clear/.code={%
+    \expandafter\global\expandafter\let\csname tikz@lgcb@@\tikz@lib@graph@name\endcsname\relax%
+  }
+}%
+
+
+
+
+\def\tikz@lib@graph@pack@node@list{%
+  {%
+    \let\tikz@lg@packed\pgfutil@empty%
+    \let\tikz@lg@do\tikz@lg@packer%
+    \tikz@lib@graph@node@list%
+    \expandafter
+  }\expandafter%
+  \def\expandafter\tikz@lib@graph@node@list\expandafter{\tikz@lg@packed}%
+}%
+
+\def\tikz@lg@packer#1{%
+  \expandafter\ifx\csname tikz@lg@p@#1\endcsname\pgf@stop%
+  \else%
+    \expandafter\let\csname tikz@lg@p@#1\endcsname\pgf@stop%
+    \expandafter\def\expandafter\tikz@lg@packed\expandafter{\tikz@lg@packed\tikz@lg@do{#1}}
+  \fi
+}%
+
+
+
+\def\tikzgraphforeachcolorednode#1#2{%
+  \tikz@lib@graph@pack@node@list%
+  \expandafter\def\expandafter\iftikz@lib@graph@color@picker\expandafter{\csname iftikz@lgc@#1@\endcsname}%
+  \let\tikz@lib@graph@action#2%
+  \let\tikz@lg@do\tikz@lg@pick%
+  \tikz@lib@graph@node@list%
+}%
+\def\tikz@lg@pick#1{
+  {%
+    \csname tikz@lgc@#1\endcsname%
+    \iftikz@lib@graph@color@picker
+      \global\tikz@color@testtrue%
+    \else%
+      \global\tikz@color@testfalse%
+    \fi%
+  }%
+  \iftikz@color@test\tikz@lib@graph@action{#1}\fi%
+}%
+
+
+
+
+\def\tikzgraphpreparecolor#1#2#3{%
+  \let\tikz@lib@graph@count#2%
+  \tikz@lib@graph@count0\relax
+  \def\tikz@lib@graph@prefix{#3}%
+  \tikzgraphforeachcolorednode{#1}\tikz@lib@graph@prepare%
+}%
+
+\def\tikz@lib@graph@prepare#1{%
+  \advance\tikz@lib@graph@count by1\relax%
+  \expandafter\def\csname\tikz@lib@graph@prefix\the\tikz@lib@graph@count\endcsname{#1}%
+}%
+
+
+
+
+
+\tikzgraphsset{
+  complete bipartite/.style 2 args={operator={
+    \def\tikz@lg@shoreb{#2}%
+    \tikzgraphforeachcolorednode{#1}\tikz@lib@graph@bipartite@outer
+  }},
+  complete bipartite/.default={target'}{source'},
+  induced complete bipartite/.style 2 args={
+    induced independent set={#1},
+    induced independent set={#2},
+    complete bipartite={#1}{#2}
+  },
+  induced complete bipartite/.default={target'}{source'},
+}%
+
+\def\tikz@lib@graph@bipartite@outer#1{%
+  \def\tikz@lib@graph@from{#1}%
+  {%
+    \tikzgraphforeachcolorednode{\tikz@lg@shoreb}\tikz@lib@graph@bipartite@inner%
+  }%
+}%
+
+\def\tikz@lib@graph@bipartite@inner#1{%
+  \def\pgf@temp{#1}%
+  \ifx\pgf@temp\tikz@lib@graph@from\else%
+    \tikz@lib@graph@default@new@edge{\tikz@lib@graph@from}{#1}%
+  \fi%
+}%
+
+\def\tikz@lib@graph@default@new@edge#1#2{%
+  \pgfkeysgetvalue{/tikz/graphs/@edges styling}\pgf@temp
+  \pgfkeysgetvalue{/tikz/graphs/@edges node}\pgf@temp@b
+  \let\tikz@lib@add@temp\pgfutil@empty%
+  \tikz@lib@graph@add@edge@annotations{a}{#1}
+  \tikz@lib@graph@add@edge@annotations{b}{#2}
+  \expandafter\expandafter\expandafter\def%
+  \expandafter\expandafter\expandafter\pgf@temp%
+  \expandafter\expandafter\expandafter{\expandafter\pgf@temp\tikz@lib@add@temp}%
+  \expandafter\expandafter\expandafter\tikz@lib@graph@default@new@edge@%
+  \expandafter\expandafter\expandafter{\expandafter\pgf@temp\expandafter}\expandafter{\pgf@temp@b}{#1}{#2}%
+}%
+\def\tikz@lib@graph@default@new@edge@#1#2#3#4{%
+  \iftikz@lib@graph@simple%
+    \edef\tikz@temp{{\pgfkeysvalueof{/tikz/graphs/default edge kind}}{#3}{#4}}
+    \expandafter\tikz@lib@graph@set@simple@edge\tikz@temp{#1}{#2}%
+  \else%
+    \pgfkeys{/tikz/graphs/.cd,new \pgfkeysvalueof{/tikz/graphs/default edge kind}={#3}{#4}{#1}{#2}}%
+  \fi%
+}%
+\def\tikz@lib@graph@add@edge@annotations#1#2{%
+  \ifcsname tikz@lgc#1@@#2\endcsname%
+    \expandafter\let\expandafter\tikz@lg@temp@\csname tikz@lgc#1@@#2\endcsname%
+    \ifx\tikz@lg@temp@\relax\else
+      \expandafter\tikz@lib@graph@add@edge@annotations@\tikz@lg@temp@%
+      \let\tikz@lib@add@temp\tikz@lib@final@edge@style
+    \fi%
+  \fi%
+}%
+\def\tikz@lib@graph@add@edge@annotations@#1#2{
+  \expandafter\def\expandafter\pgf@temp\expandafter{\pgf@temp,#1}%
+  \expandafter\def\expandafter\pgf@temp@b\expandafter{\pgf@temp@b#2}%
+}%
+\def\tikz@lib@final@edge@style{,after source and target edge/.try}%
+
+
+\tikzgraphsset{
+  clique/.style={operator={
+      \tikzgraphpreparecolor{#1}\c@pgf@counta{tikz@lg}%
+      \tikz@lg@clique@loop%
+    }},
+  clique/.default=all
+}%
+
+\def\tikz@lg@clique@loop{%
+  \ifnum\c@pgf@counta=0\relax%
+  \else
+    \c@pgf@countb=\c@pgf@counta\relax%
+    \tikz@lg@clique@loop@inner%
+    \advance\c@pgf@counta by-1\relax%
+    \expandafter\tikz@lg@clique@loop%
+  \fi%
+}%
+
+\def\tikz@lg@clique@loop@inner{%
+  \advance\c@pgf@countb by-1\relax%
+  \ifnum\c@pgf@countb>0\relax%
+    \tikz@lib@graph@default@new@edge{\csname tikz@lg\the\c@pgf@countb\endcsname}{\csname tikz@lg\the\c@pgf@counta\endcsname}%
+    \expandafter\tikz@lg@clique@loop@inner%
+  \fi%
+}%
+
+
+
+\tikzgraphsset{
+  induced independent set/.style={operator={
+      \pgfkeysgetvalue{/tikz/graphs/default edge kind}\tikz@lg@default%
+      \pgfkeyssetvalue{/tikz/graphs/default edge kind}{-!-}%
+      \tikzgraphpreparecolor{#1}\c@pgf@counta{tikz@lg}%
+      \tikz@lg@indep@loop%
+      \pgfkeyslet{/tikz/graphs/default edge kind}\tikz@lg@default%
+    }},
+  induced independent set/.default=all
+}%
+
+\def\tikz@lg@indep@loop{%
+  \ifnum\c@pgf@counta=0\relax%
+  \else
+    \c@pgf@countb=\c@pgf@counta\relax%
+    \tikz@lg@indep@loop@inner%
+    \advance\c@pgf@counta by-1\relax%
+    \expandafter\tikz@lg@indep@loop%
+  \fi%
+}%
+
+\def\tikz@lg@indep@loop@inner{%
+  \advance\c@pgf@countb by-1\relax%
+  \ifnum\c@pgf@countb>0\relax%
+    \tikz@lib@graph@default@new@edge{\csname tikz@lg\the\c@pgf@counta\endcsname}{\csname tikz@lg\the\c@pgf@countb\endcsname}%
+    \expandafter\tikz@lg@indep@loop@inner%
+  \fi%
+}%
+
+
+
+\tikzgraphsset{
+  path/.style={operator={%
+      \let\tikz@lg@prev\relax%
+        \tikzgraphforeachcolorednode{#1}\tikz@lib@graph@path@do%
+  }},
+  path/.default=all,
+  induced path/.style={induced independent set={#1},path={#1}},
+  induced path/.default=all,
+}%
+
+\def\tikz@lib@graph@path@do#1{%
+  \ifx\tikz@lg@prev\relax%
+  \else%
+    \tikz@lib@graph@default@new@edge{\tikz@lg@prev}{#1}%
+  \fi
+  \def\tikz@lg@prev{#1}%
+}%
+
+
+
+\tikzgraphsset{
+  cycle/.style={operator={%
+    \let\tikz@lg@prev\relax%
+    \let\tikz@lg@first\relax%
+    \tikzgraphforeachcolorednode{#1}\tikz@lib@graph@cycle@do%
+    \ifx\tikz@lg@first\relax%
+    \else%
+      \tikz@lib@graph@default@new@edge{\tikz@lg@prev}{\tikz@lg@first}%
+    \fi%
+  }},
+  cycle/.default=all,
+  induced cycle/.style={induced independent set={#1},cycle={#1}},
+  induced cycle/.default=all,
+}%
+
+\def\tikz@lib@graph@cycle@do#1{%
+  \ifx\tikz@lg@prev\relax%
+    \def\tikz@lg@prev{#1}%
+    \let\tikz@lg@first\tikz@lg@prev%
+  \else%
+    \tikz@lib@graph@default@new@edge{\tikz@lg@prev}{#1}%
+    \def\tikz@lg@prev{#1}%
+  \fi%
+}%
+
+
+
+
+
+\tikzgraphsset{
+  matching and star/.style 2 args={operator=%
+    {%
+      \tikzgraphpreparecolor{#1}\c@pgf@counta{tikz@lg}
+      \c@pgf@countb=0\relax%
+      \let\tikz@lg@prev\relax
+      \tikzgraphforeachcolorednode{#2}\tikz@lib@graph@flow@do%
+      \tikz@lib@graph@flow@rest%
+    }%
+  },
+  matching and star/.default={target'}{source'}
+}%
+
+\def\tikz@lib@graph@flow@do#1{%
+  \advance\c@pgf@countb by1\relax%
+  \ifnum\c@pgf@countb>\c@pgf@counta\relax%
+    \c@pgf@countb=\c@pgf@counta\relax%
+  \fi%
+  \ifnum\c@pgf@countb>0\relax%
+    \tikz@lib@graph@default@new@edge{\csname tikz@lg\the\c@pgf@countb\endcsname}{#1}%
+  \fi%
+  \def\tikz@lg@prev{#1}%
+}%
+
+\def\tikz@lib@graph@flow@rest{%
+  \ifnum\c@pgf@countb<\c@pgf@counta\relax%
+    \ifnum\c@pgf@countb>0\relax%
+      \advance\c@pgf@countb by1\relax%
+      \tikz@lib@graph@default@new@edge{\csname tikz@lg\the\c@pgf@countb\endcsname}{\tikz@lg@prev}%
+      \expandafter\tikz@lib@graph@flow@rest%
+    \fi%
+  \fi%
+}%
+
+
+
+
+\tikzgraphsset{
+  matching/.style 2 args={operator=
+    {%
+      \tikzgraphpreparecolor{#1}\c@pgf@counta{tikz@lg}
+      \c@pgf@countb=0\relax%
+      \tikzgraphforeachcolorednode{#2}\tikz@lib@graph@matching@do%
+    }%
+  },
+  matching/.default={target'}{source'}
+}%
+
+\def\tikz@lib@graph@matching@do#1{%
+  \advance\c@pgf@countb by1\relax%
+  \ifnum\c@pgf@countb>\c@pgf@counta\relax%
+  \else%
+    \tikz@lib@graph@default@new@edge{\csname tikz@lg\the\c@pgf@countb\endcsname}{#1}%
+  \fi%
+}%
+
+
+
+
+
+
+\tikzgraphsset{
+  butterfly/.style={operator=
+    {}{%
+      \pgfkeys{/tikz/graphs/butterfly/.cd,#1}%
+      \ifnum\pgfkeysvalueof{/tikz/graphs/butterfly/level}=0\relax%
+        \tikzgraphinvokeoperator{matching and star={\pgfkeysvalueof{/tikz/graphs/butterfly/from}}{\pgfkeysvalueof{/tikz/graphs/butterfly/to}}}%
+      \else%
+        {%
+          \tikzgraphpreparecolor{\pgfkeysvalueof{/tikz/graphs/butterfly/from}}\c@pgf@counta{tikz@lg}
+          \c@pgf@countb=0\relax%
+          \tikzgraphforeachcolorednode{\pgfkeysvalueof{/tikz/graphs/butterfly/to}}\tikz@lib@graph@butterfly@do%
+        }%
+        \iftikz@butterfly@prime\else\tikzgraphinvokeoperator{matching and star={\pgfkeysvalueof{/tikz/graphs/butterfly/from}}{\pgfkeysvalueof{/tikz/graphs/butterfly/to}}}\fi%
+      \fi%
+    }%
+  },
+  butterfly/.default=,
+  butterfly/level/.initial=1,
+  butterfly/from/.initial=target',
+  butterfly/to/.initial=source',
+  butterfly'/.style={operator={}{\tikz@butterfly@primetrue\pgfkeysalso{butterfly={#1}}}},
+  butterfly'/.default=,
+}%
+
+\newif\iftikz@butterfly@prime
+
+\def\tikz@lib@graph@butterfly@do#1{%
+  \advance\c@pgf@countb by1\relax%
+  \c@pgf@countc=\pgfkeysvalueof{/tikz/graphs/butterfly/level}\relax%
+  {%
+    \count0=\c@pgf@countc\relax%
+    \multiply\count0 by2\relax%
+    \count1=\c@pgf@countb\relax%
+    \advance\count1 by-1\relax%
+    \count2=\count1\relax%
+    \count3=\count1\relax%
+    \divide\count1 by\count0\relax%
+    \multiply\count1 by\count0\relax%
+    \advance\count2 by-\count1\relax%
+    \ifnum\count2<\c@pgf@countc\relax%
+      \advance\count3 by \c@pgf@countc\relax%
+    \else%
+      \advance\count3 by -\c@pgf@countc\relax%
+    \fi%
+    \expandafter%
+  }%
+  \expandafter\c@pgf@countc\the\count3\relax%
+  \advance\c@pgf@countc by1\relax%
+  \ifnum\c@pgf@countc>\c@pgf@counta\relax%
+    \c@pgf@countc=\c@pgf@counta\relax%
+  \fi%
+  \tikz@lib@graph@default@new@edge{\csname tikz@lg\the\c@pgf@countc\endcsname}{#1}%
+}%
+
+
+
+
+\tikzgraphsset{no edges/.style={operator=\relax}}%
+
+
+
+
+\tikzgraphsset{
+  grid/.style={operator={
+      \tikzgraphpreparecolor{#1}\c@pgf@counta{tikz@lg}%
+      \c@pgf@countb=0\relax%
+      \tikzgraphpreparewrapafter%
+      \tikz@lg@grid@loop%
+    }%
+  },
+  grid/.default=all
+}%
+
+\def\tikzgraphpreparewrapafter{%
+  \pgfkeysgetvalue{/tikz/graphs/wrap after}\tikz@temp%
+  \ifnum\tikz@temp=0\relax%
+    \pgfmathparse{sqrt(\tikzgraphVnum)}%
+    \pgfmathint{\pgfmathresult}%
+    \edef\tikzgraphwrapafter{\pgfmathresult}%
+  \else%
+    \edef\tikzgraphwrapafter{\tikz@temp}
+  \fi%
+}%
+
+\def\tikz@lg@grid@loop{%
+  \ifnum\c@pgf@counta=0\relax%
+  \else%
+    \advance\c@pgf@countb by 1\relax%
+    \pgfmathmod{\c@pgf@countb-1}{\tikzgraphwrapafter}%
+    \pgfmathint{\pgfmathresult}%
+    \ifnum\pgfmathresult>0%
+      \pgfmathsubtract{\c@pgf@countb}{1}%
+      \pgfmathint{\pgfmathresult}%
+      \tikz@lib@graph@default@new@edge{\csname tikz@lg\the\c@pgf@countb\endcsname}{\csname tikz@lg\pgfmathresult\endcsname}%
+    \fi%
+    \pgfmathparse{\c@pgf@countb <= \tikzgraphwrapafter}%
+    \ifnum\pgfmathresult=0%
+      \pgfmathsubtract{\c@pgf@countb}{\tikzgraphwrapafter}%
+      \pgfmathint{\pgfmathresult}%
+      \tikz@lib@graph@default@new@edge{\csname tikz@lg\pgfmathresult\endcsname}{\csname tikz@lg\the\c@pgf@countb\endcsname}%
+    \fi%
+    \advance\c@pgf@counta by-1\relax%
+    \expandafter\tikz@lg@grid@loop%
+  \fi%
+}%
+
+
+
+
+
+\tikzgraphsset{
+  placement/.cd,
+  compute position/.code=\tikz@lib@graph@linear@pos,
+  place/.code={%
+    \pgfkeys{/tikz/graphs/placement/compute position}%
+    \aftergroup\tikz@lib@graph@reset@locals%
+    \pgfkeyssetvalue{/tikz/graphs/placement/element count}{0}%
+    \pgfkeyssetvalue{/tikz/graphs/placement/chain count}{0}%
+    \pgfkeyssetvalue{/tikz/graphs/placement/depth}{0}%
+    \pgfkeyssetvalue{/tikz/graphs/placement/width}{0}%
+    \pgfkeyssetvalue{/tikz/graphs/placement/local depth}{0}%
+    \pgfkeyssetvalue{/tikz/graphs/placement/local width}{0}%
+  },
+  element count/.initial=0,
+  chain count/.initial=0,
+  depth/.initial=0,
+  width/.initial=0,
+  level/.initial=0,
+  logical node depth/.code=\def\pgfmathresult{1},
+  logical node width/.code=\def\pgfmathresult{1},
+}%
+
+\def\tikz@lib@graph@reset@locals{%
+  \gdef\tikz@lib@graph@group@depth{0}%
+  \gdef\tikz@lib@graph@group@width{0}%
+}%
+
+
+
+\tikzgraphsset{
+  Cartesian placement/.style={
+    placement/place,
+    placement/compute position/.code=\tikz@lib@graph@linear@pos%
+  },
+  chain shift/.initial={(1,0)},
+  group shift/.initial={(0,-1)},
+  grow right/.style={
+    placement/place,
+    chain shift={(#1,0)},
+    @auto anchor horizontal=center,
+    placement/logical node width/.code=\def\pgfmathresult{1}
+  },
+  grow right/.default=1,
+  grow left/.style={
+    placement/place,
+    chain shift={(-#1,0)},
+    @auto anchor horizontal=center,
+    placement/logical node width/.code=\def\pgfmathresult{1}
+  },
+  grow left/.default=1,
+  grow up/.style={
+    placement/place,
+    chain shift={(0,#1)},
+    @auto anchor horizontal=center,
+    placement/logical node width/.code=\def\pgfmathresult{1}
+  },
+  grow up/.default=1,
+  grow down/.style={
+    placement/place,
+    chain shift={(0,-#1)},
+    @auto anchor vertical=center,
+    placement/logical node width/.code=\def\pgfmathresult{1}
+  },
+  grow down/.default=1,
+  branch right/.style={
+    placement/place,
+    group shift={(#1,0)},
+    @auto anchor horizontal=center,
+    placement/logical node depth/.code=\def\pgfmathresult{1}
+  },
+  branch right/.default=1,
+  branch left/.style={
+    placement/place,
+    group shift={(-#1,0)},
+    @auto anchor horizontal=center,
+    placement/logical node depth/.code=\def\pgfmathresult{1}
+  },
+  branch left/.default=1,
+  branch up/.style={
+    placement/place,
+    group shift={(0,#1)},
+    @auto anchor vertical=center,
+    placement/logical node depth/.code=\def\pgfmathresult{1}
+  },
+  branch up/.default=1,
+  branch down/.style={
+    placement/place,
+    group shift={(0,-#1)},
+    @auto anchor vertical=center,
+    placement/logical node depth/.code=\def\pgfmathresult{1}
+  },
+  branch down/.default=1,
+  grow right sep/.style={
+    Cartesian placement,
+    chain shift={(1pt,0)},
+    @auto anchor horizontal=west,
+    placement/logical node width/.code=\tikz@lib@graph@width@sep{##1}{#1}
+  },
+  grow right sep/.default=1em,
+  grow left sep/.style={
+    Cartesian placement,
+    chain shift={(-1pt,0)},
+    @auto anchor horizontal=east,
+    placement/logical node width/.code=\tikz@lib@graph@width@sep{##1}{#1}
+  },
+  grow left sep/.default=1em,
+  grow up sep/.style={
+    Cartesian placement,
+    chain shift={(0,1pt)},
+    @auto anchor vertical=south,
+    placement/logical node width/.code=\tikz@lib@graph@depth@sep{##1}{#1}
+  },
+  grow up sep/.default=1em,
+  grow down sep/.style={
+    Cartesian placement,
+    chain shift={(0,-1pt)},
+    @auto anchor vertical=north,
+    placement/logical node width/.code=\tikz@lib@graph@depth@sep{##1}{#1}
+  },
+  grow down sep/.default=1em,
+  grow right sep/.style={
+    Cartesian placement,
+    chain shift={(1pt,0)},
+    @auto anchor horizontal=west,
+    placement/logical node width/.code=\tikz@lib@graph@width@sep{##1}{#1}
+  },
+  branch right sep/.style={
+    Cartesian placement,
+    group shift={(1pt,0)},
+    @auto anchor horizontal=west,
+    placement/logical node depth/.code=\tikz@lib@graph@width@sep{##1}{#1}
+  },
+  branch right sep/.default=1em,
+  branch left sep/.style={
+    Cartesian placement,
+    group shift={(-1pt,0)},
+    @auto anchor horizontal=east,
+    placement/logical node depth/.code=\tikz@lib@graph@width@sep{##1}{#1}
+  },
+  branch left sep/.default=1em,
+  branch up sep/.style={
+    Cartesian placement,
+    group shift={(0,1pt)},
+    @auto anchor vertical=south,
+    placement/logical node depth/.code=\tikz@lib@graph@depth@sep{##1}{#1}
+  },
+  branch up sep/.default=1em,
+  branch down sep/.style={
+    Cartesian placement,
+    group shift={(0,-1pt)},
+    @auto anchor vertical=north,
+    placement/logical node depth/.code=\tikz@lib@graph@depth@sep{##1}{#1}
+  },
+  branch down sep/.default=1em,
+  @auto anchor horizontal/.style={
+    nodes={anchor=\csname tikz@lib@graph@auto@\tikz@lib@graph@auto@h @\tikz@lib@graph@auto@v\endcsname},
+    /utils/exec=\def\tikz@lib@graph@auto@h{#1}
+  },
+  @auto anchor vertical/.style={
+    nodes={anchor=\csname tikz@lib@graph@auto@\tikz@lib@graph@auto@h @\tikz@lib@graph@auto@v\endcsname},
+    /utils/exec=\def\tikz@lib@graph@auto@v{#1}
+  },
+  no placement/.style={
+    placement/place,
+    placement/compute position/.code=%
+  }
+}%
+
+\def\tikz@lib@graph@auto@h{center}%
+\def\tikz@lib@graph@auto@v{center}%
+
+\def\tikz@lib@graph@auto@center@center{center}%
+\def\tikz@lib@graph@auto@west@center{west}%
+\def\tikz@lib@graph@auto@east@center{east}%
+\def\tikz@lib@graph@auto@center@north{north}%
+\def\tikz@lib@graph@auto@west@north{north west}%
+\def\tikz@lib@graph@auto@east@north{north east}%
+\def\tikz@lib@graph@auto@center@south{south}%
+\def\tikz@lib@graph@auto@west@south{south west}%
+\def\tikz@lib@graph@auto@east@south{south east}%
+
+\def\tikz@lib@graph@linear@pos{%
+  \pgfkeysgetvalue{/tikz/graphs/chain shift}\tikz@temp
+  \expandafter\tikz@scan@one@point\expandafter\pgf@process\tikz@temp
+  \pgf@process{\pgfpointscale{\pgfkeysvalueof{/tikz/graphs/placement/width}}{}}%
+  \pgf@xa=\pgf@x%
+  \pgf@ya=\pgf@y%
+  \pgfkeysgetvalue{/tikz/graphs/group shift}\tikz@temp
+  \expandafter\tikz@scan@one@point\expandafter\pgf@process\tikz@temp
+  \pgf@process{\pgfpointscale{\pgfkeysvalueof{/tikz/graphs/placement/depth}}{}}%
+  \advance\pgf@xa by\pgf@x%
+  \advance\pgf@ya by\pgf@y%
+  \edef\tikz@lib@graph@shift{(\the\pgf@xa,\the\pgf@ya)}
+  \pgfkeys{/tikz/graphs/nodes/.expanded={shift={\tikz@lib@graph@shift}}}
+}%
+
+
+\def\tikz@lib@graph@width@sep#1#2{%
+  \pgf@process{\pgfpointdiff{\pgfpointanchor{#1}{west}}{\pgfpointanchor{#1}{east}}}%
+  \pgfmathparse{#2+\the\pgf@x}%
+}%
+
+\def\tikz@lib@graph@depth@sep#1#2{%
+  \pgf@process{\pgfpointdiff{\pgfpointanchor{#1}{south}}{\pgfpointanchor{#1}{north}}}%
+  \pgfmathparse{#2+\the\pgf@y}%
+}%
+
+
+
+\tikzgraphsset{,
+  circular placement/.style={
+    placement/place,
+    placement/compute position/.code=\tikz@lib@graph@circular@pos,%
+    placement/logical node depth/.code=\def\pgfmathresult{1},
+    placement/logical node width/.code=\def\pgfmathresult{1},
+  },
+  clockwise/.style={
+    circular placement,
+    group polar shift={(-360/#1:0)}
+  },
+  clockwise/.default=\tikzgraphVnum,
+  counterclockwise/.style={
+    circular placement,
+    group polar shift={(360/#1:0)}
+  },
+  counterclockwise/.default=\tikzgraphVnum,
+  chain polar shift/.initial={(0:1cm)},
+  group polar shift/.initial={(60:0)},
+  radius/.initial=1cm,
+  phase/.initial=90,
+}%
+
+\def\tikz@lib@graph@circular@pos{%
+  \pgfkeysgetvalue{/tikz/graphs/chain polar shift}\tikz@temp
+  \expandafter\tikz@lib@graph@decompose@polar\tikz@temp%
+  \pgf@process{\pgfpointscale{\pgfkeysvalueof{/tikz/graphs/placement/width}}{}}%
+  \pgf@xa=\pgf@x%
+  \pgf@ya=\pgf@y%
+  \pgfkeysgetvalue{/tikz/graphs/group polar shift}\tikz@temp
+  \expandafter\tikz@lib@graph@decompose@polar\tikz@temp%
+  \pgf@process{\pgfpointscale{\pgfkeysvalueof{/tikz/graphs/placement/depth}}{}}%
+  \advance\pgf@xa by\pgf@x%
+  \advance\pgf@ya by\pgf@y%
+  \pgfmathparse{\pgfkeysvalueof{/tikz/graphs/radius}}%
+  \advance\pgf@ya by\pgfmathresult pt%
+  \pgfmathsetmacro\tikz@temp{\the\pgf@xa+\pgfkeysvalueof{/tikz/graphs/phase}}%
+  \edef\tikz@lib@graph@shift{(\tikz@temp:\the\pgf@ya)}
+  \pgfkeys{/tikz/graphs/nodes/.expanded={shift={\tikz@lib@graph@shift}}}
+}%
+
+
+\def\tikz@lib@graph@decompose@polar(#1:#2){%
+  \pgfmathsetlength\pgf@x{#1}%
+  \pgfmathsetlength\pgf@y{#2}%
+}%
+
+
+\tikzgraphsset{
+  grid placement/.style={
+    placement/place,
+    placement/compute position/.code=\tikz@lib@graph@grid@pos,%
+  },
+}%
+
+
+\def\tikz@lib@graph@grid@pos{%
+  \tikzgraphpreparewrapafter%
+  \pgfkeysgetvalue{/tikz/graphs/placement/depth}\tikz@temp@depth%
+  \pgfkeysgetvalue{/tikz/graphs/placement/width}\tikz@temp@width%
+  \pgfmathsetmacro{\tikz@temp}{max(\tikz@temp@depth, \tikz@temp@width)}%
+  \pgfmathsetmacro{\tikz@temp@col}{mod(\tikz@temp,\tikzgraphwrapafter)}%
+  \pgfmathsetmacro{\tikz@temp@row}{div(\tikz@temp,\tikzgraphwrapafter)}%
+  \pgfkeysgetvalue{/tikz/graphs/group shift}\tikz@temp%
+  \expandafter\tikz@scan@one@point\expandafter\tikz@lib@graph@grid@pos@a\tikz@temp%
+  \pgfkeysgetvalue{/tikz/graphs/chain shift}\tikz@temp%
+  \expandafter\tikz@scan@one@point\expandafter\tikz@lib@graph@grid@pos@b\tikz@temp%
+  \edef\tikz@lib@graph@shift{(\the\pgf@xa,\the\pgf@ya)}
+  \pgfkeys{/tikz/graphs/nodes/.expanded={shift={\tikz@lib@graph@shift}}}
+}%
+
+\def\tikz@lib@graph@grid@pos@a#1{\pgf@process{\pgfpointscale{\tikz@temp@row}{#1}}\pgf@xa=\pgf@x\relax\pgf@ya=\pgf@y\relax}%
+\def\tikz@lib@graph@grid@pos@b#1{\pgf@process{\pgfpointscale{\tikz@temp@col}{#1}}%
+  \advance\pgf@xa by\pgf@x\relax
+  \advance\pgf@ya by\pgf@y\relax}%
+
+\tikzgraphsset{
+  wrap after/.initial=0,
+  V/.code={%
+    \def\tikzgraphV{#1}%
+    \c@pgf@counta=0\foreach \tikz@dummy in {#1} {\global\advance\c@pgf@counta by1\relax}%
+    \edef\tikzgraphVnum{\the\c@pgf@counta}
+  },
+  V={1},
+  n/.style={V={1,...,#1},name shore V/.style={name=V}},
+  W/.code={%
+    \def\tikzgraphW{#1}%
+    \c@pgf@counta=0\foreach \tikz@dummy in {#1} {\global\advance\c@pgf@counta by1\relax}%
+    \edef\tikzgraphWnum{\the\c@pgf@counta}
+  },
+  W={1},
+  m/.style={W={1,...,#1},name shore W/.style={name=W}},
+  name shore V/.style=,
+  name shore W/.style=,
+}%
+
+
+
+
+\tikzgraphsset{quick/.is if=tikz@graph@quick}%
+\newif\iftikz@graph@quick
+
+\def\tikz@lib@graphs@parse@quick@graph{
+  \begingroup%
+  \global\tikz@qnode@count0\relax%
+  \let\tikzgraphnodepath\pgfutil@empty%
+  \tikz@q@outertrue%
+  \afterassignment\tikz@lib@graphs@quick@main\let\pgf@temp=%
+}%
+
+\newcount\tikz@qnode@count
+\newif\iftikz@q@outer
+
+\def\tikz@lib@graphs@quick@main{%
+  \afterassignment\tikz@lib@graphs@quick@handle\let\pgf@let@token=%
+}%
+\def\tikz@lib@graphs@quick@handle{%
+  \ifx\pgf@let@token"%
+    \expandafter\tikz@lib@graphs@quick@first@node%
+  \else%
+    \expandafter\tikz@lib@graphs@quick@other%
+  \fi%
+}%
+\def\tikz@lib@graphs@quick@other{%
+  \let\tikz@next\tikz@lib@graphs@quick@error%
+  \ifx\pgf@let@token\egroup%
+    \let\tikz@next\tikz@lib@graphs@quick@end@group%
+  \else%
+    \ifx\pgf@let@token\bgroup%
+      \let\tikz@next\tikz@lib@graphs@quick@start@group%
+    \else%
+      \ifx\pgf@let@token\par%
+        \let\tikz@next\tikz@lib@graphs@quick@main%
+      \fi%
+    \fi
+  \fi%
+  \tikz@next%
+}%
+
+\def\tikz@lib@graphs@quick@error#1{\tikzerror{Unexpected token '\string#1' in quick graph syntax}\tikz@lib@graphs@quick@main}%
+\def\tikz@lib@graphs@quick@start@group{%
+  \pgfutil@ifnextchar[\tikz@lib@graphs@quick@start@group@{\tikzerror{Group
+      in quick graph syntax must start with options.}}
+}%
+
+\def\tikz@lib@graphs@quick@start@group@[#1]{%
+  \begingroup%
+    \tikz@q@outerfalse%
+    \tikzgraphsset{#1}%
+    \tikz@lib@graphs@quick@main%
+}%
+\def\tikz@lib@graphs@quick@end@group{%
+  \iftikz@q@outer%
+    \endgroup%
+    \pgfutil@loop%
+    \ifnum\tikz@qnode@count>0\relax%
+      \expandafter\global\expandafter\let\csname tikz@gr@q@@\csname tikz@gr@qn@@\the\tikz@qnode@count\endcsname\endcsname\relax%
+      \expandafter\global\expandafter\let\csname tikz@gr@qn@@\the\tikz@qnode@count\endcsname\relax%
+      \global\advance\tikz@qnode@count by-1\relax%
+    \pgfutil@repeat%
+    \expandafter\tikz@lib@graph@main@done%
+  \else%
+    \endgroup%
+    \expandafter\tikz@lib@graphs@end@group@%
+  \fi%
+}%
+\def\tikz@lib@graphs@end@group@{%
+  \pgfutil@ifnextchar;{\expandafter\tikz@lib@graphs@quick@main\pgfutil@gobble}{%
+    \pgfutil@ifnextchar,{\expandafter\tikz@lib@graphs@quick@main\pgfutil@gobble}{%
+      \tikzerror{Graph groups in quick syntax must be followed by a semicolon or a comma.}%
+    }%
+  }%
+}%
+
+
+\def\tikz@lib@graphs@quick@first@node{%
+  \let\tikz@quick@prev@node\relax%
+  \tikz@lib@graphs@quick@node%
+}%
+
+\def\tikz@lib@graphs@quick@node#1"{%
+  \def\tikzgraphnodename{#1}%
+  \let\tikzgraphnodetext\tikzgraphnodename%
+  \iftikzgraphsautonumbernodes
+    \edef\tikzgraphnodename{\tikzgraphnodename\tikz@lib@auto@sep\the\tikz@lib@auto@number}%
+    \global\advance\tikz@lib@auto@number by1\relax%
+  \fi
+  \pgfutil@ifnextchar/\tikz@lib@graphs@quick@text\tikz@lib@graphs@quick@opt%
+}%
+\def\tikz@lib@graphs@quick@text/"#1"{%
+  \def\tikzgraphnodetext{#1}%
+  \tikz@lib@graphs@quick@opt%
+}%
+\def\tikz@lib@graphs@quick@opt{%
+  \pgfutil@ifnextchar[\tikz@lib@graphs@quick@withopt{\tikz@lib@graphs@quick@withopt[]}%
+}%
+\def\tikz@lib@graphs@quick@withopt[#1]{%
+  \expandafter\ifx\csname tikz@gr@q@@\tikzgraphnodename\endcsname\relax%
+    \global\advance\tikz@qnode@count by1\relax%
+    \expandafter\global\expandafter\let\csname tikz@gr@q@@\tikzgraphnodename\endcsname\pgfutil@empty%
+    \expandafter\global\expandafter\let\csname tikz@gr@qn@@\the\tikz@qnode@count\endcsname\tikzgraphnodename%
+    \let\tikzgraphnodefullname\tikzgraphnodename%
+    \let\tikzgraphnodeas\tikzgraphnodeas@default%
+    \node [%
+      name=\tikzgraphnodename,%
+      graphs/redirect unknown to tikz,
+      /tikz/graphs/.cd,%
+      /tikz/graphs/@nodes styling,%
+      #1]%
+      {%
+        \tikzgraphnodeas%
+      };%
+  \else%
+    \tikzgdlatenodeoptionacallback{\tikzgraphnodename}%
+    \node also[graphs/redirect unknown to tikz,/tikz/graphs/.cd,#1](\tikzgraphnodename);%
+  \fi%
+  \tikz@lig@graph@quikc@make@edge@if@necessary%
+  \tikz@lib@graphs@quick@scan@after@node%
+}%
+
+\def\tikz@lig@graph@quikc@make@edge@if@necessary{%
+  \ifx\tikz@quick@prev@node\relax%
+  \else%
+    \tikz@lib@graphs@quick@make@edge%
+  \fi%
+}%
+
+\def\tikz@lib@graphs@quick@scan@after@node{%
+  \pgfutil@ifnextchar,\tikz@lib@graphs@quick@comma{%
+    \pgfutil@ifnextchar;\tikz@lib@graphs@quick@semi{%
+      \pgfutil@ifnextchar\egroup{\tikz@lib@graphs@quick@semi;}{%
+        \pgfutil@ifnextchar\par{\expandafter\tikz@lib@graphs@quick@scan@after@node\tikz@lib@graphs@quick@gobble@par}%
+        \tikz@lib@graphs@quick@connector}}}%
+}%
+\long\def\tikz@lib@graphs@quick@gobble@par#1{}%
+
+\def\tikz@lib@graphs@quick@comma,{\tikz@lib@graphs@quick@main}%
+\def\tikz@lib@graphs@quick@semi;{\tikz@lib@graphs@quick@main}%
+\def\tikz@lib@graphs@quick@connector#1#2{%
+  \def\tikz@lib@graphs@quick@edge@kind{#1#2}%
+  \pgfutil@ifnextchar>\tikz@lib@graphs@back@edge{%
+    \pgfutil@ifnextchar[\tikz@lib@graphs@quick@connector@handle@opt{\tikz@lib@graphs@quick@connector@handle@opt[]}%
+  }%
+}%
+\def\tikz@lib@graphs@back@edge#1{%
+  \expandafter\def\expandafter\tikz@lib@graphs@quick@edge@kind\expandafter{\tikz@lib@graphs@quick@edge@kind#1}%
+  \pgfutil@ifnextchar[\tikz@lib@graphs@quick@connector@handle@opt{\tikz@lib@graphs@quick@connector@handle@opt[]}%
+}%
+\def\tikz@lib@graphs@quick@connector@handle@opt[#1]{%
+  \def\tikz@lib@graphs@quick@edge@options{#1}%
+  \let\tikz@quick@prev@node\tikzgraphnodename%
+  \tikz@lib@graphs@quick@scan@after@connector%
+}%
+\def\tikz@lib@graphs@quick@scan@after@connector{%
+  \pgfutil@ifnextchar\par{\expandafter\tikz@lib@graphs@quick@scan@after@connector\tikz@lib@graphs@quick@gobble@par}{%
+    \pgfutil@ifnextchar"{\expandafter\tikz@lib@graphs@quick@node\pgfutil@gobble}{%
+      \tikzerror{Quotation marks expected after edge connector}%
+      }%
+  }%
+}%
+
+\def\tikz@lib@graphs@quick@make@edge{%
+  {
+    \expandafter\tikz@lib@graphs@quick@make@edge@styling\expandafter{\tikz@lib@graphs@quick@edge@options}%
+    \expandafter\expandafter\expandafter\tikz@lib@graphs@quick@make@edge@for%
+    \expandafter\expandafter\expandafter{\expandafter\tikz@quick@prev@node\expandafter}\expandafter{\tikzgraphnodename}%
+  }
+}%
+
+\def\tikz@lib@graphs@quick@make@edge@styling#1{%
+  \tikz@enable@edge@quotes%
+  \tikzgraphsset{.unknown/.code=\tikz@lib@graph@unknown@edge@option{##1},#1}%
+}%
+
+\def\tikz@lib@graphs@quick@make@edge@for#1#2{%
+  \pgfkeysgetvalue{/tikz/graphs/@edges styling}\pgf@tempa
+  \pgfkeysgetvalue{/tikz/graphs/@edges node}\pgf@temp@b
+  \expandafter\expandafter\expandafter\tikz@lib@graphs@quick@make@edge@for@with%
+  \expandafter\expandafter\expandafter{\expandafter\pgf@tempa\expandafter}\expandafter{\pgf@temp@b}{#1}{#2}%
+}%
+
+\def\tikz@lib@graphs@quick@make@edge@for@with#1#2#3#4{%
+  \tikzgraphsset{new \tikz@lib@graphs@quick@edge@kind={#3}{#4}{#1}{#2}}%
+}%
+
+\endinput

preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/graphs/tikzlibrarygraphs.standard.code.tex

@@ -0,0 +1,72 @@
+
+\ProvidesFileRCS{tikzlibrarygraphs.standard.code.tex}
+
+\usetikzlibrary{graphs}%
+
+
+
+\tikzgraphsset{
+  declare={subgraph I_n}%
+  {
+    \foreach \tikz@lib@graph@node@num in \tikzgraphV
+    { \tikz@lib@graph@node@num }
+  },
+  declare={subgraph I_nm}%
+  {
+    subgraph I_n [name shore V] -- [no edges]
+    subgraph I_n [name shore W, V/.expand once=\tikzgraphW]
+  },
+  declare={subgraph K_n}%
+  {
+    [clique]
+    subgraph I_n
+  },
+  declare={subgraph K_nm}%
+  {
+    [color class=shore V,
+     color class=shore W,
+     complete bipartite={shore V}{shore W}]
+    subgraph I_n [name shore V, shore V] -- [no edges]
+    subgraph I_n [name shore W, V/.expand once=\tikzgraphW, shore W]
+  },
+  declare={subgraph C_n}%
+  {
+    [cycle]
+    subgraph I_n
+  },
+  declare={subgraph P_n}%
+  {
+    [path]
+    subgraph I_n
+  },
+  declare={subgraph Grid_n}%
+  {
+    [grid]
+    subgraph I_n
+  },
+  p/.initial=0.5,
+  declare={subgraph G_np}%
+  {
+    [/utils/exec={
+      \pgfmathsetmacro\tikz@lib@lg@p{\pgfkeysvalueof{/tikz/graphs/p}}
+      \let\tikz@lib@gnp@edges\pgfutil@empty%
+      \foreach \tikz@lib@graph@node@a [count=\tikz@lib@g@count@a] in \tikzgraphV
+        \foreach \tikz@lib@graph@node@b [count=\tikz@lib@g@count@b] in \tikzgraphV
+        {
+          \ifnum\tikz@lib@g@count@a<\tikz@lib@g@count@b\relax
+            \pgfmathparse{rnd}
+            \ifdim\pgfmathresult pt<\tikz@lib@lg@p pt%
+              \ifx\tikz@lib@gnp@edges\pgfutil@empty
+                \xdef\tikz@lib@gnp@edges{\tikz@lib@graph@node@a--\tikz@lib@graph@node@b}%
+              \else
+                \xdef\tikz@lib@gnp@edges{\tikz@lib@gnp@edges,\tikz@lib@graph@node@a--\tikz@lib@graph@node@b}%
+              \fi
+            \fi
+          \fi
+        }
+      }]
+      \foreach \tikz@lg@temp in \tikz@lib@gnp@edges {
+        [parse/.expand once=\tikz@lg@temp]
+      }
+  },
+}%

preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/tikzexternalshared.code.tex

@@ -0,0 +1,1265 @@
+
+\toksdef\t@tikzexternal@tmpa=0
+\toksdef\t@tikzexternal@tmpb=1
+
+\newif\iftikzexternal@nestedflag
+\newif\iftikzexternal@verboseuptodate
+\newif\iftikzexternal@verboseio
+\newif\iftikzexternal@genfigurelist
+\newif\iftikzexternal@onlynamed
+\newif\iftikzexternal@file@isuptodate
+\newif\iftikzexternal@force@remake
+\newif\iftikzexternal@optimize
+\newif\iftikzexternal@export@enabled
+\tikzexternal@export@enabledtrue
+
+\gdef\c@tikzexternal@version{2}
+
+\newif\iftikzexternalremakenext
+\newif\iftikzexternal@verbose@optimize
+\tikzexternal@verbose@optimizetrue
+
+\newif\iftikzexternalexportnext
+\tikzexternalexportnexttrue
+
+\def\tikzifexternalizing#1#2{%
+    \ifpgf@external@grabshipout #1\else #2\fi
+}%
+\def\tikzifexternalizingnext#1#2{%
+    \ifpgf@external@grabshipout
+        \tikzexternalgetnextfilename\tikzexternal@temp
+        \tikzifexternaljobnamematches\tikzexternal@temp{#1}{#2}%
+    \else
+        #2%
+    \fi
+}%
+\def\tikzifexternalizingcurrent#1#2{%
+    \ifpgf@external@grabshipout
+        \tikzexternalgetcurrentfilename\tikzexternal@temp
+        \ifx\tikzexternal@temp\pgfutil@empty
+            #2%
+        \else
+            \tikzifexternaljobnamematches\tikzexternal@temp{#1}{#2}%
+        \fi
+    \else
+        #2%
+    \fi
+}%
+
+\def\tikzifexternaljobnamematches#1#2#3{%
+    \edef\pgf@tempa{\expandafter\string\csname#1\endcsname}%
+    \edef\pgf@tempb{\expandafter\string\csname\pgfactualjobname\endcsname}%
+    \ifx\pgf@tempa\pgf@tempb #2\else#3 \fi%
+}%
+
+
+\pgfutil@IfUndefined{pdfshellescape}{%
+    \pgfutil@IfUndefined{pdf@shellescape}{%
+        \def\tikzexternalcheckshellescape{0}%
+    }{%
+        \let\tikzexternalcheckshellescape=\pdf@shellescape
+    }%
+}{%
+    \let\tikzexternalcheckshellescape=\pdfshellescape
+}%
+\ifnum\tikzexternalcheckshellescape=1
+    \def\tikzexternalcheckshellescape{\pgfkeysvalueof{/tikz/external/shell escape}\space}%
+\else
+    \def\tikzexternalcheckshellescape{}%
+\fi
+
+\newif\iftikzexternal@auto@detect@jobname
+
+\pgfqkeys{/tikz/external}{
+    figure list/.is if=tikzexternal@genfigurelist,
+    aux in dpth/.style={/pgf/images/aux in dpth={#1}},%
+    disable dependency files/.code={%
+        \let\tikzexternalfiledependsonfile@ACTIVE=\tikzexternalfiledependsonfile
+    },
+    mode/.is choice,
+    mode/only graphics/.code   = {%
+        \def\tikzexternal@opmode{0}%
+        \pgfkeysalso{/pgf/images/aux in dpth=true}%
+    },
+    mode/no graphics/.code     = {\def\tikzexternal@opmode{1}},
+    mode/only pictures/.code   = {\def\tikzexternal@opmode{1}},
+    mode/graphics if exists/.code= {%
+        \def\tikzexternal@opmode{2}%
+        \pgfkeysalso{/pgf/images/aux in dpth=true}%
+    },
+    mode/list only/.code       = {\def\tikzexternal@opmode{3}\tikzexternal@genfigurelisttrue},
+    mode/convert with system call/.code={%
+        \def\tikzexternal@opmode{4}%
+        \pgfkeysalso{/tikz/external/figure list=false,/pgf/images/aux in dpth=true}%
+    },
+    mode/list and make/.code   = {%
+        \def\tikzexternal@opmode{5}%
+        \pgfkeysalso{/tikz/external/figure list=true,/pgf/images/aux in dpth=true}%
+    },
+    mode=convert with system call,
+    force remake/.is if=tikzexternal@force@remake,
+    force remake/.default=true,
+    failed ref warnings for/.initial={\ref,\cite,\pageref},
+    export next/.is if=tikzexternalexportnext,
+    export/.is if=tikzexternal@export@enabled,
+    remake next/.is if=tikzexternalremakenext,
+    remake next/.default=true,
+    verbose IO/.is if=tikzexternal@verboseio,
+    verbose IO/.default=true,
+    verbose IO=true,
+    verbose optimize/.is if=tikzexternal@verbose@optimize,
+    verbose up to date/.is if=tikzexternal@verboseuptodate,
+    verbose/.style={
+        verbose IO=#1,
+        verbose optimize=#1,
+        verbose up to date=#1,
+    },
+    shell escape/.initial=-shell-escape,
+    read main aux/.is if=pgfexternalreadmainaux,
+    image discarded text/.initial={%
+        [[ \textsc{Image Discarded Due To} \texttt{`/tikz/external/%
+                \ifcase\tikzexternal@opmode\relax
+                    mode=only graphics%
+                \or
+                    mode=no graphics%
+                \or
+                    mode=graphics if exists%
+                \or
+                    mode=list only%
+                \or
+                    mode=convert with system call%
+                \or
+                    mode=list and make%
+                \fi
+        '}~]]%
+        \pgfutil@ifundefined{tikzexternal@warning@at@end}{%
+            \pgfutil@ifundefined{AtEndDocument}{}{%
+                \AtEndDocument{%
+                    \message{! Package tikz Warning: Some images are not up-to-date and need to be generated. }%
+                }%
+            }%
+            \gdef\tikzexternal@warning@at@end{1}%
+        }{}%
+    },
+    optimize/.is choice,
+    optimize/true/.code={%
+        \tikzexternal@optimizetrue
+        \iftikzexternal@optimize
+            \ifpgf@external@grabshipout
+                \tikzexternal@optimize@REPLACE
+            \fi
+        \fi
+    },
+    optimize/false/.code={%
+        \tikzexternal@optimizefalse%
+        \tikzexternal@optimize@RESTORE
+    },%
+    optimize=true,
+    optimize away text/.code={[ \textsc{\string#1\ optimized away because it does not contribute to exported PDF}]},
+    optimize/install/.code={},%
+    optimize/restore/.code={},%
+    optimize command away/.code 2 args={%
+        \expandafter\global\expandafter\let\csname\string#1@ORIG\endcsname=#1%
+        \pgfkeysalso{%
+            /tikz/external/optimize/install/.append code={%
+                \def#1{\tikzexternal@optimize@away@cmd{#1}{#2}}%
+            },
+            /tikz/external/optimize/restore/.append code={%
+                \expandafter\let\expandafter#1\csname\string#1@ORIG\endcsname
+            }
+        }%
+        \iftikzexternal@optimize
+            \ifpgf@external@grabshipout
+                \tikzexternal@optimize@REPLACE
+            \fi
+        \fi
+    },
+    optimize command away=\includegraphics,
+    optimize command away=\pgfincludeexternalgraphics,
+    optimize latex env away/.code={%
+        \expandafter\let\expandafter\pgf@tempa\csname #1\endcsname
+        \expandafter\global\expandafter\let\csname #1@ORIG\endcsname=\pgf@tempa%
+        \pgfkeysalso{%
+            /tikz/external/optimize/install/.append code={%
+                \pgfutil@namedef{#1}{\tikzexternal@optimize@away@latex@env{#1}}%
+            },
+            /tikz/external/optimize/restore/.append code={%
+                \pgfutil@namelet{#1}{#1@ORIG}%
+            }%
+        }%
+    },
+    only named/.is if=tikzexternal@onlynamed,
+    only named/.default=true,
+    figure name/.initial=\tikzexternal@realjob-figure,
+    reset counter/.code={%
+        \expandafter\gdef\csname c@tikzext@no@#1\endcsname{0}%
+    },%
+    prefix/.code={\tikzsetexternalprefix{#1}},
+    up to date check/.is choice,
+    up to date check/simple/.code={\def\tikzexternal@uptodate@mode{0}},
+    up to date check/md5/.code={\def\tikzexternal@uptodate@mode{1}},
+    up to date check/diff/.code={\def\tikzexternal@uptodate@mode{2}},
+    up to date check=md5,
+}
+
+\expandafter\def\csname tikzexternal@driver@pgfsys-luatex.def\endcsname{%
+    \pgfkeyssetvalue{/tikz/external/system call}{%
+        lualatex \tikzexternalcheckshellescape -halt-on-error -interaction=batchmode -jobname "\image" "\texsource"%
+    }%
+}%
+\expandafter\def\csname tikzexternal@driver@pgfsys-pdftex.def\endcsname{%
+    \pgfutil@IfUndefined{directlua}{%
+        \pgfkeyssetvalue{/tikz/external/system call}{%
+            pdflatex \tikzexternalcheckshellescape -halt-on-error -interaction=batchmode -jobname "\image" "\texsource"%
+        }%
+    }{%
+        \pgfkeyssetvalue{/tikz/external/system call}{%
+            lualatex \tikzexternalcheckshellescape -halt-on-error -interaction=batchmode -jobname "\image" "\texsource"%
+        }%
+    }%
+}%
+\expandafter\def\csname tikzexternal@driver@pgfsys-xetex.def\endcsname{%
+    \pgfkeyssetvalue{/tikz/external/system call}{%
+        xelatex \tikzexternalcheckshellescape -halt-on-error -interaction=batchmode -jobname "\image" "\texsource"%
+    }%
+}%
+\expandafter\def\csname tikzexternal@driver@pgfsys-dvips.def\endcsname{%
+    \pgfkeyssetvalue{/tikz/external/system call}{%
+        latex \tikzexternalcheckshellescape -halt-on-error -interaction=batchmode -jobname "\image" "\texsource" %
+        && dvips -o "\image".ps "\image".dvi %
+    }%
+}%
+
+\pgfutil@ifundefined{tikzexternal@driver@\pgfsysdriver}{%
+    \csname tikzexternal@driver@pgfsys-pdftex.def\endcsname
+}{%
+    \csname tikzexternal@driver@\pgfsysdriver\endcsname
+}%
+
+
+\def\tikzsetfigurename#1{\pgfkeyssetvalue{/tikz/external/figure name}{#1}}%
+\def\tikzappendtofigurename#1{\pgfkeys{/tikz/external/figure name/.add={}{#1}}}
+
+\def\tikzsetexternalprefix#1{\def\tikzexternal@filenameprefix{#1}}
+\tikzsetexternalprefix{}
+
+\def\tikzexternalize{%
+    \pgfutil@ifnextchar[{%
+        \tikzexternalize@opt
+    }{%
+        \tikzexternalize@opt[]%
+    }%
+}%
+\def\tikzexternalize@opt[#1]{%
+    \pgfutil@ifnextchar\bgroup{%
+        \tikzexternal@auto@detect@jobnamefalse
+        \tikzexternalize@opt@withname[#1]%
+    }{%
+        \tikzexternal@auto@detect@jobnametrue
+        \pgfutil@ifundefined{tikzexternalrealjob}{%
+            \let\tikzexternalrealjob=\jobname
+        }{}%
+        \def\pgf@tempa{\tikzexternalize@opt@withname[#1]}%
+        \expandafter\pgf@tempa\expandafter{\tikzexternalrealjob}%
+    }%
+}%
+\def\tikzexternalize@opt@withname[#1]#2{%
+    \gdef\tikzexternalrealjob{#2}%
+    \if1\tikzexternalize@hasbeencalled
+    \else
+        \pgfqkeys{/tikz/external}{#1}%
+        \def\tikzexternal@realjob{#2}%
+        \tikzexternalauxlock@init
+        \pgfrealjobname{#2}%
+        \def\tikzexternalize@hasbeencalled{1}%
+        \tikzexternalenable
+        \def\tikzexternal@determineimgextension##1:##2\relax{\gdef\tikzexternalimgextension{##1}}%
+        \xdef\pgf@tempa{\pgfsys@imagesuffixlist}%
+        \expandafter\tikzexternal@determineimgextension\pgf@tempa:\relax
+        \pgfutil@ifundefined{includegraphics}{%
+            \let\tikzexternal@orig@includegraphics=\relax
+        }{%
+            \let\tikzexternal@orig@includegraphics=\includegraphics
+        }%
+        \let\tikzexternalfiledependsonfile=\tikzexternalfiledependsonfile@ACTIVE
+        \let\tikzpicturedependsonfile=\tikzpicturedependsonfile@ACTIVE
+    \fi
+}
+\def\tikzexternalize@hasbeencalled{0}%
+
+\def\tikzifexternalizehasbeencalled#1#2{%
+    \if1\tikzexternalize@hasbeencalled
+        #1%
+    \else
+        #2%
+    \fi
+}%
+
+\def\tikzexternalauxlock@init{%
+    \if4\tikzexternal@opmode
+        \ifpgfexternalreadmainaux
+            \edef\pgf@tempa{\expandafter\string\csname\tikzexternal@realjob\endcsname}%
+            \edef\pgf@tempb{\expandafter\string\csname\jobname\endcsname}%
+            \ifx\pgf@tempa\pgf@tempb
+                \tikzexternalauxlock@setlock{0}%
+            \else
+                \tikzexternalauxlock@getlockvalue
+                \if1\tikzexternallocked
+                    \pgfexternalreadmainauxfalse
+                \else
+                    \pgfexternalreadmainauxtrue
+                \fi
+            \fi
+        \else
+            \def\tikzexternalauxlock@setlock##1{}%
+        \fi
+    \fi
+}
+\def\tikzexternalauxlock@getlockvalue{%
+    \openin\r@pgf@reada=\tikzexternal@realjob.auxlock
+    \ifeof\r@pgf@reada
+        \def\tikzexternallocked{0}%
+    \else
+        \read\r@pgf@reada to\pgf@tempa
+        \pgf@tempa
+        \pgfutil@ifundefined
+            {tikzexternallocked}
+            {\def\tikzexternallocked{1}}%
+            {}%
+    \fi
+    \closein\r@pgf@reada
+}%
+\def\tikzexternalauxlock@setlock#1{%
+    \immediate\openout\w@pgf@writea=\tikzexternal@realjob.auxlock
+    \immediate\write\w@pgf@writea{\noexpand\def\noexpand\tikzexternallocked{#1}}%
+    \immediate\closeout\w@pgf@writea
+}
+
+
+\def\pgf@external@grab@refundefinedtrue@code{%
+    \gdef\noexpand\tikzexternal@systemcall@reschedule@to@end@document{1}%
+}%
+
+\def\tikzexternalimgextension{}%
+
+\def\tikzexternaldisable{%
+    \tikzexternaldisable@nofading
+    \pgfutil@ifundefined{tikzexternal@orig@tikzfadingfrompicture}
+    {}%
+    {%
+        \let\tikzfadingfrompicture=\tikzexternal@orig@tikzfadingfrompicture
+        \let\endtikzfadingfrompicture=\tikzexternal@orig@endtikzfadingfrompicture
+        \let\tikzfading=\tikzexternal@orig@tikzfading
+    }%
+}%
+\def\tikzexternaldisable@nofading{%
+    \let\tikz=\tikzexternal@origtikz
+    \tikzexternal@TEXDIALECT@restore@picture
+    \iftikzexternal@optimize
+        \ifpgf@external@grabshipout
+            \tikzexternal@optimize@RESTORE
+        \fi
+    \fi
+}
+\def\tikzexternalenable{%
+    \if\tikzexternalize@hasbeencalled1%
+        \let\tikz=\tikzexternal@tikz@replacement
+        \tikzexternal@TEXDIALECT@installreplacement@picture
+        \pgfutil@ifundefined{tikzfadingfrompicture}%
+        {}%
+        {%
+            \pgfutil@ifundefined{tikzexternal@orig@tikzfadingfrompicture}{%
+                \let\tikzexternal@orig@tikzfadingfrompicture=\tikzfadingfrompicture
+                \let\tikzexternal@orig@endtikzfadingfrompicture=\endtikzfadingfrompicture
+                \let\tikzexternal@orig@tikzfading=\tikzfading
+            }{}%
+            \def\tikzfadingfrompicture{%
+                \begingroup
+                \tikzexternaldisable@nofading
+                \tikzexternal@orig@tikzfadingfrompicture}%
+            \def\endtikzfadingfrompicture{%
+                \tikzexternal@orig@endtikzfadingfrompicture
+                \endgroup}%
+            \def\tikzfading[##1]{%
+                \begingroup
+                \tikzexternaldisable@nofading
+                \tikzexternal@orig@tikzfading[##1]%
+                \endgroup}%
+        }%
+        \iftikzexternal@optimize
+            \ifpgf@external@grabshipout
+                \tikzexternal@optimize@REPLACE
+            \fi
+        \fi
+    \fi
+}%
+
+\def\tikzsetnextfilename#1{\gdef\tikzexternal@nextfile{#1}}
+\tikzsetnextfilename{}
+
+
+\long\gdef\tikzexternal@TEXDIALECT@collectpicture#1#2\endtikzpicture{#1{#2}}
+\def\tikzexternal@TEXDIALECT@begpicture{\tikzpicture}
+\def\tikzexternal@TEXDIALECT@endpicture{\endtikzpicture}%
+\def\tikzexternal@TEXDIALECT@installreplacement@picture{%
+    \let\tikzpicture=\tikzexternal@tikzpicture@replacement
+}%
+\def\tikzexternal@TEXDIALECT@restore@picture{%
+    \let\tikzpicture=\tikzexternal@origpicture
+}%
+
+
+
+
+\let\tikzexternal@origtikz=\tikz
+\let\tikzexternal@origpicture=\tikzpicture
+\let\tikzexternal@origendpicture=\endtikzpicture
+\let\tikzexternal@curfilename=\relax
+
+\def\tikzexternal@tikzpicture@replacement{%
+    \leavevmode
+    \global\tikzexternal@file@isuptodatetrue%
+    \tikzexternal@getnextfilename\tikzexternal@curfilename
+    \ifx\tikzexternal@curfilename\pgfutil@empty
+        \ifpgf@external@grabshipout
+            \iftikzexternal@optimize
+                \let\tikzexternal@next=\tikzexternal@skipfigure
+            \else
+                \let\tikzexternal@next=\tikzexternal@normalpicture@nographics
+            \fi
+        \else
+            \let\tikzexternal@next=\tikzexternal@normalpicture@nographics
+        \fi
+    \else
+        \ifpgf@external@grabshipout
+            \tikzifexternaljobnamematches\tikzexternal@curfilename{%
+                \let\tikzexternal@next=\tikzexternal@externalizefig
+            }{%
+                \iftikzexternal@optimize
+                    \let\tikzexternal@next=\tikzexternal@skipfigure
+                \else
+                    \let\tikzexternal@next=\tikzexternal@normalpicture@nographics
+                \fi
+            }%
+        \else
+            \ifcase\tikzexternal@opmode\relax
+                \let\tikzexternal@next=\tikzexternal@forcegraphics
+            \or
+                \let\tikzexternal@next=\tikzexternal@normalpicture@nographics
+            \or
+                \let\tikzexternal@next=\tikzexternal@externalizefig
+            \or
+                \let\tikzexternal@next=\tikzexternal@listmodepicture
+            \or
+                \let\tikzexternal@next=\tikzexternal@externalizefig@systemcall
+            \or
+                \let\tikzexternal@next=\tikzexternal@list@and@makefile@mode@picture
+            \fi
+        \fi
+    \fi
+    \tikzexternal@next
+}%
+
+\def\tikzexternal@tikz@replacement{%
+    \pgfutil@ifnextchar[{\tikzexternal@tikz@replacement@opt}{\tikzexternal@tikz@replacement@opt[]}%
+}%
+\def\tikzexternal@tikz@replacement@opt[#1]{%
+    \pgfutil@ifnextchar\bgroup{\tikzexternal@tikz@replacement@opt@{#1}}{\tikzexternal@tikz@replacement@opt@@{#1}}%
+}
+\long\def\tikzexternal@tikz@replacement@opt@#1#2{%
+    \tikzexternal@tikz@replacement@opt@process{#1}{#2}%
+}%
+\def\tikzexternal@tikz@replacement@opt@@#1{%
+  \def\tikz@next{\tikzexternal@tikz@replacement@collectnormalsemicolon{#1}}%
+  \ifnum\the\catcode`\;=\active\relax%
+    \def\tikz@next{\tikzexternal@tikz@replacement@collectactivesemicolon{#1}}%
+  \fi%
+  \tikz@next}
+\long\def\tikzexternal@tikz@replacement@collectnormalsemicolon#1#2;{%
+    \tikzexternal@tikz@replacement@opt@process{#1}{#2;}%
+}%
+{
+  \catcode`\;=\active
+  \long\gdef\tikzexternal@tikz@replacement@collectactivesemicolon#1#2;{%
+    \tikzexternal@tikz@replacement@opt@process{#1}{#2;}%
+  }
+}
+\long\def\tikzexternal@tikz@replacement@opt@process#1#2{%
+    \begingroup
+    \t@tikzexternal@tmpa=\expandafter{\tikzexternal@TEXDIALECT@begpicture[#1]#2}%
+    \t@tikzexternal@tmpb=\expandafter{\tikzexternal@TEXDIALECT@endpicture}%
+    \xdef\pgf@tempa{\the\t@tikzexternal@tmpa\the\t@tikzexternal@tmpb}%
+    \endgroup
+    \pgf@tempa
+}
+
+\def\tikzexternal@getnextfilename@advancecount{%
+    \begingroup
+    \c@pgf@counta=\csname c@tikzext@no@\tikzexternal@figurename\endcsname\relax
+    \advance\c@pgf@counta by1
+    \expandafter\xdef\csname c@tikzext@no@\tikzexternal@figurename\endcsname{\the\c@pgf@counta}%
+    \endgroup
+}%
+
+\def\tikzexternalgetnextfilename#1{%
+    \begingroup
+    \let\tikzexternal@getnextfilename@advancecount\relax%
+    \let\tikzexternal@getnextfilename@resetglobals=\relax%
+    \def\tikzexternal@protocol@to@file##1{}%
+    \tikzexternal@getnextfilename#1%
+    \pgfmath@smuggleone#1%
+    \endgroup
+}%
+
+\def\tikzexternalgetcurrentfilename#1{%
+    \ifx\tikzexternal@curfilename\relax
+        \let#1=\pgfutil@empty
+    \else
+        \let#1=\tikzexternal@curfilename
+    \fi
+}
+
+\def\tikzexternal@getnextfilename#1{%
+    \let#1=\pgfutil@empty
+    \iftikzexternal@export@enabled
+        \iftikzexternalexportnext
+            \begingroup
+            \t@tikzexternal@tmpa=\expandafter{\tikzexternal@filenameprefix}%
+            \ifx\tikzexternal@nextfile\pgfutil@empty
+                \iftikzexternal@onlynamed
+                    \xdef\pgf@tempa{}%
+                \else
+                    \pgfkeysgetvalue{/tikz/external/figure name}\tikzexternal@figurename
+                    \pgfutil@ifundefined{c@tikzext@no@\tikzexternal@figurename}{%
+                        \expandafter\gdef\csname c@tikzext@no@\tikzexternal@figurename\endcsname{0}%
+                    }{}%
+                    \t@tikzexternal@tmpb=\expandafter{\tikzexternal@figurename}%
+                    \xdef\pgf@tempa{\the\t@tikzexternal@tmpa\the\t@tikzexternal@tmpb\csname c@tikzext@no@\tikzexternal@figurename\endcsname}%
+                    \tikzexternal@getnextfilename@advancecount
+                \fi
+            \else
+                \t@tikzexternal@tmpb=\expandafter{\tikzexternal@nextfile}%
+                \xdef\pgf@tempa{\the\t@tikzexternal@tmpa\the\t@tikzexternal@tmpb}%
+            \fi
+            \endgroup
+            \let#1=\pgf@tempa
+        \fi
+    \fi
+    \tikzexternal@getnextfilename@resetglobals%
+    \tikzexternal@protocol@to@file#1%
+}%
+
+\def\tikzexternal@getnextfilename@resetglobals{%
+    \global\let\tikzexternal@nextfile=\pgfutil@empty
+    \global\tikzexternalexportnexttrue
+}%
+
+\def\tikzexternal@protocol@to@file#1{%
+    \ifpgf@external@grabshipout%
+    \else
+        \iftikzexternal@genfigurelist
+            \edef\tikzexternal@temp{#1}%
+            \ifx\tikzexternal@temp\pgfutil@empty
+            \else
+                \pgfutil@ifundefined{tikzexternal@listmode@openedfile}{%
+                    \message{Opening '\tikzexternal@realjob.figlist' for writing.}%
+                    \begingroup
+                        \globaldefs=1
+                        \csname newwrite\endcsname\tikzexternal@outfile
+                    \endgroup
+                    \immediate\openout\tikzexternal@outfile=\tikzexternal@realjob.figlist\relax
+                    \gdef\tikzexternal@listmode@openedfile{1}%
+                    \if\tikzexternal@opmode5%
+                        \tikzexternal@list@and@make@prepare
+                    \fi
+                }{}%
+                \iftikzexternal@verboseio
+                    \pgf@typeout{Writing '#1' to '\tikzexternal@realjob.figlist'.}%
+                \fi
+                \immediate\write\tikzexternal@outfile{#1}%
+                \if\tikzexternal@opmode5%
+                    \tikzexternal@list@and@make@gentarget{#1}%
+                \fi
+            \fi
+        \fi
+    \fi
+}%
+
+\def\tikzexternal@list@and@make@gentarget#1{%
+    \tikzexternal@assemble@systemcall{#1}{\pgf@tempa}%
+    \def\tikzexternal@tempb{\pgfutilstrreplace{^^J}{^^J\tikzexternal@TABchar}}%
+    \expandafter\tikzexternal@tempb\expandafter{\pgf@tempa}%
+    \let\pgf@tempa=\pgfretval
+    \iftikzexternal@verboseio
+        \pgf@typeout{Writing '#1' to '\tikzexternal@realjob.makefile'.}%
+    \fi
+    \global\tikzexternal@file@isuptodatetrue%
+    \tikzexternal@checkforceremake%
+    \immediate\write\tikzexternal@outmakefile{#1\tikzexternalimgextension: \iftikzexternal@file@isuptodate\else FORCEREMAKE\fi}%
+    \immediate\write\tikzexternal@outmakefile{\tikzexternal@TABchar\pgf@tempa}%
+    \immediate\write\tikzexternal@outmakefile{}%
+}
+
+\def\tikzexternal@list@and@make@prepare{%
+    \iftikzexternal@verboseio
+        \pgf@typeout{Opening '\tikzexternal@realjob.makefile' for writing.}%
+    \fi
+    \begingroup
+        \globaldefs=1
+        \csname newwrite\endcsname\tikzexternal@outmakefile
+    \endgroup
+    \immediate\openout\tikzexternal@outmakefile=\tikzexternal@realjob.makefile\relax
+    \immediate\write\tikzexternal@outmakefile{ALL_FIGURE_NAMES=\tikzexternal@DOLLARchar(shell cat \tikzexternal@realjob.figlist)}%
+    \immediate\write\tikzexternal@outmakefile{ALL_FIGURES=\tikzexternal@DOLLARchar(ALL_FIGURE_NAMES:\tikzexternal@PERCENTchar=\tikzexternal@PERCENTchar\tikzexternalimgextension)}%
+    \immediate\write\tikzexternal@outmakefile{}%
+    \immediate\write\tikzexternal@outmakefile{allimages: \tikzexternal@DOLLARchar(ALL_FIGURES)}%
+    \immediate\write\tikzexternal@outmakefile{\tikzexternal@TABchar @echo All images exist now. Use make -B to re-generate them.}%
+    \immediate\write\tikzexternal@outmakefile{}%
+    \immediate\write\tikzexternal@outmakefile{FORCEREMAKE:}%
+    \immediate\write\tikzexternal@outmakefile{}%
+    \immediate\write\tikzexternal@outmakefile{-include $(ALL_FIGURE_NAMES:\tikzexternal@PERCENTchar=\tikzexternal@PERCENTchar.\tikzexternaldepext)}%
+    \immediate\write\tikzexternal@outmakefile{}%
+    \tikzexternalmakefiledefaultdeprule
+    \immediate\write\tikzexternal@outmakefile{}%
+    \tikzexternal@outmakefile@pendingcommands
+    \pgfutil@ifundefined{AtEndDocument}{}{%
+        \AtEndDocument{\pgf@typeout{===== mode=`list and make': Use 'make -f \tikzexternal@realjob.makefile' to generate all images. Then, re-run (pdf)latex \tikzexternal@realjob. =====}}%
+    }%
+}%
+\def\tikzexternaldepext{dep}
+
+\def\tikzexternalmakefiledefaultdeprule{%
+    \immediate\write\tikzexternal@outmakefile{\tikzexternal@PERCENTchar.\tikzexternaldepext:}%
+    \immediate\write\tikzexternal@outmakefile{\tikzexternal@TABchar mkdir -p \tikzexternal@normal@dq $(dir $@)\tikzexternal@normal@dq}%
+    \immediate\write\tikzexternal@outmakefile{\tikzexternal@TABchar touch \tikzexternal@normal@dq $@\tikzexternal@normal@dq\space \tikzexternal@HASHchar\space will be filled later.}%
+}%
+
+\def\tikzexternalifwritesmakefile#1#2{%
+    \if5\tikzexternal@opmode #1\else #2\fi
+}%
+\def\tikzexternal@outmakefile@pendingcommands{}%
+
+\def\tikzexternalwritetomakefile#1{%
+    \if\tikzexternal@opmode5%
+        \pgfutil@ifundefined{tikzexternal@outmakefile}{%
+            \expandafter\gdef\expandafter\tikzexternal@outmakefile@pendingcommands\expandafter{%
+                \tikzexternal@outmakefile@pendingcommands
+                \immediate\write\tikzexternal@outmakefile{#1}%
+            }%
+        }{%
+            \immediate\write\tikzexternal@outmakefile{#1}%
+        }%
+    \fi
+}%
+
+\def\tikzexternal@dep@file@name{}
+
+\def\tikzexternalfiledependsonfile@ACTIVE#1#2{%
+    \begingroup
+    \def\tikzpicturedependsonfile@name{#1}%
+    \ifx\tikzpicturedependsonfile@name\pgfutil@empty
+    \else
+        \tikzifexternalizingcurrent
+            {\tikzexternalfiledependsonfile@append@to@dep@file{#1}{#2}}%
+            {\tikzexternalfiledependsonfile@append@to@makefile{#1}{#2}}%
+    \fi
+    \endgroup
+}%
+\def\tikzexternalfiledependsonfile#1#2{}%
+
+\def\tikzexternalfiledependsonfile@append@to@dep@file#1#2{%
+    \tikzexternalgetcurrentfilename\tikzpicturedependsonfile@name
+    \edef\tikzpicturedependsonfile@name{\tikzpicturedependsonfile@name.\tikzexternaldepext}%
+    \ifx\tikzexternal@dep@file@name\tikzpicturedependsonfile@name
+    \else
+        \pgfutil@ifundefined{tikzexternal@dep@file}{%
+            \begingroup
+                \globaldefs=1
+                \csname newwrite\endcsname\tikzexternal@dep@file
+            \endgroup
+        }{}%
+        \ifx\tikzexternal@dep@file@name\pgfutil@empty
+        \else
+            \immediate\closeout\tikzexternal@dep@file
+        \fi
+        \global\let\tikzexternal@dep@file@name=\tikzpicturedependsonfile@name
+        \immediate\openout\tikzexternal@dep@file=\tikzexternal@dep@file@name\relax
+    \fi
+    \immediate\write\tikzexternal@dep@file{#1\tikzexternalimgextension: #2}%
+}
+
+\def\tikzexternalfiledependsonfile@append@to@makefile#1#2{%
+    \edef\tikzexternal@temp{#1\tikzexternalimgextension: #2}%
+    \expandafter\tikzexternalwritetomakefile\expandafter{\tikzexternal@temp}%
+}
+
+\def\tikzpicturedependsonfile@ACTIVE#1{%
+    \begingroup
+    \tikzexternalgetcurrentfilename\tikzpicturedependsonfile@name
+    \ifx\tikzpicturedependsonfile@name\pgfutil@empty
+        \tikzexternalgetnextfilename\tikzpicturedependsonfile@name
+    \fi
+    \expandafter\tikzexternalfiledependsonfile\expandafter{\tikzpicturedependsonfile@name}{#1}%
+    \endgroup
+}%
+\def\tikzpicturedependsonfile#1{}%
+
+
+\def\tikzexternal@externalizefig{%
+    \ifpgf@external@grabshipout%
+        \expandafter\tikzexternal@externalizefig@GRAB%
+    \else
+        \expandafter\tikzexternal@externalizefig@mode@graphics@if@exists
+    \fi%
+}
+\def\tikzexternal@externalizefig@mode@graphics@if@exists{%
+    \gdef\pgf@filename{}%
+    \xdef\pgf@tempa{\noexpand\pgf@findfile\pgfsys@imagesuffixlist:+{\tikzexternal@curfilename}}%
+    \pgf@tempa
+    \ifx\pgf@filename\pgfutil@empty%
+        \expandafter\tikzexternal@normalpicture@nographics
+    \else
+        \expandafter\tikzexternal@forcegraphics
+    \fi
+}%
+
+
+\def\tikzexternal@optimize@away@cmd#1#2{%
+    \pgfutil@ifnextchar[{%
+        \tikzexternal@optimize@away@cmd@{#1}{#2}%
+    }{%
+        \tikzexternal@optimize@away@cmd@{#1}{#2}[]%
+    }%
+}%
+\def\tikzexternal@optimize@away@cmd@#1#2[#3]{%
+    \def\tikz@temp{#2}%
+    \ifx\tikz@temp\pgfutil@empty
+        \def\tikz@temp{\tikzexternal@optimize@away@cmd@auto{#1}{#3}}%
+    \else
+        \ifcase#2\relax
+            \def\tikzexternal@optimize@away@cmd@manual{%
+                \tikzexternal@optimize@away@cmd@@@{#1}{#3}{}%
+            }%
+        \or
+            \def\tikzexternal@optimize@away@cmd@manual##1{%
+                \tikzexternal@optimize@away@cmd@@@{#1}{#3}{{##1}}%
+            }%
+        \or
+            \def\tikzexternal@optimize@away@cmd@manual##1##2{%
+                \tikzexternal@optimize@away@cmd@@@{#1}{#3}{{##1}{##2}}%
+            }%
+        \or
+            \def\tikzexternal@optimize@away@cmd@manual##1##2##3{%
+                \tikzexternal@optimize@away@cmd@@@{#1}{#3}{{##1}{##2}{##3}}%
+            }%
+        \or
+            \def\tikzexternal@optimize@away@cmd@manual##1##2##3##4{%
+                \tikzexternal@optimize@away@cmd@@@{#1}{#3}{{##1}{##2}{##3}{##4}}%
+            }%
+        \or
+            \def\tikzexternal@optimize@away@cmd@manual##1##2##3##4##5{%
+                \tikzexternal@optimize@away@cmd@@@{#1}{#3}{{##1}{##2}{##3}{##4}{##5}}%
+            }%
+        \or
+            \def\tikzexternal@optimize@away@cmd@manual##1##2##3##4##5##6{%
+                \tikzexternal@optimize@away@cmd@@@{#1}{#3}{{##1}{##2}{##3}{##4}{##5}{##6}}%
+            }%
+        \or
+            \def\tikzexternal@optimize@away@cmd@manual##1##2##3##4##5##6##7{%
+                \tikzexternal@optimize@away@cmd@@@{#1}{#3}{{##1}{##2}{##3}{##4}{##5}{##6}{##7}}%
+            }%
+        \or
+            \def\tikzexternal@optimize@away@cmd@manual##1##2##3##4##5##6##7##8{%
+                \tikzexternal@optimize@away@cmd@@@{#1}{#3}{{##1}{##2}{##3}{##4}{##5}{##6}{##7}{##8}}%
+            }%
+        \or
+            \def\tikzexternal@optimize@away@cmd@manual##1##2##3##4##5##6##7##8##9{%
+                \tikzexternal@optimize@away@cmd@@@{#1}{#3}{{##1}{##2}{##3}{##4}{##5}{##6}{##7}{##8}{##9}}%
+            }%
+        \fi
+        \def\tikz@temp{\tikzexternal@optimize@away@cmd@manual}%
+    \fi
+    \tikz@temp
+}%
+\def\tikzexternal@optimize@away@cmd@auto#1#2{%
+    \pgfutil@ifnextchar\bgroup{%
+        \tikzexternal@optimize@away@cmd@auto@{#1}{#2}%
+    }{%
+        \tikzexternal@optimize@away@cmd@auto@{#1}{#2}{<no argument in curly braces>}%
+    }
+}%
+
+\def\tikzexternal@optimize@away@cmd@auto@#1#2#3{%
+    \tikzexternal@optimize@away@cmd@@@{#1}{#2}{{#3}}%
+}%
+\def\tikzexternal@optimize@away@cmd@@@#1#2#3{%
+    \begingroup
+    \toks0={#1[#2]#3}%
+    \iftikzexternal@verbose@optimize
+        \pgf@typeout{The command '\the\toks0' has been optimized away. Use '/tikz/external/optimize=false' to disable this.}%
+    \fi
+    \endgroup
+    \begingroup
+    \pgfkeysvalueof{/tikz/external/optimize away text/.@cmd}#1\pgfeov%
+    \endgroup
+}%
+
+\def\tikzexternal@optimize@away@latex@env#1{%
+    \def\tikzexternal@optimize@away@latex@env@{#1}%
+    \begingroup
+        \def\tikzexternal@laTeX@collect@until@end@tikzpicturetikzpicturestring{#1}%
+        \tikzexternal@TEXDIALECT@collectpicture\tikzexternal@optimize@away@latex@env@close
+}%
+\long\def\tikzexternal@optimize@away@latex@env@close#1{%
+    \iftikzexternal@verbose@optimize
+        \pgf@typeout{The complete contents of \string\begin{tikzexternal@optimize@away@latex@env@} up to the next \end{tikzexternal@optimize@away@latex@env@} has been optimized away because it does not contribute to the exported PDF. Use '/tikz/external/optimize=false' to disable this.}%
+    \fi
+    \endgroup
+    \expandafter\let\csname end\tikzexternal@optimize@away@latex@env@\endcsname=\relax
+    \expandafter\end\expandafter{\tikzexternal@optimize@away@latex@env@}%
+}%
+
+\def\tikzexternal@optimize@REPLACE{%
+    \pgfkeysvalueof{/tikz/external/optimize/install/.@cmd}\pgfeov
+}%
+
+\def\tikzexternal@optimize@RESTORE{%
+    \pgfkeysvalueof{/tikz/external/optimize/restore/.@cmd}\pgfeov
+}%
+
+\def\tikzexternal@closeenvironments{%
+    \let\endtikzpicture=\relax
+    \tikzexternal@TEXDIALECT@endpicture
+    \let\endtikzpicture=\tikzexternal@origendpicture
+    \let\tikzexternal@curfilename=\relax
+}
+
+\def\tikzexternal@skipfigure{%
+    \tikzexternal@TEXDIALECT@collectpicture\tikzexternal@skipfigure@@
+}
+\long\def\tikzexternal@skipfigure@@#1{%
+    \iftikzexternal@verbose@optimize
+        \pgf@typeout{A tikzpicture has been optimized away. Use '/tikz/external/optimize=false' to disable this.}%
+    \fi
+    \tikzexternal@closeenvironments
+    \pgfkeysvalueof{/tikz/external/optimize away text/.@cmd}tikzpicture\pgfeov%
+}
+
+\def\tikzexternal@normalpicture@nographics{%
+    \tikzexternal@nestedflagfalse
+    \let\tikzpicture=\tikzexternal@normalpicture@begreplace
+    \let\endtikzpicture=\tikzexternal@normalpicture@endreplace
+    \tikzpicture
+}
+\def\tikzexternal@normalpicture@begreplace{%
+    \begingroup
+    \tikzexternal@nestedflagtrue
+    \tikzexternal@origpicture
+}
+\def\tikzexternal@normalpicture@endreplace{%
+    \tikzexternal@origendpicture
+    \endgroup
+    \iftikzexternal@nestedflag
+    \else
+        \let\tikzpicture=\tikzexternal@tikzpicture@replacement
+        \let\endtikzpicture=\tikzexternal@origendpicture
+    \fi
+}%
+
+\def\tikzexternal@forcegraphics{%
+    \tikzexternal@TEXDIALECT@collectpicture\tikzexternal@forcegraphics@@
+}
+\long\def\tikzexternal@forcegraphics@@#1{\tikzexternal@forcegraphics@@@}%
+\def\tikzexternal@forcegraphics@@@{%
+    \if5\tikzexternal@opmode
+        \let\tikz@refundefinedtrue@@=\G@refundefinedtrue
+        \gdef\G@refundefinedtrue{%
+            \tikz@refundefinedtrue@@
+            \tikzexternal@forceremake@undefined@reference@handler
+        }%
+    \fi
+    \expandafter\pgfincludeexternalgraphics\expandafter{\tikzexternal@curfilename}%
+    \if5\tikzexternal@opmode
+        \global\let\G@refundefinedtrue=\tikz@refundefinedtrue@@
+    \fi
+    \tikzexternal@closeenvironments
+}
+
+\def\tikzexternal@forceremake@undefined@reference@handler{%
+    \pgf@typeout{===== 'mode=list and make': encountered undefined reference in current picture. Adding dependency to FORCEREMAKE. Rerun make to update the picture.' ========^^J}%
+    \tikzpicturedependsonfile{FORCEREMAKE}%
+}%
+
+\def\tikzexternal@listmodepicture{%
+    \tikzexternal@TEXDIALECT@collectpicture\tikzexternal@listmodepicture@@
+}
+\long\def\tikzexternal@listmodepicture@@#1{\tikzexternal@listmodepicture@@@}
+\def\tikzexternal@listmodepicture@@@{%
+    \pgfkeysvalueof{/tikz/external/image discarded text}%
+    \tikzexternal@closeenvironments
+}
+
+\def\tikzexternal@list@and@makefile@mode@picture{%
+    \tikzexternal@TEXDIALECT@collectpicture\tikzexternal@list@and@makefile@mode@picture@
+}%
+\long\def\tikzexternal@list@and@makefile@mode@picture@#1{%
+    \tikzexternal@check@uptodate@mode{#1}%
+    \gdef\pgf@filename{}%
+    \xdef\pgf@tempa{\noexpand\pgf@findfile\pgfsys@imagesuffixlist:+{\tikzexternal@curfilename}}%
+    \pgf@tempa
+    \ifx\pgf@filename\pgfutil@empty%
+        \expandafter\tikzexternal@listmodepicture@@@
+    \else
+        \expandafter\tikzexternal@forcegraphics@@@
+    \fi
+}%
+
+\def\tikzexternal@externalizefig@before@grab{%
+    \pgfutil@IfUndefined{TP@holdbox}{%
+    }{%
+        \global\setbox\TP@holdbox\vbox{}%
+    }%
+}%
+
+\def\tikzexternal@externalizefig@GRAB{%
+    \ifpgf@external@grabshipout
+        \iftikzexternal@optimize
+            \tikzexternal@optimize@RESTORE
+        \fi
+        \tikzexternal@externalizefig@before@grab
+    \fi
+    \def\tikzpicture{%
+        \def\tikzpicture{%
+            \begingroup
+            \def\endtikzpicture{%
+                \tikzexternal@origendpicture
+                \endgroup
+            }%
+            \tikzexternal@origpicture
+        }%
+        \pgf@external@grab{\tikzexternal@curfilename}%
+        \tikzexternal@origpicture
+    }%
+    \def\endtikzpicture{%
+        \tikzexternal@origendpicture
+        \pgf@externalend
+        \tikzexternal@ensure@nonempty@floats
+        \let\tikzpicture=\tikzexternal@tikzpicture@replacement
+        \let\endtikzpicture=\tikzexternal@origendpicture
+        \iftikzexternal@optimize
+            \ifpgf@external@grabshipout
+                \tikzexternal@optimize@REPLACE
+            \fi
+        \fi
+    }%
+    \tikzpicture
+}%
+
+\def\tikzexternal@ensure@nonempty@floats{%
+    tikzexternal: picture has been externalized. This text is required to avoid empty floats.
+}%
+
+\def\tikzexternal@externalizefig@systemcall{%
+    \tikzexternal@TEXDIALECT@collectpicture\tikzexternal@externalizefig@systemcall@@
+}
+
+{
+\catcode`\"=12
+\catcode`\'=12
+\catcode`\;=12
+\catcode`\&=12
+\catcode`\-=12
+\xdef\tikzexternal@normal@dq{"}
+\xdef\tikzexternal@normal@sq{'}
+\xdef\tikzexternal@normal@semic{;}
+\xdef\tikzexternal@normal@and{&}
+\xdef\tikzexternal@normal@dash{-}
+\catcode`\"=13
+\catcode`\'=13
+\catcode`\;=13
+\catcode`\&=13
+\catcode`\-=13
+\gdef\tikzexternal@activate@normal@dq{\let"=\tikzexternal@normal@dq}
+\gdef\tikzexternal@activate@normal@sq{\let'=\tikzexternal@normal@sq}
+\gdef\tikzexternal@activate@normal@semic{\let;=\tikzexternal@normal@semic}
+\gdef\tikzexternal@activate@normal@and{\let&=\tikzexternal@normal@and}
+\gdef\tikzexternal@activate@normal@dash{\let-=\tikzexternal@normal@dash}
+\catcode`\|=0
+\catcode`\\=12
+|xdef|tikzexternal@normal@backslash{\}%
+}
+{
+\catcode`\^^I=12
+\catcode`\$=12
+\catcode`\%=12
+\catcode`\#=12
+\gdef\tikzexternal@HASHchar{#}
+\gdef\tikzexternal@TABchar{^^I}\gdef\tikzexternal@PERCENTchar{%}\xdef\tikzexternal@DOLLARchar{$}}
+
+\def\tikzexternal@assemble@systemcall#1#2{%
+    \begingroup
+        \def\image{#1}%
+        \iftikzexternal@auto@detect@jobname
+            \edef\texsource{\string\def\string\tikzexternalrealjob{\tikzexternal@realjob}\string\input{\tikzexternal@realjob}}%
+        \else
+            \let\texsource=\tikzexternal@realjob
+        \fi
+        \ifnum\the\catcode`\"=13 \tikzexternal@activate@normal@dq\fi
+        \ifnum\the\catcode`\'=13 \tikzexternal@activate@normal@sq\fi
+        \ifnum\the\catcode`\;=13 \tikzexternal@activate@normal@semic\fi
+        \ifnum\the\catcode`\-=13 \tikzexternal@activate@normal@dash\fi
+        \let\\=\tikzexternal@normal@backslash
+        \xdef#2{\pgfkeysvalueof{/tikz/external/system call}}%
+    \endgroup
+}%
+\long\def\tikzexternal@externalizefig@systemcall@@#1{%
+    \tikzexternal@externalizefig@systemcall@uptodatecheck{#1}%
+    \tikzexternal@assemble@systemcall{\tikzexternal@curfilename}{\pgf@tempa}%
+    \global\let\tikzexternal@cursyscall=\pgf@tempa
+    \gdef\tikzexternal@typeset@picture@on@failure{1}%
+    \iftikzexternal@file@isuptodate
+        \iftikzexternal@verboseio
+            \pgf@typeout{===== Image '\tikzexternal@curfilename' is up-to-date. ======}%
+        \fi
+        \let\pgf@filename=\tikzexternal@curfilename
+    \else
+        \begingroup
+        \tikzexternalauxlock@setlock1%
+        \tikzexternal@externalizefig@systemcall@call{\tikzexternal@cursyscall}%
+        \tikzexternalauxlock@setlock0%
+        \expandafter\tikzexternal@externalizefig@systemcall@assertsuccess\expandafter{\tikzexternal@cursyscall}%
+        \pgfmath@smuggleone\pgf@filename
+        \endgroup
+    \fi
+    \ifx\pgf@filename\pgfutil@empty
+        \if1\tikzexternal@typeset@picture@on@failure
+            \begingroup
+            \toks0={%
+                \tikzexternaldisable
+            }%
+            \toks1={%
+                \tikzpicture
+                #1%
+            }%
+            \toks2={%
+                \tikzexternal@TEXDIALECT@endpicture
+                \tikzexternalenable
+            }%
+            \xdef\tikzexternal@externalizefig@systemcall@next{%
+                \the\toks0
+                \noexpand\scantokens{\the\toks1 }%
+                \the\toks2
+            }%
+            \endgroup
+        \else
+            \gdef\tikzexternal@externalizefig@systemcall@next{\tikzexternal@closeenvironments}%
+        \fi
+    \else
+        \gdef\tikzexternal@systemcall@reschedule@to@end@document{0}%
+        \expandafter\pgfincludeexternalgraphics\expandafter{\tikzexternal@curfilename}%
+        \if1\tikzexternal@systemcall@reschedule@to@end@document
+            \pgfutil@IfUndefined{AtVeryEndDocument}{%
+            }{%
+                \pgf@typeout{===== The previous system call resulted in undefined references inside of the output file. Rescheduling it for \string\end{document}. ========}%
+                \expandafter\tikzexternal@externalizefig@systemcall@reschedule\expandafter{\tikzexternal@cursyscall}%
+            }%
+        \fi
+        \gdef\tikzexternal@externalizefig@systemcall@next{\tikzexternal@closeenvironments}%
+    \fi
+    \tikzexternal@externalizefig@systemcall@next
+}%
+
+\def\tikzexternal@externalizefig@systemcall@call#1{%
+    \iftikzexternal@verboseio
+        \pgf@typeout{===== 'mode=convert with system call': Invoking '#1' ========}%
+    \fi
+    \pgfutil@shellescape{#1}%
+}%
+
+\def\tikzexternal@checkforceremake{%
+    \iftikzexternal@force@remake
+        \global\tikzexternal@file@isuptodatefalse
+    \else
+        \iftikzexternalremakenext
+            \global\tikzexternal@file@isuptodatefalse
+            \global\tikzexternalremakenextfalse
+        \fi
+    \fi
+}
+
+\pgfutil@IfUndefined{pdfmdfivesum}{%
+}{%
+    \let\tikzexternal@mdfivesum=\pdfmdfivesum
+}%
+
+\long\def\tikzexternal@computemdfivesum#1{%
+    \t@tikzexternal@tmpb={#1}%
+    \edef\tikzexternal@temp{\the\t@tikzexternal@tmpb}%
+    \edef\pgfretval{\tikzexternal@mdfivesum{\meaning\tikzexternal@temp}}%
+}
+\long\def\tikzexternal@computemdfivesum@diff@fallback#1{%
+    \t@tikzexternal@tmpb={#1}%
+    \edef\tikzexternal@temp{\the\t@tikzexternal@tmpb}%
+    \edef\pgfretval{\meaning\tikzexternal@temp}%
+}
+
+\long\def\tikzexternal@hashfct@serialize@std#1{%
+    \noexpand\def\noexpand\tikzexternallastkey{#1}%
+}%
+
+\long\def\tikzexternal@hashfct@serialize@tok#1{%
+    \noexpand\begingroup
+        \noexpand\toks0={#1}%
+        \noexpand\xdef\noexpand\tikzexternallastkey{\noexpand\the\noexpand\toks0 }%
+    \noexpand\endgroup
+}%
+
+\def\tikzexternal@check@uptodate@ext{.md5}
+
+\def\tikzexternal@check@uptodate@mode@warn@fallback{%
+    \message{Package tikz Warning: The key 'up to date check=md5' is impossible, there is no macro to compute MD5. Falling back to 'up to date check=diff'.}%
+    \global\let\tikzexternal@check@uptodate@mode@warn@fallback=\relax
+}%
+
+\long\def\tikzexternal@check@uptodate@mode#1{%
+    \if1\tikzexternal@uptodate@mode
+        \pgfutil@IfUndefined{tikzexternal@mdfivesum}{%
+            \tikzexternal@check@uptodate@mode@warn@fallback
+            \def\tikzexternal@uptodate@mode{2}%
+        }{}%
+    \fi
+    \ifcase\tikzexternal@uptodate@mode
+        \let\tikzexternal@hashfct=\pgfutil@empty
+        \let\tikzexternal@hashfct@serialize=\pgfutil@empty
+    \or
+        \let\tikzexternal@hashfct=\tikzexternal@computemdfivesum
+        \let\tikzexternal@hashfct@serialize=\tikzexternal@hashfct@serialize@std
+    \or
+        \let\tikzexternal@hashfct=\tikzexternal@computemdfivesum@diff@fallback
+        \let\tikzexternal@hashfct@serialize=\tikzexternal@hashfct@serialize@tok
+    \fi
+    \ifx\tikzexternal@hashfct\pgfutil@empty
+    \else
+        \tikzpicturedependsonfile{\tikzexternal@curfilename\tikzexternal@check@uptodate@ext}%
+        \tikzexternal@hashfct{#1}%
+        \let\tikzexternal@lastkey@new=\pgfretval
+        \begingroup
+        \global\let\tikzexternallastkey=\pgfutil@empty
+        \openin\r@pgf@reada=\tikzexternal@curfilename\tikzexternal@check@uptodate@ext\relax %
+        \ifeof\r@pgf@reada
+        \else
+            \endlinechar=-1 %
+            \read\r@pgf@reada to\pgf@tempa
+            \pgf@tempa
+        \fi
+        \closein\r@pgf@reada
+        \let\tikzexternal@lastkey=\tikzexternallastkey
+        \pgfmath@smuggleone\tikzexternal@lastkey
+        \endgroup
+        \edef\tikzexternal@lastkey@normalized{\meaning\tikzexternal@lastkey}%
+        \edef\tikzexternal@lastkey@new@normalized{\meaning\tikzexternal@lastkey@new}%
+        \iftikzexternal@verboseuptodate
+            \pgf@typeout{Up-to-date check of \tikzexternal@curfilename: new \tikzexternal@lastkey@new@normalized; old \tikzexternal@lastkey@normalized.^^J}%
+        \fi
+        \ifx\tikzexternal@lastkey@normalized\tikzexternal@lastkey@new@normalized
+            \tikzexternal@file@isuptodatetrue
+        \else
+            \tikzexternal@file@isuptodatefalse
+            \immediate\openout\w@pgf@writea=\tikzexternal@curfilename\tikzexternal@check@uptodate@ext\relax%
+            \immediate\write\w@pgf@writea{\tikzexternal@hashfct@serialize{\tikzexternal@lastkey@new}\tikzexternal@PERCENTchar}%
+            \immediate\closeout\w@pgf@writea
+        \fi
+    \fi
+}
+
+\long\def\tikzexternal@externalizefig@systemcall@uptodatecheck#1{%
+    \tikzexternal@check@uptodate@mode{#1}%
+    \tikzexternal@checkforceremake
+    \iftikzexternal@file@isuptodate
+        \gdef\pgf@filename{}%
+        \xdef\pgf@tempa{\noexpand\pgf@findfile\pgfsys@imagesuffixlist:+{\tikzexternal@curfilename}}%
+        \pgf@tempa
+        \ifx\pgf@filename\pgfutil@empty%
+            \global\tikzexternal@file@isuptodatefalse
+        \fi
+    \fi
+}%
+
+\def\tikzexternal@externalizefig@systemcall@assertsuccess#1{%
+    \gdef\pgf@filename{}%
+    \xdef\pgf@tempa{\noexpand\pgf@findfile\pgfsys@imagesuffixlist:+{\tikzexternal@curfilename}}%
+    \pgf@tempa
+    \ifx\pgf@filename\pgfutil@empty%
+        \tikzexternal@externalizefig@systemcall@handleexception{#1}%
+    \fi
+}%
+\def\tikzexternal@externalizefig@systemcall@handleexception@msg#1{%
+    \tikzerror{Sorry, the system call '#1' did NOT result in a usable output file '\tikzexternal@curfilename' (expected one of \pgfsys@imagesuffixlist). Please verify that you have enabled system calls. For pdflatex, this is 'pdflatex -shell-escape'. Sometimes it is also named 'write 18' or something like that. Or maybe the command simply failed? Error messages can be found in '\tikzexternal@curfilename.log'. If you continue now, I'll try to typeset the picture}{}%
+}
+\def\tikzexternal@externalizefig@systemcall@handleexception@retry@later#1{%
+    \gdef\tikzexternal@systemcall@reschedule@to@end@document{0}%
+    \expandafter\pgfexternalreaddpth\expandafter{\tikzexternal@curfilename}%
+    \if1\tikzexternal@systemcall@reschedule@to@end@document
+        \pgfutil@IfUndefined{AtVeryEndDocument}{%
+            \tikzexternal@externalizefig@systemcall@handleexception@msg{#1}%
+        }{%
+            \pgf@typeout{===== The last system call resulted in an EMPTY output file. Maybe it is part of \string\ref. Rescheduling it for \string\end{document}. ========}%
+            \gdef\tikzexternal@typeset@picture@on@failure{0}%
+            \tikzexternal@externalizefig@systemcall@reschedule{#1}%
+        }%
+    \else
+        \tikzexternal@externalizefig@systemcall@handleexception@msg{#1}%
+    \fi
+}
+
+\def\tikzexternal@externalizefig@systemcall@reschedule#1{%
+    \t@tikzexternal@tmpb={%
+        \global\let\tikzexternal@externalizefig@systemcall@handleexception=\tikzexternal@externalizefig@systemcall@handleexception@msg%
+        \tikzexternal@externalizefig@systemcall@call{#1}%
+        \tikzexternal@externalizefig@systemcall@assertsuccess{#1}%
+    }%
+    \xdef\pgfutil@tempa{%
+        \noexpand\def\noexpand\tikzexternal@curfilename{\tikzexternal@curfilename}%
+        \the\t@tikzexternal@tmpb
+    }%
+    \expandafter\AtVeryEndDocument\expandafter{\pgfutil@tempa}%
+    \gdef\tikzexternal@has@rescheduled@something{1}%
+}%
+\let\tikzexternal@externalizefig@systemcall@handleexception=\tikzexternal@externalizefig@systemcall@handleexception@retry@later%
+
+\def\tikzexternal@has@rescheduled@something{0}%
+\pgfutil@IfUndefined{AtVeryEndDocument}{}{%
+    \AtVeryEndDocument{%
+        \if1\tikzexternal@has@rescheduled@something
+            \pgf@typeout{===== tikzexternal: \string\end{document} reached. Working on rescheduled images to resolve references... ========}%
+        \fi
+    }%
+}
+
+\def\pgfexternal@error@no@shipout{%
+    \begingroup
+        \begingroup
+        \immediate\openout\pgf@plotwrite=\pgfactualjobname.dpth
+        \let\w@pgfexternal@auxout=\pgf@plotwrite
+        \pgfexternalstorecommand@isexporting{\gdef\noexpand\tikzexternal@systemcall@reschedule@to@end@document{1}}%
+        \immediate\closeout\pgf@plotwrite
+        \endgroup
+    \tikzexternal@assemble@systemcall{\pgfactualjobname}{\pgf@tempa}%
+    \toks0=\expandafter{\pgf@tempa}%
+    \tikzerror{Sorry, image externalization failed: the resulting image was EMPTY. I tried to externalize '\pgfactualjobname', but it seems there is no such image in the document!?
+ \if\tikzexternal@opmode4 ^^J
+\space\space You are currently using 'mode=convert with system call'. This problem can happen if the image (or one of the images preceding it) was declared inside of a \string\label{} (i.e. in the .aux file): 'convert with system call' has no access to the main aux file.^^J
+\space\space Possible solutions in this case:^^J
+\space\space (a) Try using 'mode=list and make',^^J
+\space\space (b) Issue the externalization command '\the\toks0' *manually* (also check the preceding externalized images, perhaps the file name sequence is not correct).^^J
+\space\space Repeat: the resulting image was EMPTY, your attention is required
+\else
+    \if\tikzexternal@opmode5 ^^J
+\space\space You are currently using 'mode=list and make'. Possible solutions:^^J
+\space\space (a) Try to delete `\tikzexternal@realjob.makefile'. Perhaps it is not up-to-date.^^J
+\space\space (b) Perhaps pictures are declared inside of \string\label{} and the .aux file is not up-to-date. Re-run latex, perhaps re-generate the graphics as well.^^J
+\space\space Repeat: the resulting image was EMPTY, your attention is required
+    \fi
+\fi}%
+    \endgroup
+}%

preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibrary3d.code.tex

@@ -0,0 +1,97 @@
+
+\ProvidesFileRCS{tikzlibrary3d.code.tex}
+
+
+
+
+\tikzdeclarecoordinatesystem{xyz cylindrical}
+{%
+  \pgfset{/tikz/cs/.cd,angle=0,radius=0,z=0,#1}%
+  \pgfpointcylindrical{\tikz@cs@angle}{\tikz@cs@xradius}{\tikz@cs@z}%
+}%
+
+\tikzdeclarecoordinatesystem{xyz spherical}
+{%
+  \pgfset{/tikz/cs/.cd,angle=0,radius=0,latitude=0,longitude=0,#1}%
+  \pgfpointspherical{\tikz@cs@angle}{\tikz@cs@latitude}{\tikz@cs@xradius}%
+}%
+
+\pgfset{/tikz/cs/longitude/.store in=\tikz@cs@angle}%
+\pgfset{/tikz/cs/latitude/.store in=\tikz@cs@latitude}%
+
+
+
+\tikzoption{plane origin}{\def\tikz@plane@origin{\tikz@scan@one@point\pgfutil@firstofone#1}}%
+\tikzoption{plane x}{\def\tikz@plane@x{\tikz@scan@one@point\pgfutil@firstofone#1}}%
+\tikzoption{plane y}{\def\tikz@plane@y{\tikz@scan@one@point\pgfutil@firstofone#1}}%
+
+\let\tikz@plane@origin=\pgfpointorigin
+\def\tikz@plane@x{\pgfpointxy{1}{0}}%
+\def\tikz@plane@y{\pgfpointxy{0}{1}}%
+
+\tikzoption{canvas is plane}[]{
+  \tikz@canvas@is@plane
+}%
+\tikzoption{canvas is xy plane at z}[]{%
+  \def\tikz@plane@origin{\pgfpointxyz{0}{0}{#1}}%
+  \def\tikz@plane@x{\pgfpointxyz{1}{0}{#1}}%
+  \def\tikz@plane@y{\pgfpointxyz{0}{1}{#1}}%
+  \tikz@canvas@is@plane
+}%
+\tikzoption{canvas is yx plane at z}[]{%
+  \def\tikz@plane@origin{\pgfpointxyz{0}{0}{#1}}%
+  \def\tikz@plane@x{\pgfpointxyz{0}{1}{#1}}%
+  \def\tikz@plane@y{\pgfpointxyz{1}{0}{#1}}%
+  \tikz@canvas@is@plane
+}%
+\tikzoption{canvas is xz plane at y}[]{%
+  \def\tikz@plane@origin{\pgfpointxyz{0}{#1}{0}}%
+  \def\tikz@plane@x{\pgfpointxyz{1}{#1}{0}}%
+  \def\tikz@plane@y{\pgfpointxyz{0}{#1}{1}}%
+  \tikz@canvas@is@plane
+}%
+\tikzoption{canvas is zx plane at y}[]{%
+  \def\tikz@plane@origin{\pgfpointxyz{0}{#1}{0}}%
+  \def\tikz@plane@x{\pgfpointxyz{0}{#1}{1}}%
+  \def\tikz@plane@y{\pgfpointxyz{1}{#1}{0}}%
+  \tikz@canvas@is@plane
+}%
+\tikzoption{canvas is yz plane at x}[]{%
+  \def\tikz@plane@origin{\pgfpointxyz{#1}{0}{0}}%
+  \def\tikz@plane@x{\pgfpointxyz{#1}{1}{0}}%
+  \def\tikz@plane@y{\pgfpointxyz{#1}{0}{1}}%
+  \tikz@canvas@is@plane
+}%
+\tikzoption{canvas is zy plane at x}[]{%
+  \def\tikz@plane@origin{\pgfpointxyz{#1}{0}{0}}%
+  \def\tikz@plane@x{\pgfpointxyz{#1}{0}{1}}%
+  \def\tikz@plane@y{\pgfpointxyz{#1}{1}{0}}%
+  \tikz@canvas@is@plane
+}%
+
+
+
+
+\def\tikz@canvas@is@plane{
+  \pgf@process{\tikz@plane@x}%
+  \pgf@xa=\pgf@x%
+  \pgf@ya=\pgf@y%
+  \pgf@process{\tikz@plane@y}%
+  \pgf@xb=\pgf@x%
+  \pgf@yb=\pgf@y%
+  \pgf@process{\tikz@plane@origin}%
+  \edef\pgf@marshal{\noexpand\tikz@addtransform{%
+      \noexpand\pgftransformtriangle
+      {\noexpand\pgfqpoint{\the\pgf@x}{\the\pgf@y}}
+      {\noexpand\pgfqpoint{\the\pgf@xa}{\the\pgf@ya}}
+      {\noexpand\pgfqpoint{\the\pgf@xb}{\the\pgf@yb}}
+      \noexpand\pgftransformscale{0.035146}%
+      \noexpand\pgfsetxvec{\noexpand\pgfpoint{1cm}{0cm}}%
+      \noexpand\pgfsetyvec{\noexpand\pgfpoint{0cm}{1cm}}%
+      \noexpand\pgfsetzvec{\noexpand\pgfpoint{0cm}{0cm}}%
+    }}%
+  \pgf@marshal%
+}%
+
+
+\endinput

preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibraryangles.code.tex

@@ -0,0 +1,89 @@
+
+\ProvidesFileRCS{tikzlibraryangles.code.tex}
+
+
+\tikzset{
+  pics/angle/.style = {
+    setup code  = \tikz@lib@angle@parse#1\pgf@stop,
+    code = {},
+    background code = \tikz@lib@angle@background#1\pgf@stop,
+    foreground code = \tikz@lib@angle@foreground#1\pgf@stop,
+  },
+  pics/right angle/.style = {
+    setup code  = \tikz@lib@angle@parse#1\pgf@stop,
+    code = {},
+    background code = \tikz@lib@rightangle@background#1\pgf@stop,
+    foreground code = \tikz@lib@rightangle@foreground#1\pgf@stop,
+  },
+  pics/angle/.default=A--B--C,
+  angle eccentricity/.initial=.6,
+  angle radius/.initial=5mm,
+}%
+
+\def\tikz@lib@angle@background#1--#2--#3\pgf@stop{%
+  \path [name prefix ..] [pic actions, draw=none] (#2.center)
+    -- ++(\tikz@start@angle@temp:\tikz@lib@angle@rad pt)
+    arc [start angle=\tikz@start@angle@temp, end
+    angle=\tikz@end@angle@temp, radius=\tikz@lib@angle@rad pt] -- cycle;
+}%
+
+\def\tikz@lib@angle@foreground#1--#2--#3\pgf@stop{%
+  \path [name prefix ..] [pic actions, fill=none, shade=none]
+  ([shift={(\tikz@start@angle@temp:\tikz@lib@angle@rad pt)}]#2.center)
+    arc [start angle=\tikz@start@angle@temp, end
+    angle=\tikz@end@angle@temp, radius=\tikz@lib@angle@rad pt];
+  \ifx\tikzpictext\relax\else%
+    \def\pgf@temp{\node()[name prefix
+      ..,at={([shift={({.5*\tikz@start@angle@temp+.5*\tikz@end@angle@temp}:\pgfkeysvalueof{/tikz/angle
+            eccentricity}*\tikz@lib@angle@rad pt)}]#2.center)}]}
+    \expandafter\pgf@temp\expandafter[\tikzpictextoptions]{\tikzpictext};%
+  \fi
+}%
+
+\def\tikz@lib@rightangle@background#1--#2--#3\pgf@stop{%
+  \path [name prefix ..] [pic actions, draw=none] (#2.center)
+    -- ++(\tikz@start@angle@temp:\tikz@lib@angle@rad pt)
+    -- ++(\tikz@end@angle@temp:\tikz@lib@angle@rad pt)
+    -- ++(\tikz@start@angle@temp:-\tikz@lib@angle@rad pt)
+    -- cycle;
+}%
+
+\def\tikz@lib@rightangle@foreground#1--#2--#3\pgf@stop{%
+  \path [name prefix ..] [pic actions, fill=none, shade=none]
+  ([shift={(\tikz@start@angle@temp:\tikz@lib@angle@rad pt)}]#2.center)
+  -- ++(\tikz@end@angle@temp:\tikz@lib@angle@rad pt)
+  -- ++(\tikz@start@angle@temp:-\tikz@lib@angle@rad pt);
+  \ifx\tikzpictext\relax\else%
+    \def\pgf@temp{\node()[name prefix
+      ..,at={([shift={({.5*\tikz@start@angle@temp+.5*\tikz@end@angle@temp}:\pgfkeysvalueof{/tikz/angle
+            eccentricity}*1.4142136*\tikz@lib@angle@rad pt)}]#2.center)}]}
+    \expandafter\pgf@temp\expandafter[\tikzpictextoptions]{\tikzpictext};%
+  \fi
+}%
+
+\def\tikz@lib@angle@parse#1--#2--#3\pgf@stop{%
+  \pgfmathsetmacro\tikz@lib@angle@rad{\pgfkeysvalueof{/tikz/angle radius}}
+  \ifdim\tikz@lib@angle@rad pt>0pt\else\def\tikz@lib@angle@rad{12}\fi%
+  \pgf@process{\pgfpointanchor{#2}{center}}%
+  \pgf@xa=\pgf@x%
+  \pgf@ya=\pgf@y%
+  \pgf@process{\pgfpointanchor{#1}{center}}%
+  \pgf@xb=\pgf@x%
+  \pgf@yb=\pgf@y%
+  \pgf@process{\pgfpointanchor{#3}{center}}%
+  \pgf@xc=\pgf@x%
+  \pgf@yc=\pgf@y%
+  \advance\pgf@xb by-\pgf@xa%
+  \advance\pgf@yb by-\pgf@ya%
+  \advance\pgf@xc by-\pgf@xa%
+  \advance\pgf@yc by-\pgf@ya%
+  \pgfmathsetmacro{\tikz@start@angle@temp}{atan2(\the\pgf@yb,\the\pgf@xb)}
+  \pgfmathsetmacro{\tikz@end@angle@temp}{atan2(\the\pgf@yc,\the\pgf@xc)}
+  \ifdim\tikz@end@angle@temp pt<\tikz@start@angle@temp pt%
+    \pgfmathsetmacro{\tikz@start@angle@temp}{\tikz@start@angle@temp-360}%
+  \fi%
+}%
+
+
+
+\endinput

preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibraryanimations.code.tex

@@ -0,0 +1,790 @@
+
+\ProvidesFileRCS{tikzlibraryanimations.code.tex}
+
+\usepgfmodule{animations}%
+
+
+
+
+\def\tikz@collect@scope@anims#1{%
+  \let\tikz@scope@anims\pgfutil@empty%
+  \let\tikz@collect@command#1%
+  \tikz@collect@scope@anims@parse%
+}%
+\def\tikz@collect@scope@anims@parse{%
+  \pgfutil@ifnextchar[{\tikz@collect@scope@anims@opt}{%
+    \pgfutil@ifnextchar:{\tikz@collect@scope@anims@go}{%
+      \tikz@collect@scope@anims@done}}%
+}%
+\def\tikz@collect@scope@anims@done{%
+  \expandafter\tikz@collect@command\expandafter[\tikz@scope@anims]%
+}%
+\def\tikz@collect@scope@anims@opt[{%
+  \expandafter\tikz@collect@command\expandafter[\tikz@scope@anims%
+}%
+\def\tikz@collect@scope@anims@go:#1=#2{%
+  \expandafter\def\expandafter\tikz@scope@anims\expandafter{\tikz@scope@anims animate={myself:={:{#1}={#2}}},}%
+  \tikz@collect@scope@anims@parse%
+}%
+
+
+
+
+
+\def\tikzanimateset{\pgfqkeys{/tikz/animate}}%
+\tikzanimateset{
+  .code={
+    \pgfkeys{/handlers/first char syntax=true}
+    \pgfkeyssetvalue{/handlers/first char syntax/\expandafter\meaning\string"}{\tikz@animation@value}%
+    \def\tikz@anim@t{0}%
+    \def\tikz@anim@t@base{0}%
+    \def\tikz@anim@t@current{0}%
+    \tikzanimateset{#1}
+  },
+  scope/.code=\tikz@anim@scope{#1}{}{},
+  sync/.code=\tikz@anim@sync@scope{#1}{}{},
+  entry/.code=\tikz@anim@make@entry,
+  object/.code=\tikz@anim@set@object{#1},
+  attribute/.code=\tikz@anim@set@attr{#1},
+  id/.code=\tikz@anim@set@id{#1},
+  time/.code=\tikz@anim@set@time{#1},
+  value/.code=\tikz@anim@add{\tikz@anim@value{#1}},%
+  remember/.code=\pgfmathadd@{\tikz@anim@t}{\tikz@anim@t@base}\global\let#1\pgfmathresult,
+  resume/.code=\tikz@anim@resume{#1},
+  fork/.code={\tikz@anim@parse@time{#1}\pgfmathadd@\tikz@anim@t\tikz@anim@t@base\let\tikz@anim@t@base\pgfmathresult\def\tikz@anim@t{0}},
+  fork/.default = 0later,
+  base/.style={scope={/utils/exec=\let\tikz@animation@time\tikz@anim@base@text,#1,entry}},
+}%
+
+\tikzset{
+  make snapshot of/.code=\edef\tikz@temp{#1}\ifx\tikz@temp\pgfutil@empty\else\pgfsnapshot{#1}\fi,
+  make snapshot after/.code=\edef\tikz@temp{#1}\ifx\tikz@temp\pgfutil@empty\else\pgfsnapshotafter{#1}\fi,
+  make snapshot if necessary/.code=\ifpgfsysanimationsupported\else\pgfsnapshot{#1}\fi,
+  make snapshot if necessary/.default=0s,
+}%
+
+\def\tikz@anim@scope#1#2#3{%
+  {#2\tikzanimateset{#1}#3}%
+}%
+\def\tikz@anim@sync@scope#1#2#3{%
+  {%
+    #2%
+    \tikzanimateset{#1}%
+    #3%
+    \pgfmathadd@{\tikz@anim@t}{\tikz@anim@t@base}%
+    \expandafter%
+  }\expandafter\pgfmathsubtract@\expandafter{\pgfmathresult}{\tikz@anim@t@base}%
+  \tikz@anim@set@time{\pgfmathresult}%
+}%
+
+\def\tikz@anim@set@time#1{%
+  \tikz@anim@parse@time{#1}%
+  \let\tikz@anim@t@current\tikz@anim@t%
+  \pgfmathadd@\tikz@anim@t\tikz@anim@t@base%
+  \let\tikz@animation@time\pgfmathresult%
+}%
+
+\def\tikz@anim@value#1{%
+  \def\tikz@anim@result{#1}
+  \ifx\tikz@anim@result\pgf@special@current@text%
+  \else%
+    \ifx\tikz@animation@parser\relax%
+    \else%
+      \tikz@animation@parser{#1}%
+    \fi%
+  \fi%
+}%
+
+
+\def\tikz@anim@resume#1{%
+  \pgfparsetime{#1}%
+  \pgfmathsubtract@{\pgftimeresult}{\tikz@anim@t@base}%
+  \tikz@anim@set@time{\pgfmathresult}%
+}%
+
+
+
+\def\tikz@animation@syntax@check#1#2{%
+  \def\tikz@animation@rest{#1}%
+  \expandafter\pgfutil@in@\expandafter:\expandafter{\tikz@key}%
+  \ifpgfutil@in@%
+    \expandafter\tikz@anim@parse@colon\tikz@key\pgf@stop%
+  \else%
+    #2%
+  \fi%
+}%
+
+\def\tikz@anim@parse@colon#1:#2\pgf@stop{%
+  \expandafter\tikz@anim@sync@scope\expandafter{\tikz@animation@rest}{%
+    \tikz@anim@set@object{#1}%
+    \pgfutil@in@_{#2}%
+    \ifpgfutil@in@%
+      \tikz@anim@parse@under#2\pgf@stop%
+    \else%
+      \tikz@anim@parse@under#2_\pgf@stop%
+    \fi%
+    }{\tikz@anim@make@entry}%
+}%
+
+\def\tikz@anim@parse@under#1_#2\pgf@stop{%
+  \tikz@anim@set@attr{#1}%
+  \tikz@anim@set@id{#2}%
+}%
+
+\def\tikz@anim@set@attr#1{%
+  \pgfkeys@spdef\tikz@anim@a{#1}%
+  \ifx\tikz@anim@a\pgfutil@empty%
+  \else%
+    \let\tikz@anim@tl@attributes\tikz@anim@a%
+  \fi%
+}%
+
+\def\tikz@anim@set@id#1{%
+  \pgfkeys@spdef\tikz@anim@a{#1}%
+  \ifx\tikz@anim@a\pgfutil@empty%
+  \else%
+    \let\tikz@anim@tl@id\tikz@anim@a%
+  \fi%
+}%
+
+\def\tikz@anim@set@object#1{%
+  \pgfkeys@spdef\tikz@anim@a{#1}%
+  \ifx\tikz@anim@a\pgfutil@empty%
+  \else%
+    \let\tikz@anim@tl@objects\tikz@anim@a%
+  \fi%
+}%
+
+
+
+\def\tikz@animation@value#1{%
+  \tikz@animation@value@parser#1\pgf@stop%
+}%
+
+\def\tikz@animation@value@parser"#1"{%
+  \def\tikz@animation@value@head{#1}%
+  \pgfutil@ifnextchar\pgf@stop{\tikz@animation@value@rest=}{%
+    \pgfutil@ifnextchar b\tikz@animation@value@rest@base\tikz@animation@value@rest%
+  }%
+}%
+\def\tikz@animation@value@rest=#1\pgf@stop{%
+  \tikz@anim@sync@scope{#1}{\expandafter\tikz@anim@add\expandafter{\expandafter\tikz@anim@value\expandafter{\tikz@animation@value@head}}}{\tikz@anim@make@entry}%
+}%
+
+\def\tikz@animation@value@rest@base base{%
+  \tikz@anim@sync@scope{}{\let\tikz@animation@time\tikz@anim@base@text\expandafter\tikz@anim@add\expandafter{\expandafter\tikz@anim@value\expandafter{\tikz@animation@value@head}}}{\tikz@anim@make@entry}%
+  \pgfutil@ifnextchar\pgf@stop{\tikz@animation@value@rest=}{\tikz@animation@value@rest}%
+}%
+
+
+
+
+
+\def\tikz@anim@simple@parse#1{} %
+
+\def\tikz@anim@slant@parse#1{\pgfmathsetmacro\tikz@anim@result{atan(#1)}}%
+
+\def\tikz@anim@dashpattern@parse#1{%
+  \pgfmathsetmacro\tikz@anim@dash@phase{\tikz@dashphase}%
+  \def\tikz@dashpattern{}%
+  \expandafter\tikz@scandashon\pgfutil@gobble#1o\@nil%
+  \edef\tikz@anim@result{{\tikz@dashpattern}{\tikz@anim@dash@phase pt}}%
+}%
+\def\tikz@anim@dashoffset@parse#1{%
+  \pgfmathparse{#1}%
+  \edef\tikz@anim@result{{\tikz@dashpattern}{\pgfmathresult pt}}%
+}%
+\def\tikz@anim@dash@parse#1{%
+  \tikz@anim@dash@parse@#1\pgf@stop%
+}%
+\def\tikz@anim@dash@parse@#1phase#2\pgf@stop{%
+  \pgfmathsetmacro\tikz@anim@dash@phase{#2}%
+  \def\tikz@dashpattern{}%
+  \expandafter\tikz@scandashon\pgfutil@gobble#1o\@nil%
+  \edef\tikz@anim@result{{\tikz@dashpattern}{\tikz@anim@dash@phase pt}}%
+}%
+
+\def\tikz@anim@xshift@parse#1{\pgfmathparse{#1}\edef\tikz@anim@result{\noexpand\pgfqpoint{\pgfmathresult pt}{0pt}}}%
+\def\tikz@anim@yshift@parse#1{\pgfmathparse{#1}\edef\tikz@anim@result{\noexpand\pgfqpoint{0pt}{\pgfmathresult pt}}}%
+
+\def\tikz@anim@xscale@parse#1{\pgfmathparse{#1}\edef\tikz@anim@result{\pgfmathresult,1}}%
+\def\tikz@anim@yscale@parse#1{\pgfmathparse{#1}\edef\tikz@anim@result{1,\pgfmathresult}}%
+
+\def\tikz@anim@shift@parse#1{\tikz@scan@one@point\tikz@anim@do@shift#1}%
+\def\tikz@anim@do@shift#1{\def\tikz@anim@result{#1}}%
+
+\def\tikz@anim@position@parse#1{%
+  \begingroup%
+    \let\tikz@transform=\relax%
+    \pgf@xc-\pgf@pt@x%
+    \pgf@yc-\pgf@pt@y%
+    \pgfsettransform\tikz@anim@saved@transform%
+    \tikz@scan@one@point\tikz@anim@do@position#1}%
+\def\tikz@anim@do@position#1{%
+    \pgf@process{\pgfpointtransformed{#1}}%
+    \advance\pgf@x by\pgf@xc%
+    \advance\pgf@y by\pgf@yc%
+    \xdef\tikz@anim@temp{\noexpand\pgfqpoint{\the\pgf@x}{\the\pgf@y}}%
+  \endgroup%
+  \let\tikz@anim@result\tikz@anim@temp%
+}%
+
+\def\tikz@anim@view@parse#1{\tikz@anim@view@parse@#1\pgf@stop}%
+\def\tikz@anim@view@parse@{%
+  \pgfutil@ifnextchar({\tikz@scan@one@point\tikz@anim@view@parse@a}{\tikz@anim@view@node}%
+}%
+\def\tikz@anim@view@parse@a#1{%
+  \def\tikz@anim@result{{#1}}%
+  \pgfutil@ifnextchar r{\tikz@anim@view@parsed@rec}{\tikz@scan@one@point\tikz@anim@view@parse@b}%
+}%
+\def\tikz@anim@view@parsed@rec rectangle{\tikz@scan@one@point\tikz@anim@view@parse@b}%
+\def\tikz@anim@view@parse@b#1{%
+  \expandafter\def\expandafter\tikz@anim@result\expandafter{\tikz@anim@result{#1}}%
+  \pgfutil@ifnextchar\pgf@stop\pgfutil@gobble{\tikzerror{Wrong view syntax}}%
+}%
+\def\tikz@anim@view@node#1\pgf@stop{%
+  \expandafter\ifx\csname pgf@sh@ns@#1\endcsname\relax%
+    \tikzerror{Undefined node '#1'}%
+  \else%
+    {%
+      \pgf@process{\pgfpointanchor{#1}{west}}%
+      \pgf@xa\pgf@x \pgf@ya\pgf@y
+      \pgf@xb\pgf@x \pgf@yb\pgf@y
+      \pgf@process{\pgfpointanchor{#1}{north}}%
+      \ifdim\pgf@x<\pgf@xa \pgf@xa=\pgf@x\fi%
+      \ifdim\pgf@x>\pgf@xb \pgf@xb=\pgf@x\fi%
+      \ifdim\pgf@y<\pgf@ya \pgf@ya=\pgf@y\fi%
+      \ifdim\pgf@y>\pgf@yb \pgf@yb=\pgf@y\fi%
+      \pgf@process{\pgfpointanchor{#1}{south}}%
+      \ifdim\pgf@x<\pgf@xa \pgf@xa=\pgf@x\fi%
+      \ifdim\pgf@x>\pgf@xb \pgf@xb=\pgf@x\fi%
+      \ifdim\pgf@y<\pgf@ya \pgf@ya=\pgf@y\fi%
+      \ifdim\pgf@y>\pgf@yb \pgf@yb=\pgf@y\fi%
+      \pgf@process{\pgfpointanchor{#1}{east}}%
+      \ifdim\pgf@x<\pgf@xa \pgf@xa=\pgf@x\fi%
+      \ifdim\pgf@x>\pgf@xb \pgf@xb=\pgf@x\fi%
+      \ifdim\pgf@y<\pgf@ya \pgf@ya=\pgf@y\fi%
+      \ifdim\pgf@y>\pgf@yb \pgf@yb=\pgf@y\fi%
+      \xdef\tikz@anim@result{{\noexpand\pgfqpoint{\the\pgf@xa}{\the\pgf@ya}}{\noexpand\pgfqpoint{\the\pgf@xb}{\the\pgf@yb}}}
+    }%
+  \fi%
+}%
+
+\def\tikz@anim@path@parse#1{%
+  {%
+    \setbox0=\hbox{{%
+        \pgfinterruptpath%
+        \expandafter\tikz@scan@next@command#1\pgf@stop%
+        \pgfsyssoftpath@getcurrentpath\tikz@anim@result%
+        \pgfprocessround{\tikz@anim@result}{\tikz@anim@result}%
+        \global\let\tikz@anim@result\tikz@anim@result%
+        \endpgfinterruptpath%
+      }}%
+  }%
+}%
+
+
+
+\def\tikz@anim@along#1#2{%
+  {%
+    \setbox0=\hbox{{%
+        \pgfinterruptpath%
+        \pgf@relevantforpicturesizefalse%
+        \iftikz@anim@is@position%
+          \let\tikz@transform=\relax%
+          \pgf@x-\pgf@pt@x%
+          \pgf@y-\pgf@pt@y%
+          \edef\tikz@anim@along@shift{\pgf@xc\the\pgf@x\pgf@yc\the\pgf@y}%
+          \pgfsettransformentries#1%
+        \else%
+          \pgftransformreset%
+        \fi
+        \tikz@scan@next@command#2\pgf@stop%
+        \pgfsyssoftpath@getcurrentpath\tikz@anim@parsed@path%
+        \pgfprocessround{\tikz@anim@parsed@path}{\tikz@anim@parsed@path}%
+        \iftikz@anim@is@position%
+          \tikz@anim@shift@path%
+          \global\let\tikz@anim@parsed@path\tikz@anim@patched@path%
+        \else%
+          \global\let\tikz@anim@parsed@path\tikz@anim@parsed@path%
+        \fi%
+        \endpgfinterruptpath%
+      }}%
+  }%
+  \pgfanimationset{along softpath/.expand once=\tikz@anim@parsed@path}%
+}%
+
+\def\tikz@anim@shift@path{%
+  \let\tikz@anim@patched@path\pgfutil@empty%
+  \tikz@anim@along@shift%
+  \expandafter\tikz@anim@shift@path@\tikz@anim@parsed@path\pgf@stop%
+}%
+\def\tikz@anim@shift@path@{%
+  \pgfutil@ifnextchar\pgf@stop\pgfutil@gobble{%
+    \pgfutil@ifnextchar\bgroup\tikz@anim@shift@path@sub\tikz@anim@shift@path@copy}%
+}%
+\def\tikz@anim@shift@path@copy#1{%
+  \expandafter\def\expandafter\tikz@anim@patched@path\expandafter{\tikz@anim@patched@path#1}%
+  \tikz@anim@shift@path@%
+}%
+\def\tikz@anim@shift@path@sub#1#2{%
+  \pgf@x#1%
+  \pgf@y#2%
+  \advance\pgf@x by\pgf@xc%
+  \advance\pgf@y by\pgf@yc%
+  \edef\tikz@temp{{\the\pgf@x}{\the\pgf@y}}%
+  \expandafter\tikz@anim@shift@path@copy\expandafter{\tikz@temp}%
+}%
+
+
+
+\def\tikz@anim@parse@origin#1{%
+  \tikz@scan@one@point\tikz@anim@parse@origin@#1\relax%
+}%
+\def\tikz@anim@parse@origin@#1{\tikz@anim@add{\pgfanimationset{origin={#1}}}}%
+
+
+
+\def\tikz@anim@tl@objects{}%
+\def\tikz@anim@tl@attributes{}%
+\def\tikz@anim@tl@id{default}%
+
+\let\tikz@anim@tl@exec@options\pgfutil@empty
+\let\tikz@anim@tl@early@options\pgfutil@empty
+
+\def\tikz@anim@add@early#1{\expandafter\def\expandafter\tikz@anim@tl@early@options\expandafter{\tikz@anim@tl@early@options#1}}%
+\def\tikz@anim@add@once@early#1{%
+  \global\advance\tikz@anim@once@count by1\relax%
+  \expandafter\expandafter\expandafter\def\expandafter\expandafter\expandafter\tikz@anim@tl@early@options%
+  \expandafter\expandafter\expandafter{\expandafter\tikz@anim@tl@early@options\expandafter\tikz@anim@exec@once\expandafter{\the\tikz@anim@once@count}{#1}}%
+}%
+\def\tikz@anim@add#1{\expandafter\def\expandafter\tikz@anim@tl@exec@options\expandafter{\tikz@anim@tl@exec@options#1}}%
+\def\tikz@anim@add@once#1{%
+  \global\advance\tikz@anim@once@count by1\relax%
+  \expandafter\expandafter\expandafter\def\expandafter\expandafter\expandafter\tikz@anim@tl@exec@options%
+  \expandafter\expandafter\expandafter{\expandafter\tikz@anim@tl@exec@options\expandafter\tikz@anim@exec@once\expandafter{\the\tikz@anim@once@count}{#1}}%
+}%
+\newcount\tikz@anim@once@count%
+\def\tikz@anim@exec@once#1#2{%
+  \expandafter\ifx\csname tikz@anim@once@#1\endcsname\pgf@stop%
+  \else%
+    \expandafter\let\csname tikz@anim@once@#1\endcsname\pgf@stop%
+    #2%
+  \fi%
+}%
+
+\newif\iftikz@anim@do@entry
+
+\def\tikz@anim@make@entry{%
+  \tikz@anim@do@entrytrue%
+  \ifx\tikz@anim@tl@objects\pgfutil@empty\tikz@anim@do@entryfalse\fi%
+  \ifx\tikz@anim@tl@attributes\pgfutil@empty\tikz@anim@do@entryfalse\fi%
+  \ifx\tikz@anim@tl@exec@options\pgfutil@empty\ifx\tikz@anim@tl@early@options\pgfutil@empty\tikz@anim@do@entryfalse\fi\fi%
+  \iftikz@anim@do@entry%
+    \foreach\tikz@anim@tl@object in\tikz@anim@tl@objects{%
+      \expandafter\tikzanimationattributesset\expandafter{\tikz@anim@tl@attributes}%
+    }%
+  \fi%
+}%
+
+\def\tikzanimationattributesset#1{\pgfqkeys{/tikz/animate/attributes}{#1}}%
+
+\tikzanimationattributesset{
+  .unknown/.code={
+    \let\tikz@anim@attribute@name\pgfkeyscurrentname
+    \expandafter\let\expandafter\pgf@temp\csname tikz@anim@def@pgf@attr@\tikz@anim@attribute@name\endcsname%
+    \ifx\pgf@temp\relax%
+      \tikzerror{Unknown animation attribute '\tikz@anim@attribute@name'}%
+    \else%
+      \expandafter\tikz@timeline@config\expandafter\tikz@anim@tl@object\expandafter\tikz@anim@attribute@name\expandafter\tikz@anim@tl@id\expandafter{\tikz@anim@configs}%
+      \edef\pgf@marshal{\noexpand\tikz@timeline@entry{\tikz@anim@tl@object}{\tikz@anim@attribute@name}{\tikz@anim@tl@id}}%
+      \expandafter\expandafter\expandafter\def\expandafter\expandafter\expandafter\pgf@marshal\expandafter\expandafter\expandafter{\expandafter\pgf@marshal\expandafter{\tikz@anim@tl@early@options}}%
+      \expandafter\expandafter\expandafter\pgf@marshal\expandafter\expandafter\expandafter{\expandafter\expandafter\expandafter\tikz@anim@entry\expandafter\expandafter\expandafter{\expandafter\tikz@anim@tl@exec@options\expandafter\def\expandafter\tikz@animation@time\expandafter{\tikz@animation@time}}}%
+    \fi%
+  }
+}%
+\let\tikz@anim@configs\pgfutil@empty
+
+\def\tikz@anim@entry#1{%
+  \let\tikz@anim@result\pgfutil@empty%
+  \pgf@anim@reset@linear%
+  #1%
+  \ifx\tikz@anim@result\pgfutil@empty%
+  \else%
+    \ifx\tikz@animation@time\pgfutil@empty%
+    \else%
+      \ifx\tikz@animation@time\tikz@anim@base@text%
+        \expandafter\pgf@anim@base\expandafter{\tikz@anim@result}%
+      \else%
+        \expandafter\expandafter\expandafter\pgf@anim@entry%
+        \expandafter\expandafter\expandafter{\expandafter\tikz@animation@time\expandafter}\expandafter{\tikz@anim@result}%
+      \fi%
+    \fi%
+  \fi%
+}%
+\let\tikz@animation@time\pgfutil@empty%
+\def\tikz@anim@base@text{base}%
+
+\tikzanimateset{
+  .unknown/.code={%
+    \let\tikz@key\pgfkeyscurrentname%
+    \tikz@animation@syntax@check{#1}{\tikz@anim@options{#1}}%
+  }
+}%
+
+
+\def\tikz@anim@options#1{
+  \let\tikz@anim@key\pgfkeyscurrentname%
+  \pgfqkeys{/tikz/animate/options}{\tikz@anim@key/.try={#1}}%
+  \ifpgfkeyssuccess%
+  \else%
+    \def\tikz@anim@unparsed@value{#1}%
+    \expandafter\tikz@anim@time@test\tikz@anim@key\pgf@stop%
+  \fi%
+}%
+
+\tikzanimateset{
+  options/.cd,
+  name/.code=\tikz@anim@add{\pgfanimationset{name={#1}}},
+  forever/.code=\tikz@anim@add{\pgfanimationset{freeze at end}},
+  freeze/.code=\tikz@anim@add{\pgfanimationset{freeze at end}},
+  restart/.code=\tikz@anim@add{\pgfanimationset{restart={#1}}},
+  repeats/.code=\tikz@anim@add{\pgfanimationset{repeats={#1}}},
+  repeats/.default=,
+  repeat/.code=\tikz@anim@add{\pgfanimationset{repeats={#1}}},
+  repeat/.default=,
+  begin/.code=\tikz@anim@add@once{\pgfanimationset{begin={#1}}},
+  end/.code=\tikz@anim@add@once{\pgfanimationset{end={#1}}},
+  begin on/.code=\tikz@anim@event{begin}{#1},
+  end on/.code=\tikz@anim@event{begin}{#1},
+  begin snapshot/.code=\tikz@anim@add{\pgfanimationset{begin snapshot={#1}}},
+  origin/.code=\tikz@anim@parse@origin{#1},
+  transform/.code=\tikz@anim@add{\pgfanimationset{transform={\let\tikz@transform\relax\tikzset{#1}}}},
+  along/.code=\tikz@anim@handle@along#1\pgf@stop,
+  entry control/.code=\tikz@anim@add{\pgfanimationset{entry control={#1}}},
+  exit control/.code=\tikz@anim@add{\pgfanimationset{exit control={#1}}},
+  stay/.code=\tikz@anim@add{\pgfanimationset{stay}},
+  jump/.code=\tikz@anim@add{\pgfanimationset{jump}},
+  ease/.style={
+    entry control={1-(#1)}{1},
+    exit control={#1}{0}
+  },
+  ease/.default=0.5,
+  ease in/.style={
+    entry control={1-(#1)}{1},
+  },
+  ease in/.default=0.5,
+  ease out/.style={
+    exit control={#1}{0},
+  },
+  ease out/.default=0.5,
+  arrows/.code=\tikz@anim@add@early{\pgfanimationset{arrows={#1}}},
+  shorten >/.code=\tikz@anim@add@early{\pgfanimationset{shorten >={#1}}},
+  shorten </.code=\tikz@anim@add@early{\pgfanimationset{snorten <={#1}}},
+}%
+\newif\iftikz@anim@along
+
+\def\tikz@anim@t{0}%
+
+\def\tikz@anim@handle@along#1{%
+  \pgfutil@ifnextchar s{\tikz@anim@handle@sloped{#1}}{\tikz@anim@handle@upright{#1}}%
+}%
+\def\tikz@anim@handle@sloped#1sloped{%
+  \pgfgettransform\tikz@anim@trans@pre%
+  \expandafter\tikz@anim@add@once%
+  \expandafter{%
+    \expandafter\tikz@anim@along\expandafter{\tikz@anim@trans@pre}{#1}%
+    \pgfsysanimkeycanvastransform{%
+      \pgf@xc\pgf@pt@x%
+      \pgf@yc\pgf@pt@y%
+      \pgftransformreset%
+      \pgf@pt@x\pgf@xc%
+      \pgf@pt@y\pgf@yc%
+      {\pgflowlevelsynccm}%
+    }{\pgftransforminvert\pgflowlevelsynccm}%
+    \pgfanimationset{rotate along=true}%
+  }%
+  \def\tikz@anim@configs{\tikz@anim@alongtrue}%
+  \tikz@anim@handle@in%
+}%
+\def\tikz@anim@handle@upright#1upright{%
+  \pgfgettransform\tikz@anim@trans@pre%
+  \expandafter\tikz@anim@add@once%
+  \expandafter{%
+    \expandafter\tikz@anim@along\expandafter{\tikz@anim@trans@pre}{#1}%
+    \pgfsysanimkeycanvastransform{}{}%
+  }%
+  \def\tikz@anim@configs{\tikz@anim@alongtrue}%
+  \tikz@anim@handle@in%
+}%
+\def\tikz@anim@handle@in{%
+  \pgfutil@ifnextchar i{\tikz@anim@handle@in@yes}{\tikz@anim@handle@in@no}%
+}%
+\def\tikz@anim@handle@in@no\pgf@stop{}%
+\def\tikz@anim@handle@in@yes in#1\pgf@stop{%
+  \tikzanimateset{scope={time=0,value=0,entry,time=#1,value=1,entry}}%
+}%
+
+
+
+\def\tikz@anim@event#1#2{%
+  {%
+    \let\pgf@anim@id\pgfutil@empty%
+    \pgfqkeys{/pgf/animation/events}{#2}%
+  \expandafter}%
+  \expandafter\def\expandafter\tikz@anim@temp@id\expandafter{\pgf@anim@id}%
+  \ifx\tikz@anim@temp@id\pgfutil@empty%
+    \def\tikz@temp{#1 on={of id=\tikz@anim@current@id,#2}}%
+  \else
+    \expandafter\tikz@anim@event@setter\expandafter{\tikz@anim@temp@id}{#1}{#2}%
+  \fi%
+  \expandafter\tikz@anim@add@once\expandafter{\expandafter\pgfanimationset\expandafter{\tikz@temp}}%
+}%
+\def\tikz@anim@event@setter#1#2#3{%
+  \def\tikz@temp{#2 on={#3,of id=#1}}%
+}%
+
+\def\tikz@anim@time@test#1#2\pgf@stop{%
+  \edef\tikz@temp{\meaning#1}%
+  \expandafter\ifx\csname tikz@anim@test@\tikz@temp\endcsname\relax%
+    \tikzerror{I do not know the timing key '#1#2' to which you passed '\tikz@anim@unparsed@value'}%
+  \else%
+    \expandafter\tikz@anim@sync@scope\expandafter{\tikz@anim@unparsed@value}{\tikz@anim@set@time{#1#2}}{\tikz@anim@make@entry}%
+  \fi%
+}%
+
+\def\tikz@anim@parse@time#1{%
+  \pgfutil@in@{later\pgf@stop}{#1\pgf@stop}%
+  \ifpgfutil@in@%
+    \tikz@anim@parse@later#1\pgf@stop%
+  \else%
+    \pgfparsetime{#1}\let\tikz@anim@t\pgftimeresult%
+  \fi%
+}%
+\def\tikz@anim@parse@later#1later\pgf@stop{%
+  \pgfparsetime{#1+\tikz@anim@t@current}\let\tikz@anim@t\pgftimeresult%
+}%
+
+\expandafter\let\csname tikz@anim@test@the character 0\endcsname\pgfutil@empty
+\expandafter\let\csname tikz@anim@test@the character 1\endcsname\pgfutil@empty
+\expandafter\let\csname tikz@anim@test@the character 2\endcsname\pgfutil@empty
+\expandafter\let\csname tikz@anim@test@the character 3\endcsname\pgfutil@empty
+\expandafter\let\csname tikz@anim@test@the character 4\endcsname\pgfutil@empty
+\expandafter\let\csname tikz@anim@test@the character 5\endcsname\pgfutil@empty
+\expandafter\let\csname tikz@anim@test@the character 6\endcsname\pgfutil@empty
+\expandafter\let\csname tikz@anim@test@the character 7\endcsname\pgfutil@empty
+\expandafter\let\csname tikz@anim@test@the character 8\endcsname\pgfutil@empty
+\expandafter\let\csname tikz@anim@test@the character 9\endcsname\pgfutil@empty
+\expandafter\let\csname tikz@anim@test@the character -\endcsname\pgfutil@empty
+\expandafter\let\csname tikz@anim@test@the character +\endcsname\pgfutil@empty
+\expandafter\let\csname tikz@anim@test@the character .\endcsname\pgfutil@empty
+\expandafter\let\csname tikz@anim@test@the character (\endcsname\pgfutil@empty
+
+
+
+
+
+
+\def\tikzanimationdefineattribute#1#2{%
+  \expandafter\def\csname tikz@anim@def@pgf@attr@#1\endcsname{#1}%
+  \expandafter\let\csname tikz@anim@def@no@node@#1\endcsname\pgfutil@empty
+  \expandafter\let\csname tikz@anim@def@is@node@#1\endcsname\pgfutil@empty
+  \expandafter\let\csname tikz@anim@def@code@#1\endcsname\pgfutil@empty
+  \expandafter\let\csname tikz@anim@def@parser@#1\endcsname\tikz@anim@simple@parse
+  \def\tikz@anim@attr{#1}%
+  \pgfkeys{/tikz/animate/@attrdef/.cd,#2}%
+}%
+
+\pgfkeys{/tikz/animate/@attrdef/.cd,
+  pgf attribute name/.code=\expandafter\def\csname tikz@anim@def@pgf@attr@\tikz@anim@attr\endcsname{#1},
+  pgf attribute name scope/.code=\expandafter\def\csname tikz@anim@def@pgf@attr@@scope@\tikz@anim@attr\endcsname{#1},
+  pgf attribute name node/.code=\expandafter\def\csname tikz@anim@def@pgf@attr@@node@\tikz@anim@attr\endcsname{#1},
+  scope type/.code=\expandafter\def\csname tikz@anim@def@no@node@\tikz@anim@attr\endcsname{#1},
+  node type/.code=\expandafter\def\csname tikz@anim@def@is@node@\tikz@anim@attr\endcsname{#1},
+  code/.code=\expandafter\def\csname tikz@anim@def@code@\tikz@anim@attr\endcsname{#1},
+  setup/.code=\expandafter\def\csname tikz@anim@def@setup@\tikz@anim@attr\endcsname{#1},
+  parser/.code=\expandafter\def\csname tikz@anim@def@parser@\tikz@anim@attr\endcsname{#1},
+}%
+
+
+
+\def\tikzanimationdefineattributelist#1#2{%
+  \tikzanimationattributesset{#1/.style={#2}}%
+}%
+
+
+
+
+
+
+\tikzanimationdefineattributelist{color}{@color,text}%
+\tikzanimationdefineattribute{@color}{pgf attribute name=color,node type=.background}%
+\tikzanimationdefineattribute{dash pattern}{pgf attribute name=dash,parser=dashpattern, node type=.background}%
+\tikzanimationdefineattribute{dash phase}{pgf attribute name=dash,parser=dashoffset, node type=.background}%
+\tikzanimationdefineattribute{dash}{parser=dash, node type=.background}%
+\tikzanimationdefineattribute{draw opacity}{pgf attribute name=stroke opacity}%
+\tikzanimationdefineattribute{draw}{pgf attribute name=stroke, node type=.background}%
+\tikzanimationdefineattribute{fill opacity}{}%
+\tikzanimationdefineattribute{fill}{node type=.background}%
+\tikzanimationdefineattribute{line width}{node type=.background}%
+\tikzanimationdefineattribute{path}{pgf attribute name=softpath, scope type=.path, node type=.background.path, parser=path}%
+\tikzanimationdefineattribute{opacity}{}%
+\tikzanimationdefineattribute{position}{%
+  pgf attribute name=\iftikz@anim@along motion\else translate\fi,
+  parser=\iftikz@anim@along simple\else position\fi,
+  setup=\tikz@anim@position@setup,
+}%
+\tikzanimationdefineattribute{rotate}{}%
+\tikzanimationdefineattribute{scale}{}%
+\tikzanimationdefineattribute{shift}{
+  pgf attribute name=\iftikz@anim@along motion\else translate\fi,
+  parser=\iftikz@anim@along simple\else shift\fi
+}%
+\tikzanimationdefineattribute{stage}{}%
+\tikzanimationdefineattribute{text opacity}{pgf attribute name=fill opacity, node type=.text, pgf attribute name scope=none}%
+\tikzanimationdefineattribute{text}{pgf attribute name=color, node type=.text, pgf attribute name scope=none}%
+\tikzanimationdefineattribute{view}{scope type=.view, parser=view}%
+\tikzanimationdefineattribute{visible}{}%
+\tikzanimationdefineattribute{xshift}{pgf attribute name=translate, parser=xshift}%
+\tikzanimationdefineattribute{xscale}{pgf attribute name=scale, parser=xscale}%
+\tikzanimationdefineattribute{xskew}{}%
+\tikzanimationdefineattribute{xslant}{pgf attribute name=xskew, parser=slant}%
+\tikzanimationdefineattribute{yshift}{pgf attribute name=translate, parser=yshift}%
+\tikzanimationdefineattribute{yskew}{}%
+\tikzanimationdefineattribute{yslant}{pgf attribute name=yskew, parser=slant}%
+\tikzanimationdefineattribute{yscale}{pgf attribute name=scale, parser=yscale}%
+
+
+\def\tikz@anim@position@setup{%
+  \pgfgettransform\tikz@anim@saved@transform%
+  \expandafter\def\expandafter\tikz@temp\expandafter{%
+    \expandafter\def\expandafter\tikz@anim@saved@transform\expandafter{\tikz@anim@saved@transform}%
+    \pgfsysanimkeycanvastransform{}{}%
+    \tikz@anim@is@positiontrue%
+  }%
+  \expandafter\expandafter\expandafter\def%
+  \expandafter\expandafter\expandafter\tikz@anim@initial@options%
+  \expandafter\expandafter\expandafter{\expandafter\tikz@temp\tikz@anim@initial@options}%
+}%
+\newif\iftikz@anim@is@position
+
+
+
+\def\tikz@anim@id@hook{%
+  \expandafter\ifx\csname tikz@anim@att@\tikz@id@name\endcsname\relax%
+    \expandafter\ifx\csname tikz@anim@att@\tikz@auto@id\endcsname\relax%
+    \else%
+      \ifx\tikz@id@name\pgfutil@empty%
+        \def\tikz@id@name{@auto}%
+      \fi%
+      \pgfidrefnextuse\tikz@anim@current@id\tikz@id@name%
+      \csname tikz@anim@att@\tikz@auto@id\endcsname%
+      \expandafter\global\expandafter\let\csname tikz@anim@att@\tikz@auto@id\endcsname\relax%
+    \fi%
+  \else%
+    \pgfidrefnextuse\tikz@anim@current@id\tikz@id@name%
+    \csname tikz@anim@att@\tikz@id@name\endcsname%
+    \csname tikz@anim@att@\tikz@auto@id\endcsname%
+    \expandafter\global\expandafter\let\csname tikz@anim@att@\tikz@id@name\endcsname\relax%
+    \expandafter\global\expandafter\let\csname tikz@anim@att@\tikz@auto@id\endcsname\relax%
+  \fi%
+}%
+
+\expandafter\def\expandafter\tikz@id@hook\expandafter{\tikz@id@hook\tikz@anim@id@hook}%
+
+
+
+
+\def\tikzanimationattachto#1#2{%
+  {%
+    \def\tikz@anim@name{#1}%
+    \ifx\tikz@anim@name\pgfutil@empty%
+      \tikzerror{Trying to attach an animation to an unnamed object. This should not happen.}%
+    \else%
+      \expandafter\ifx\csname tikz@anim@att@\tikz@anim@name\endcsname\relax%
+        \expandafter\gdef\csname tikz@anim@att@\tikz@anim@name\endcsname{#2}%
+      \else%
+        \expandafter\let\expandafter\tikz@temp\csname tikz@anim@att@\tikz@anim@name\endcsname%
+        \expandafter\def\expandafter\tikz@temp\expandafter{\tikz@temp#2}%
+        \expandafter\global\expandafter\let\csname tikz@anim@att@\tikz@anim@name\endcsname\tikz@temp%
+      \fi%
+    \fi%
+  }%
+}%
+\def\tikz@auto@id{myself}%
+\expandafter\let\csname tikz@anim@att@\tikz@auto@id\endcsname\relax%
+
+
+
+\def\tikz@timeline@config#1#2#3#4{%
+  \expandafter\def\expandafter\tikz@temp\expandafter{\csname tikz@a@conf@#1@#2@#3\endcsname}%
+  \expandafter\ifx\tikz@temp\relax%
+    \expandafter\expandafter\expandafter\expandafter\expandafter\expandafter\expandafter\gdef\expandafter\expandafter\expandafter\tikz@temp\expandafter\expandafter\expandafter{\expandafter\expandafter\expandafter\global\expandafter\let\tikz@temp\relax}%
+  \fi%
+  \expandafter\expandafter\expandafter\expandafter\expandafter\expandafter\expandafter\gdef\expandafter\expandafter\expandafter\tikz@temp\expandafter\expandafter\expandafter{\tikz@temp#4}%
+}%
+
+
+
+
+\def\tikz@timeline@entry#1#2#3#4#5{%
+  \expandafter\ifx\csname tikz@a@tlo@#1\endcsname\relax%
+    \edef\pgf@marshal{\noexpand\tikzanimationattachto{#1}{\expandafter\noexpand\csname tikz@a@tlo@#1\endcsname}}%
+    \pgf@marshal%
+    \expandafter\gdef\csname tikz@a@tlo@#1\endcsname{\tikz@anim@cleanup{#1}}%
+  \fi%
+  \expandafter\ifx\csname tikz@a@tlc@#1@#2@#3\endcsname\relax%
+    \def\tikz@anim@initial@early@options{#4}%
+    \def\tikz@anim@initial@options{#5}%
+    \csname tikz@anim@def@setup@#2\endcsname%
+    \expandafter\global\expandafter\let\csname tikz@a@tlc@#1@#2@#3\endcsname\tikz@anim@initial@options%
+    \expandafter\global\expandafter\let\csname tikz@a@tld@#1@#2@#3\endcsname\tikz@anim@initial@early@options%
+    \expandafter\let\expandafter\pgf@temp\csname tikz@a@tlo@#1\endcsname%
+    \expandafter\def\expandafter\pgf@temp@name\expandafter{\tikz@anim@create{#1}{#2}{#3}}%
+    \expandafter\expandafter\expandafter\def\expandafter\expandafter\expandafter\pgf@temp\expandafter\expandafter\expandafter{\expandafter\pgf@temp\pgf@temp@name}%
+    \expandafter\global\expandafter\let\csname tikz@a@tlo@#1\endcsname\pgf@temp%
+  \else%
+    \expandafter\let\expandafter\pgf@temp\csname tikz@a@tld@#1@#2@#3\endcsname%
+    \expandafter\def\expandafter\pgf@temp\expandafter{\pgf@temp#4}%
+    \expandafter\global\expandafter\let\csname tikz@a@tld@#1@#2@#3\endcsname\pgf@temp%
+    \expandafter\let\expandafter\pgf@temp\csname tikz@a@tlc@#1@#2@#3\endcsname%
+    \expandafter\def\expandafter\pgf@temp\expandafter{\pgf@temp#5}%
+    \expandafter\global\expandafter\let\csname tikz@a@tlc@#1@#2@#3\endcsname\pgf@temp%
+  \fi%
+}%
+
+
+\def\tikz@anim@cleanup#1{%
+  \expandafter\global\expandafter\let\csname tikz@a@tlo@#1\endcsname\relax%
+}%
+
+\def\tikz@anim@create#1#2#3{%
+  \csname tikz@a@conf@#1@#2@#3\endcsname%
+  \iftikz@is@node%
+    \expandafter\let\expandafter\tikz@temp\csname tikz@anim@def@pgf@attr@@node@#2\endcsname%
+  \else%
+    \expandafter\let\expandafter\tikz@temp\csname tikz@anim@def@pgf@attr@@scope@#2\endcsname%
+  \fi%
+  \ifx\tikz@temp\relax%
+    \expandafter\let\expandafter\tikz@temp\csname tikz@anim@def@pgf@attr@#2\endcsname%
+  \fi%
+  \expandafter\pgfanimateattributecode\expandafter{\tikz@temp}{%
+    \iftikz@is@node%
+      \edef\tikz@anim@whom{\tikz@id@name\csname tikz@anim@def@is@node@#2\endcsname}%
+    \else%
+      \edef\tikz@anim@whom{\tikz@id@name\csname tikz@anim@def@no@node@#2\endcsname}%
+    \fi%
+    \pgfanimationset{whom=\tikz@anim@whom}%
+    \expandafter\let\expandafter\tikz@animation@parser\csname tikz@anim@\csname tikz@anim@def@parser@#2\endcsname @parse\endcsname%
+    \csname tikz@anim@def@code@#2\endcsname%
+    \csname tikz@a@tld@#1@#2@#3\endcsname%
+    \csname tikz@a@tlc@#1@#2@#3\endcsname%
+  }%
+  \expandafter\global\expandafter\let\csname tikz@a@tlc@#1@#2@#3\endcsname\relax%
+  \expandafter\global\expandafter\let\csname tikz@a@tld@#1@#2@#3\endcsname\relax%
+}%
+
+
+
+
+\endinput

preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibraryarrows.code.tex

@@ -0,0 +1,6 @@
+
+\ProvidesFileRCS{tikzlibraryarrows.code.tex}
+
+\usepgflibrary{arrows}%
+
+\endinput

preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibraryautomata.code.tex

@@ -0,0 +1,95 @@
+
+\ProvidesFileRCS{tikzlibraryautomata.code.tex}
+
+\usetikzlibrary{shapes.multipart}%
+
+
+\tikzset{every state/.style=           {}}%
+
+\tikzset{state without output/.style=  {circle,draw,minimum size=2.5em,every state}}%
+\tikzset{state with output/.style=     {circle split,draw,minimum size=2.5em,every state}}%
+
+\tikzset{accepting by arrow/.style=    {after node path=
+{
+  {
+    [to path=
+    {
+      [->,double=none,every accepting by arrow]
+      --
+      ([shift=(\tikz@accepting@angle:\tikz@accepting@distance)]\tikztostart.\tikz@accepting@angle)
+          node [shape=rectangle,anchor=\tikz@accepting@anchor] {\tikz@accepting@text}
+      }]
+    edge ()
+  }
+}}}%
+\tikzset{every accepting by arrow/.style={}}%
+\tikzset{accepting by double/.style= {double,outer sep=.5\pgflinewidth+.3pt}} %
+
+\tikzset{initial by arrow/.style=    {after node path=
+{
+  {
+    [to path=
+    {
+      [->,double=none,every initial by arrow]
+      ([shift=(\tikz@initial@angle:\tikz@initial@distance)]\tikztostart.\tikz@initial@angle)
+          node [shape=rectangle,anchor=\tikz@initial@anchor] {\tikz@initial@text}
+        -- (\tikztostart)}]
+    edge ()
+  }
+}}}%
+\tikzset{every initial by arrow/.style={}}%
+
+\tikzset{initial by diamond/.style={shape=diamond}}%
+
+
+\tikzoption{initial text}{\tikzaddafternodepathoption{\def\tikz@initial@text{#1}}}%
+\tikzoption{accepting text}{\tikzaddafternodepathoption{\def\tikz@accepting@text{#1}}}%
+
+\tikzoption{initial where}{\tikzaddafternodepathoption{\csname tikz@initial@compute@#1\endcsname}}%
+\tikzoption{accepting where}{\tikzaddafternodepathoption{\csname tikz@accepting@compute@#1\endcsname}}%
+
+\tikzoption{initial distance}{\tikzaddafternodepathoption{\def\tikz@initial@distance{#1}}}%
+\tikzoption{accepting distance}{\tikzaddafternodepathoption{\def\tikz@accepting@distance{#1}}}%
+
+\def\tikz@initial@text{start}%
+\def\tikz@accepting@text{}%
+
+\def\tikz@initial@distance{3ex}%
+\def\tikz@accepting@distance{3ex}%
+
+\def\tikz@initial@compute@above{\def\tikz@initial@angle{90}\def\tikz@initial@anchor{south}}%
+\def\tikz@initial@compute@below{\def\tikz@initial@angle{270}\def\tikz@initial@anchor{north}}%
+\def\tikz@initial@compute@left{\def\tikz@initial@angle{180}\def\tikz@initial@anchor{east}}%
+\def\tikz@initial@compute@right{\def\tikz@initial@angle{0}\def\tikz@initial@anchor{west}}%
+
+\def\tikz@initial@angle{180}%
+\def\tikz@initial@anchor{east}%
+
+\def\tikz@accepting@compute@above{\def\tikz@accepting@angle{90}\def\tikz@accepting@anchor{south}}%
+\def\tikz@accepting@compute@below{\def\tikz@accepting@angle{270}\def\tikz@accepting@anchor{north}}%
+\def\tikz@accepting@compute@left{\def\tikz@accepting@angle{180}\def\tikz@accepting@anchor{east}}%
+\def\tikz@accepting@compute@right{\def\tikz@accepting@angle{0}\def\tikz@accepting@anchor{west}}%
+
+\def\tikz@accepting@angle{0}%
+\def\tikz@accepting@anchor{west}%
+
+
+\tikzset{initial above/.style=        {initial by arrow,initial where=above}}%
+\tikzset{initial below/.style=        {initial by arrow,initial where=below}}%
+\tikzset{initial left/.style=         {initial by arrow,initial where=left}}%
+\tikzset{initial right/.style=        {initial by arrow,initial where=right}}%
+
+\tikzset{accepting above/.style=      {accepting by arrow,accepting where=above}}%
+\tikzset{accepting below/.style=      {accepting by arrow,accepting where=below}}%
+\tikzset{accepting left/.style=       {accepting by arrow,accepting where=left}}%
+\tikzset{accepting right/.style=      {accepting by arrow,accepting where=right}}%
+
+
+
+\tikzset{state/.style=                {state without output}}%
+\tikzset{accepting/.style=            {accepting by double}}%
+\tikzset{initial/.style=              {initial by arrow}}%
+
+
+
+\endinput

preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibrarybabel.code.tex

@@ -0,0 +1,9 @@
+
+\ProvidesFileRCS{tikzlibrarybabel.code.tex}
+
+\tikzset{
+  handle active characters in code,
+  handle active characters in nodes,
+}%
+
+\endinput

preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibrarybackgrounds.code.tex

@@ -0,0 +1,134 @@
+
+\ProvidesFileRCS{tikzlibrarybackgrounds.code.tex}
+
+
+
+\pgfdeclarelayer{background}%
+\pgfsetlayers{background,main}%
+
+
+\tikzset{on background layer/.style={
+    execute at begin scope={%
+      \pgfonlayer{background}%
+      \let\tikz@options=\pgfutil@empty%
+      \tikzset{every on background layer/.try,#1}%
+      \tikz@options},
+    execute at end scope={\endpgfonlayer}
+  }
+}%
+
+
+
+\tikzset{background rectangle/.style= {draw}}%
+\tikzset{background top/.style=       {draw}}%
+\tikzset{background bottom/.style=    {draw}}%
+\tikzset{background left/.style=      {draw}}%
+\tikzset{background right/.style=     {draw}}%
+\tikzset{background grid/.style=      {help lines,draw}}%
+
+\tikzoption{inner frame sep}{\def\tikz@framexsep{#1}\def\tikz@frameysep{#1}}%
+\tikzoption{inner frame xsep}{\def\tikz@framexsep{#1}}%
+\tikzoption{inner frame ysep}{\def\tikz@frameysep{#1}}%
+\def\tikz@framexsep{1ex}%
+\def\tikz@frameysep{1ex}%
+
+\tikzoption{outer frame sep}{\def\tikz@outerframexsep{#1}\def\tikz@outerframeysep{#1}}%
+\tikzoption{outer frame xsep}{\def\tikz@outerframexsep{#1}}%
+\tikzoption{outer frame ysep}{\def\tikz@outerframeysep{#1}}%
+\def\tikz@outerframexsep{0ex}%
+\def\tikz@outerframeysep{0ex}%
+
+
+
+\tikzset{loose background/.style=     {inner frame sep=2ex}}%
+\tikzset{tight background/.style=     {inner frame sep=0ex}}%
+
+
+
+
+\tikzset{framed/.style=                   {style=show background rectangle}}%
+\tikzset{gridded/.style=                  {style=show background grid}}%
+
+\tikzset{show background rectangle/.style={execute at end picture=\tikz@background@framed}}%
+\tikzset{show background top/.style=      {execute at end picture=\tikz@background@top}}%
+\tikzset{show background bottom/.style=   {execute at end picture=\tikz@background@bottom}}%
+\tikzset{show background left/.style=     {execute at end picture=\tikz@background@left}}%
+\tikzset{show background right/.style=    {execute at end picture=\tikz@background@right}}%
+\tikzset{show background grid/.style=     {execute at end picture=\tikz@background@grid}}%
+
+
+
+\def\tikz@background@save{%
+  \pgftransformreset%
+  \ifx\tikz@bg@minx\@undefined%
+    \pgf@xb=\pgf@picminx%
+    \pgf@yb=\pgf@picminy%
+    \pgf@xc=\pgf@picmaxx%
+    \pgf@yc=\pgf@picmaxy%
+    \pgfmathsetlength{\pgf@x}{\tikz@framexsep}%
+    \pgfmathsetlength{\pgf@y}{\tikz@frameysep}%
+    \advance\pgf@xb by-\pgf@x%
+    \advance\pgf@yb by-\pgf@y%
+    \advance\pgf@xc by\pgf@x%
+    \advance\pgf@yc by\pgf@y%
+    \edef\tikz@bg@minx{\the\pgf@xb}%
+    \edef\tikz@bg@miny{\the\pgf@yb}%
+    \edef\tikz@bg@maxx{\the\pgf@xc}%
+    \edef\tikz@bg@maxy{\the\pgf@yc}%
+    \pgfmathsetlength{\pgf@x}{\tikz@outerframexsep}%
+    \pgfmathsetlength{\pgf@y}{\tikz@outerframeysep}%
+    \advance\pgf@xb by-\pgf@x%
+    \advance\pgf@yb by-\pgf@y%
+    \advance\pgf@xc by\pgf@x%
+    \advance\pgf@yc by\pgf@y%
+    \edef\tikz@bg@outerminx{\the\pgf@xb}%
+    \edef\tikz@bg@outerminy{\the\pgf@yb}%
+    \edef\tikz@bg@outermaxx{\the\pgf@xc}%
+    \edef\tikz@bg@outermaxy{\the\pgf@yc}%
+  \fi%
+}%
+
+\def\tikz@background@framed{%
+  \tikz@background@save%
+  \pgfonlayer{background}
+    \path[style=background rectangle] (\tikz@bg@minx,\tikz@bg@miny) rectangle (\tikz@bg@maxx,\tikz@bg@maxy);
+  \endpgfonlayer
+}%
+
+\def\tikz@background@top{%
+  \tikz@background@save%
+  \pgfonlayer{background}
+    \path[style=background top] (\tikz@bg@outerminx,\tikz@bg@maxy) -- (\tikz@bg@outermaxx,\tikz@bg@maxy);
+  \endpgfonlayer
+}%
+
+\def\tikz@background@bottom{%
+  \tikz@background@save%
+  \pgfonlayer{background}
+    \path[style=background bottom] (\tikz@bg@outerminx,\tikz@bg@miny) -- (\tikz@bg@outermaxx,\tikz@bg@miny);
+  \endpgfonlayer
+}%
+
+\def\tikz@background@left{%
+  \tikz@background@save%
+  \pgfonlayer{background}
+    \path[style=background left] (\tikz@bg@minx,\tikz@bg@outerminy) -- (\tikz@bg@minx,\tikz@bg@outermaxy);
+  \endpgfonlayer
+}%
+
+\def\tikz@background@right{%
+  \tikz@background@save%
+  \pgfonlayer{background}
+    \path[style=background right] (\tikz@bg@maxx,\tikz@bg@outerminy) -- (\tikz@bg@maxx,\tikz@bg@outermaxy);
+  \endpgfonlayer
+}%
+
+\def\tikz@background@grid{%
+  \tikz@background@save%
+  \pgfonlayer{background}
+    \path[style=background grid] (\tikz@bg@minx,\tikz@bg@miny) grid (\tikz@bg@maxx,\tikz@bg@maxy);
+  \endpgfonlayer
+}%
+
+
+\endinput

preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibrarybending.code.tex

@@ -0,0 +1,7 @@
+
+\ProvidesFileRCS{tikzlibrarybending.code.tex}
+
+\usepgfmodule{bending}%
+\tikzset{arrows=[flex]}%
+
+\endinput

preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibrarycalc.code.tex

@@ -0,0 +1,455 @@
+
+\ProvidesFileRCS{tikzlibrarycalc.code.tex}
+
+
+
+
+\def\tikz@let@command et{%
+  \let\p=\tikz@cc@dop%
+  \let\x=\tikz@cc@dox%
+  \let\y=\tikz@cc@doy%
+  \let\n=\tikz@cc@don%
+  \pgfutil@ifnextchar i{\tikz@cc@stop@let}{\tikz@cc@handle@line}%
+}%
+\def\tikz@cc@handle@line{%
+  \pgfutil@ifnextchar\p{%
+    \tikz@cc@handle@coor%
+  }{%
+    \pgfutil@ifnextchar\n{%
+      \tikz@cc@handle@num%
+    }{%
+      \pgfutil@ifnextchar i{%
+        \tikz@cc@stop@let
+      }{%
+        \tikzerror{``\string\p'' or ``\string\n'' expected}%
+      }%
+    }%
+  }%
+}%
+\def\tikz@cc@handle@num\n#1#2=#3{%
+  \pgfmathparse{#3}%
+  \expandafter\edef\csname tikz@cc@n@#1\endcsname{\pgfmathresult\ifpgfmathunitsdeclared pt\fi}
+  \pgfutil@ifnextchar,{\tikz@cc@handle@nextline}{\tikz@cc@stop@let}%
+}%
+\def\tikz@cc@handle@coor\p#1#2={%
+  \def\tikz@cc@coord@name{#1}%
+  \tikz@scan@one@point\tikz@cc@dolet%
+}%
+\def\tikz@cc@dolet#1{%
+  \pgf@process{#1}%
+  \expandafter\edef\csname tikz@cc@p@\tikz@cc@coord@name\endcsname{\the\pgf@x,\the\pgf@y}%
+  \expandafter\edef\csname tikz@cc@x@\tikz@cc@coord@name\endcsname{\the\pgf@x}%
+  \expandafter\edef\csname tikz@cc@y@\tikz@cc@coord@name\endcsname{\the\pgf@y}%
+  \pgfutil@ifnextchar,{\tikz@cc@handle@nextline}{\tikz@cc@stop@let}%
+}%
+\def\tikz@cc@handle@nextline,{%
+  \tikz@cc@handle@line%
+}%
+\def\tikz@cc@stop@let in{%
+  \tikz@scan@next@command%
+}%
+
+\def\tikz@cc@dop#1{\csname tikz@cc@p@#1\endcsname}%
+\def\tikz@cc@dox#1{\csname tikz@cc@x@#1\endcsname}%
+\def\tikz@cc@doy#1{\csname tikz@cc@y@#1\endcsname}%
+\def\tikz@cc@don#1{\csname tikz@cc@n@#1\endcsname}%
+
+
+
+
+\def\tikz@parse@calculator#1(${%
+  \def\tikz@cc@command{#1}%
+  \begingroup%
+    \pgf@xa=0pt%
+    \pgf@ya=0pt%
+    \tikz@cc@parse+%
+}%
+
+\def\tikz@cc@parse{%
+  \pgfutil@ifnextchar${%
+    \tikz@cc@end%
+  }
+  {\pgfutil@ifnextchar+{%
+      \tikz@cc@add%
+    }{%
+      \pgfutil@ifnextchar-{%
+        \tikz@cc@sub%
+      }{%
+        \tikzerror{+ or - expected}%
+        \tikz@cc@end$%
+      }%
+    }%
+  }%
+}%
+
+\def\tikz@cc@end$#1){%
+    \xdef\tikz@marshal{\noexpand\pgfqpoint{\the\pgf@xa}{\the\pgf@ya}}%
+  \endgroup%
+  \expandafter\tikz@cc@command\expandafter{\tikz@marshal}%
+}%
+
+
+\def\tikz@cc@add+{%
+  \def\tikz@cc@factor{1}%
+  \tikz@cc@factororcoordinate%
+}%
+\def\tikz@cc@sub-{%
+  \def\tikz@cc@factor{-1}%
+  \tikz@cc@factororcoordinate%
+}%
+
+\def\tikz@cc@factororcoordinate{%
+  \pgfutil@ifnextchar({%
+    \tikz@cc@coordinate%
+  }{%
+    \tikz@cc@parse@factor%
+  }%
+}%
+
+\def\tikz@cc@parse@factor#1*({%
+  \pgfmathparse{#1*\tikz@cc@factor}%
+  \let\tikz@cc@factor=\pgfmathresult%
+  \tikz@cc@coordinate(%
+}%
+
+\def\tikz@cc@coordinate{%
+  \tikz@scan@absolute\tikz@cc@after@coordinate%
+}%
+\def\tikz@cc@after@coordinate#1{%
+  \pgf@process{#1}%
+  \pgf@xb=\pgf@x%
+  \pgf@yb=\pgf@y%
+  \tikz@cc@mid@checks%
+}%
+
+
+
+\def\tikz@cc@mid@checks{%
+  \ifnum\the\catcode`\!=\active\relax
+    \expandafter\tikz@cc@mid@checks@active
+  \else
+    \expandafter\tikz@cc@mid@checks@nonactive
+  \fi
+}%
+
+\def\tikz@cc@mid@checks@nonactive{%
+  \pgfutil@ifnextchar!{%
+    \tikz@cc@mid@nonactive%
+  }{%
+    \advance\pgf@xa by\tikz@cc@factor\pgf@xb
+    \advance\pgf@ya by\tikz@cc@factor\pgf@yb
+    \tikz@cc@parse%
+  }%
+}%
+
+\def\tikz@cc@mid@nonactive!{%
+  \pgfutil@ifnextchar({%
+    \tikz@scan@one@point\tikz@cc@project%
+  }{%
+    \tikz@cc@mid@num@nonactive%
+  }%
+}%
+
+\begingroup
+  \catcode`\!=\active
+  \gdef\tikz@cc@mid@checks@active{%
+    \pgfutil@ifnextchar!{%
+      \tikz@cc@mid@active%
+    }{%
+      \advance\pgf@xa by\tikz@cc@factor\pgf@xb
+      \advance\pgf@ya by\tikz@cc@factor\pgf@yb
+      \tikz@cc@parse%
+    }%
+  }%
+
+  \gdef\tikz@cc@mid@active!{%
+    \pgfutil@ifnextchar({%
+      \tikz@scan@one@point\tikz@cc@project%
+    }{%
+      \tikz@cc@mid@num@active%
+    }%
+  }%
+\endgroup
+
+
+\def\tikz@cc@mid@num@nonactive#1!{\tikz@cc@mid@num{#1}}%
+
+\begingroup
+  \catcode`\!=\active
+  \gdef\tikz@cc@mid@num@active#1!{\tikz@cc@mid@num{#1}}%
+\endgroup
+
+\def\tikz@cc@mid@num#1{%
+  \pgfmathparse{#1}%
+  \ifpgfmathunitsdeclared%
+    \let\tikz@cc@mid@unit=\pgfmathresult%
+    \expandafter\tikz@cc@scan@rot\expandafter\tikz@cc@after@unit%
+  \else%
+    \let\tikz@cc@mid@factor=\pgfmathresult%
+    \pgfmathparse{1-\tikz@cc@mid@factor}%
+    \let\tikz@cc@mid@factor@one=\pgfmathresult%
+    \expandafter\tikz@cc@scan@rot\expandafter\tikz@cc@after@num%
+  \fi%
+}%
+
+\def\tikz@cc@after@num#1{%
+  \pgf@process{#1}%
+  \pgf@xb=\tikz@cc@mid@factor@one\pgf@xb%
+  \pgf@yb=\tikz@cc@mid@factor@one\pgf@yb%
+  \advance\pgf@xb by\tikz@cc@mid@factor\pgf@x%
+  \advance\pgf@yb by\tikz@cc@mid@factor\pgf@y%
+  \tikz@cc@mid@checks%
+}%
+
+
+
+
+\def\tikz@cc@after@unit#1{%
+  \pgf@process{#1}%
+  \advance\pgf@x by-\pgf@xb%
+  \advance\pgf@y by-\pgf@yb%
+  \pgf@process{\pgfpointnormalised{}}%
+  \advance\pgf@xb by\tikz@cc@mid@unit\pgf@x%
+  \advance\pgf@yb by\tikz@cc@mid@unit\pgf@y%
+  \tikz@cc@mid@checks%
+}%
+
+\def\tikz@cc@project#1{%
+  \pgf@process{#1}%
+  \pgf@xc=\pgf@x%
+  \pgf@yc=\pgf@y%
+  \begingroup
+    \ifnum\the\catcode`\!=\active
+      \def\tikz@next{%
+        \endgroup
+        \expandafter\tikz@cc@scan@rot\expandafter\tikz@cc@after@project
+        \tikz@cc@scan@ex@active}%
+    \else
+      \def\tikz@next{%
+        \endgroup
+        \expandafter\tikz@cc@scan@rot\expandafter\tikz@cc@after@project
+        \tikz@cc@scan@ex@nonactive}%
+    \fi
+    \tikz@next%
+}%
+
+\def\tikz@cc@scan@ex@nonactive!{}%
+
+\begingroup
+  \catcode`\!=\active
+  \gdef\tikz@cc@scan@ex@active!{}%
+\endgroup
+
+\def\tikz@cc@after@project#1{%
+  \pgf@process{#1}%
+  \advance\pgf@x by-\pgf@xb%
+  \advance\pgf@y by-\pgf@yb%
+  \advance\pgf@xc by-\pgf@xb%
+  \advance\pgf@yc by-\pgf@yb%
+  \pgf@process{\pgfpointnormalised{}}%
+  \pgf@xc=\pgf@sys@tonumber{\pgf@xc}\pgf@x%
+  \advance\pgf@xc by\pgf@sys@tonumber{\pgf@yc}\pgf@y%
+  \advance\pgf@xb by\pgf@sys@tonumber{\pgf@xc}\pgf@x%
+  \advance\pgf@yb by\pgf@sys@tonumber{\pgf@xc}\pgf@y%
+  \tikz@cc@mid@checks%
+}%
+
+
+\def\tikz@cc@scan@rot#1{%
+  \pgfutil@ifnextchar({%
+    \tikz@scan@one@point#1%
+  }%
+  {%
+    \def\tikz@cc@scan@rot@cmd{#1}%
+    \ifnum\the\catcode`\:=\active\relax
+      \expandafter\tikz@cc@scan@one@rot@active%
+    \else
+      \expandafter\tikz@cc@scan@one@rot@nonactive%
+    \fi
+  }%
+}%
+
+\def\tikz@cc@scan@one@rot@nonactive#1:{%
+  \def\tikz@cc@scan@rot@angle{#1}%
+  \tikz@scan@one@point\tikz@cc@handle@rot%
+}%
+
+\begingroup
+  \catcode`\:=\active
+  \gdef\tikz@cc@scan@one@rot@active#1:{%
+    \def\tikz@cc@scan@rot@angle{#1}%
+    \tikz@scan@one@point\tikz@cc@handle@rot%
+  }%
+\endgroup
+
+\def\tikz@cc@handle@rot#1{%
+  \pgf@process{#1}%
+  {%
+    \pgftransformreset%
+    \pgf@xc=\pgf@x%
+    \pgf@yc=\pgf@y%
+    \pgftransformshift{\pgfqpoint{\pgf@xb}{\pgf@yb}}%
+    \pgftransformrotate{\tikz@cc@scan@rot@angle}%
+    \pgftransformshift{\pgfqpoint{-\pgf@xb}{-\pgf@yb}}%
+    \pgfpointtransformed{\pgfqpoint{\pgf@xc}{\pgf@yc}}%
+    \expandafter
+  }%
+  \edef\tikz@marshal{\noexpand\tikz@cc@scan@rot@cmd{\noexpand\pgfqpoint{\the\pgf@x}{\the\pgf@y}}}%
+  \tikz@marshal%
+}%
+
+
+
+
+
+
+\tikzdeclarecoordinatesystem{tangent}
+{%
+  \tikzset{cs/.cd,#1}%
+  \expandafter\ifx\csname tikz@tangent@\tikz@cs@type\endcsname\relax%
+    \tikzerror{I do not know how to compute the tangent to
+    a \tikz@cs@type}%
+    \pgfpointorigin%
+  \else%
+    \expandafter\tikz@scan@one@point\expandafter\tikz@lib@do@tangent\tikz@cs@point%
+  \fi%
+}%
+
+\tikzset{cs/node/.code=\tikz@cs@unpack{\tikz@cs@node}{\tikz@cs@type}{#1}}%
+\tikzset{cs/point/.store in=\tikz@cs@point}%
+
+\def\tikz@lib@do@tangent{\csname tikz@tangent@\tikz@cs@type\endcsname}%
+
+\def\tikz@tangent@coordinate#1{%
+  \pgfpointanchor{\tikz@cs@node}{center}%
+}%
+
+\def\tikz@tangent@circle#1{%
+  {%
+    \pgf@process{\pgfpointtransformed{#1}}%
+    \pgf@xa=\pgf@x%
+    \pgf@ya=\pgf@y%
+    \pgf@process{\pgfpointtransformed{\pgfpointanchor{\tikz@cs@node}{center}}}%
+    \advance\pgf@xa by-\pgf@x%
+    \advance\pgf@ya by-\pgf@y%
+    \pgftransformreset%
+    \pgftransformshift{\pgfpointanchor{\tikz@cs@node}{center}}%
+    \pgf@process{\pgfpointanchor{\tikz@cs@node}{east}}%
+    \pgf@xc=\pgf@x%
+    \pgfmathparse{veclen(\the\pgf@xa,\the\pgf@ya)}
+    \pgfmathparse{acos(\the\pgf@xc/\pgfmathresult)}
+    \ifnum\pgfkeysvalueof{/tikz/cs/solution}>1\relax%
+      \pgfmathparse{0-\pgfmathresult}%
+    \fi%
+    \let\tikz@lib@temp=\pgfmathresult%
+    \pgf@process{\pgfpointnormalised{\pgfqpoint{\pgf@xa}{\pgf@ya}}}%
+    \pgf@ya=-\pgf@y%
+    \pgftransformcm{\pgf@sys@tonumber{\pgf@x}}{\pgf@sys@tonumber{\pgf@y}}{\pgf@sys@tonumber{\pgf@ya}}{\pgf@sys@tonumber{\pgf@x}}{\pgfpointorigin}%
+    \pgf@process{\pgfpointtransformed{\pgfpointpolar{\tikz@lib@temp}{\the\pgf@xc}}}%
+  }%
+  {%
+    \pgftransforminvert%
+    \pgf@process{\pgfpointtransformed{}}%
+  }%
+}%
+
+
+
+
+\def\tikz@intersect@circle@and@circle{%
+  {%
+    \pgftransformreset%
+    \pgf@process{\pgfpointanchor{\tikz@cs@node@a}{center}}%
+    \pgf@xa=\pgf@x%
+    \pgf@ya=\pgf@y%
+    \pgf@process{\pgfpointanchor{\tikz@cs@node@a}{east}}%
+    \advance\pgf@x by-\pgf@xa%
+    \pgf@xc=\pgf@x%
+    \pgf@process{\pgfpointanchor{\tikz@cs@node@b}{center}}%
+    \pgf@xb=\pgf@x%
+    \pgf@yb=\pgf@y%
+    \pgf@process{\pgfpointanchor{\tikz@cs@node@b}{east}}%
+    \advance\pgf@x by-\pgf@xb%
+    \pgf@yc=\pgf@x%
+    \pgf@process{%
+      \pgfpointintersectionofcircles{\pgfqpoint{\pgf@xa}{\pgf@ya}}{\pgfqpoint{\pgf@xb}{\pgf@yb}}{\pgf@xc}{\pgf@yc}{\pgfkeysvalueof{/tikz/cs/solution}}%
+    }%
+  }%
+  {%
+    \pgftransforminvert%
+    \pgf@process{\pgfpointtransformed{}}%
+  }%
+}%
+
+
+\def\tikz@intersect@line@and@circle{%
+  {%
+    \expandafter\tikz@scan@one@point\expandafter\tikz@parse@line\tikz@cs@line@a%
+    \pgf@process{\pgfpointtransformed{}}%
+    \pgf@xb=\pgf@x%
+    \pgf@yb=\pgf@y%
+    \pgf@process{\pgfpointtransformed{\pgfqpoint{\pgf@xc}{\pgf@yc}}}%
+    \pgf@xa=\pgf@x%
+    \pgf@ya=\pgf@y%
+    \pgf@process{\pgfpointtransformed{\pgfpointanchor{\tikz@cs@node@b}{center}}}%
+    \advance\pgf@xa by-\pgf@x%
+    \advance\pgf@ya by-\pgf@y%
+    \advance\pgf@xb by-\pgf@x%
+    \advance\pgf@yb by-\pgf@y%
+    \pgftransformreset%
+    \pgftransformshift{\pgfpointanchor{\tikz@cs@node@b}{center}}%
+    \pgf@process{\pgfpointanchor{\tikz@cs@node@b}{east}}%
+    \edef\tikz@lib@saved@radius{\pgf@sys@tonumber{\pgf@x}}%
+    \pgf@x=\pgf@xb%
+    \pgf@y=\pgf@yb%
+    \advance\pgf@x by-\pgf@xa%
+    \advance\pgf@y by-\pgf@ya%
+    \pgf@process{\pgfpointnormalised{}}%
+    \pgf@xc=\pgf@sys@tonumber{\pgf@xa}\pgf@x%
+    \advance\pgf@xc by\pgf@sys@tonumber{\pgf@ya}\pgf@y%
+    \pgf@xc=-\pgf@xc%
+    \advance\pgf@xa by\pgf@sys@tonumber{\pgf@xc}\pgf@x%
+    \advance\pgf@ya by\pgf@sys@tonumber{\pgf@xc}\pgf@y%
+    \pgf@xc=\pgf@x%
+    \pgf@yc=\pgf@y%
+    \pgf@xb=\tikz@lib@saved@radius pt%
+    \c@pgf@counta=1\relax%
+    \loop%
+    \ifdim\pgf@xb>50pt%
+      \multiply\c@pgf@counta by2\relax%
+      \divide\pgf@xa by2\relax%
+      \divide\pgf@ya by2\relax%
+      \divide\pgf@xb by2\relax%
+    \repeat%
+    \pgf@xb=\pgf@sys@tonumber{\pgf@xb}\pgf@xb%
+    \pgf@yb=\pgf@sys@tonumber{\pgf@xa}\pgf@xa%
+    \advance\pgf@xb by-\pgf@yb%
+    \pgf@yb=\pgf@sys@tonumber{\pgf@ya}\pgf@ya%
+    \advance\pgf@xb by-\pgf@yb%
+    \ifdim\pgf@xb<0pt%
+      \pgf@xb=0pt%
+    \fi%
+    \pgfmathsqrt@{\pgf@sys@tonumber{\pgf@xb}}%
+    \pgfmathmultiply@{\pgfmathresult}{\the\c@pgf@counta}%
+    \multiply\pgf@xa by\c@pgf@counta\relax%
+    \multiply\pgf@ya by\c@pgf@counta\relax%
+    \ifnum\pgfkeysvalueof{/tikz/cs/solution}>1\relax%
+      \pgfmathsubtract{0}{\pgfmathresult}%
+    \fi%
+    \advance\pgf@xa by \pgfmathresult\pgf@xc%
+    \advance\pgf@ya by \pgfmathresult\pgf@yc%
+    \pgf@process{\pgfpointtransformed{\pgfqpoint{\pgf@xa}{\pgf@ya}}}%
+  }%
+  {%
+    \pgftransforminvert%
+    \pgf@process{\pgfpointtransformed{}}%
+  }%
+}%
+
+\def\tikz@intersect@circle@and@line{%
+  {%
+    \let\tikz@cs@node@b=\tikz@cs@node@a%
+    \let\tikz@cs@line@a=\tikz@cs@line@b%
+    \tikz@intersect@line@and@circle%
+  }%
+}%

preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibrarycalendar.code.tex

@@ -0,0 +1,398 @@
+
+\ProvidesFileRCS{tikzlibrarycalendar.code.tex}
+
+
+\pgfutil@usemodule{pgfcalendar}
+
+
+
+\tikzoption{dates}{\tikz@lib@cal@parse#1\relax}
+\def\tikz@lib@cal@parse#1to#2\relax{%
+  \def\tikz@lib@cal@start{#1}
+  \def\tikz@lib@cal@end{#2}%
+}
+\tikzoption{execute at begin day scope}{\expandafter\def\expandafter\tikz@atbegin@day\expandafter{\tikz@atbegin@day#1}}
+\tikzoption{execute at end day scope}{%
+  \def\pgf@temp{#1}%
+  \expandafter\expandafter\expandafter\def%
+  \expandafter\expandafter\expandafter\tikz@atend@day%
+  \expandafter\expandafter\expandafter{\expandafter\pgf@temp\tikz@atend@day}}
+\tikzoption{execute before day scope}{\expandafter\def\expandafter\tikz@before@day\expandafter{\tikz@before@day#1}}
+\tikzoption{execute after day scope}{\expandafter\def\expandafter\tikz@after@day\expandafter{\tikz@after@day#1}}
+
+\let\tikz@atbegin@day=\pgfutil@empty
+\let\tikz@atend@day=\pgfutil@empty
+\let\tikz@before@day=\pgfutil@empty
+\let\tikz@after@day=\pgfutil@empty
+
+
+
+
+
+
+\tikzoption{day xshift}{\def\tikz@lib@cal@xshift{#1}}
+\tikzoption{day yshift}{\def\tikz@lib@cal@yshift{#1}}
+
+\def\tikz@lib@cal@yshift{3ex}
+\def\tikz@lib@cal@xshift{3.5ex}
+
+
+
+\tikzoption{month xshift}{\def\tikz@lib@cal@month@xshift{#1}}
+\tikzoption{month yshift}{\def\tikz@lib@cal@month@yshift{#1}}
+
+\def\tikz@lib@cal@month@yshift{9ex}
+\def\tikz@lib@cal@month@xshift{9ex}
+
+
+
+
+
+\tikzoption{day code}{\def\tikzdaycode{#1}}
+\tikzoption{day text}{\def\tikzdaytext{#1}}
+\tikzoption{days}{\tikzset{every day/.append style={#1}}}
+\tikzset{every day/.style={anchor=base east}}
+
+\tikzoption{month code}{\def\tikzmonthcode{#1}}
+\tikzoption{month text}{\def\tikzmonthtext{#1}}
+\tikzset{every month/.style={}}
+
+\tikzoption{year code}{\def\tikzyearcode{#1}}
+\tikzoption{year text}{\def\tikzyeartext{#1}}
+\tikzset{every year/.style={}}
+
+\def\tikzdaycode{\node[name=\pgfcalendarsuggestedname,every day]{\tikzdaytext};}
+\def\tikzmonthcode{\node[every month]{\tikzmonthtext};}
+\def\tikzyearcode{\node[every year]{\tikzyeartext};}
+
+\def\tikzdaytext{\%d-}
+\def\tikzmonthtext{\%mt}
+\def\tikzyeartext{\%y0}
+
+
+
+\tikzoption{tikz@lib@cal@width}{\def\tikz@lib@cal@width{#1}}
+
+\def\tikz@lib@cal@width{1}
+
+
+\tikzset{day list downward/.style={%
+  execute before day scope={
+    \ifdate{day of month=1}{\ifdate{equals=\pgfcalendarbeginiso}{}
+      {%
+        \pgfmathsetlength{\pgf@y}{\tikz@lib@cal@month@yshift}%
+        \pgftransformyshift{-\pgf@y}
+      }%
+    }{}%
+  },
+  execute after day scope={\pgfmathsetlength{\pgf@y}{\tikz@lib@cal@yshift}\pgftransformyshift{-\pgf@y}},
+  tikz@lib@cal@width=1
+}}
+\tikzset{day list upward/.style={%
+  execute before day scope={
+    \ifdate{day of month=1}{\ifdate{equals=\pgfcalendarbeginiso}{}
+      {%
+        \pgftransformyshift{\tikz@lib@cal@month@yshift}%
+      }%
+    }{}%
+  },
+  execute after day scope={\pgftransformyshift\tikz@lib@cal@yshift},
+  tikz@lib@cal@width=1
+}}
+\tikzset{day list right/.style={%
+  execute before day scope={
+    \ifdate{day of month=1}{\ifdate{equals=\pgfcalendarbeginiso}{}
+      {%
+        \pgftransformxshift{\tikz@lib@cal@month@xshift}%
+      }%
+    }{}%
+  },
+  execute after day scope={\pgftransformxshift\tikz@lib@cal@xshift},
+  tikz@lib@cal@width=30%
+}}
+
+\tikzset{day list left/.style={%
+  execute before day scope={
+    \ifdate{day of month=1}{\ifdate{equals=\pgfcalendarbeginiso}{}
+      {%
+        \pgfmathsetlength{\pgf@x}{\tikz@lib@cal@month@xshift}
+        \pgftransformxshift{-\pgf@x}%
+      }%
+    }{}%
+  },
+  execute after day scope={
+    \pgfmathsetlength{\pgf@x}{\tikz@lib@cal@xshift}
+    \pgftransformxshift{-\pgf@x}%
+  },
+  tikz@lib@cal@width=30%
+}}
+
+
+
+
+\tikzset{week list/.style={%
+  execute before day scope={%
+    \ifdate{day of month=1}{\ifdate{equals=\pgfcalendarbeginiso}{}
+      {%
+        \pgfmathsetlength{\pgf@y}{\tikz@lib@cal@month@yshift}%
+        \pgftransformyshift{-\pgf@y}
+      }%
+    }{}%
+  },
+  execute at begin day scope={%
+    \pgfmathsetlength\pgf@x{\tikz@lib@cal@xshift}%
+    \pgf@x=\pgfcalendarcurrentweekday\pgf@x%
+    \pgftransformxshift{\pgf@x}%
+  },
+  execute after day scope={%
+    \ifdate{Sunday}{%
+      \pgfmathsetlength{\pgf@y}{\tikz@lib@cal@yshift}%
+      \pgftransformyshift{-\pgf@y}
+    }{}%
+  },
+  tikz@lib@cal@width=7
+}}
+
+
+
+
+\tikzset{month list/.style={%
+  execute before day scope={%
+    \ifdate{day of month=1}{\ifdate{equals=\pgfcalendarbeginiso}{}
+      {%
+        \pgfmathsetlength{\pgf@y}{\tikz@lib@cal@month@yshift}%
+        \pgftransformyshift{-\pgf@y}
+      }%
+    }{}%
+    \ifdate{day of month=1}
+    {%
+      \edef\tikz@lib@cal@month@list@start{\pgfcalendarcurrentweekday}%
+    }{}%
+    \ifdate{equals=\pgfcalendarbeginiso}%
+    {%
+      {%
+        \c@pgf@counta=\pgfcalendarcurrentjulian%
+        \advance\c@pgf@counta by-\pgfcalendarcurrentday%
+        \advance\c@pgf@counta by1\relax%
+        \pgfcalendarjuliantoweekday{\c@pgf@counta}{\c@pgf@countb}%
+        \xdef\pgf@temp{\the\c@pgf@countb}%
+      }%
+      \let\tikz@lib@cal@month@list@start=\pgf@temp%
+    }{}%
+  },
+  execute at begin day scope={%
+    \pgfmathsetlength\pgf@xa{\tikz@lib@cal@xshift}%
+    \pgf@xb=\pgfcalendarcurrentday\pgf@xa%
+    \advance\pgf@xb by\tikz@lib@cal@month@list@start\pgf@xa%
+    \advance\pgf@xb by-\pgf@xa\relax%
+    \pgftransformxshift{\pgf@xb}%
+  },
+  tikz@lib@cal@width=37
+}}
+
+
+
+
+
+\tikzset{month label left/.style={%
+  execute before day scope={\ifdate{day of month=1}{\tikzmonthcode}{}},
+  every month/.append style={anchor=base east,xshift=-3.5ex}
+}}
+
+\tikzset{month label left vertical/.style={%
+  execute before day scope={\ifdate{day of month=1}{\tikzmonthcode}{}},
+  every month/.append style={anchor=base east,xshift=-4.5ex,yshift=2.25ex,rotate=90}
+}}
+
+\tikzset{month label right/.style={%
+execute before day scope={\ifdate{day of month=1}{%
+    {%
+      \pgfmathsetlength{\pgf@xa}{\tikz@lib@cal@xshift}%
+      \pgftransformxshift{\tikz@lib@cal@width\pgf@xa}%
+      \pgftransformxshift{-\pgf@xa}%
+      \tikzmonthcode%
+    }}{}},
+  every month/.append style={anchor=base west,xshift=1ex}
+}}
+
+\tikzset{month label right vertical/.style={%
+  execute before day scope={\ifdate{day of month=1}{%
+    {%
+      \pgfmathsetlength{\pgf@xa}{\tikz@lib@cal@xshift}%
+      \pgftransformxshift{\tikz@lib@cal@width\pgf@xa}%
+      \pgftransformxshift{-\pgf@xa}%
+      \tikzmonthcode%
+    }}{}},
+  every month/.append style={anchor=base west,xshift=2ex,yshift=2.25ex,rotate=-90}
+}}
+
+\tikzset{month label above centered/.style={%
+  execute before day scope={%
+    \ifdate{day of month=1}{%
+      {
+        \pgfmathsetlength{\pgf@xa}{\tikz@lib@cal@xshift}%
+        \pgf@xb=\tikz@lib@cal@width\pgf@xa%
+        \advance\pgf@xb by-\pgf@xa%
+        \pgf@xb=.5\pgf@xb%
+        \pgftransformxshift{\pgf@xb}%
+        \pgftransformxshift{-1.5ex}%
+        \pgfmathsetlength{\pgf@y}{\tikz@lib@cal@yshift}%
+        \pgftransformyshift{1.25\pgf@y}
+        \tikzmonthcode%
+      }
+    }{}},
+  every month/.append style={anchor=base}
+}}
+
+\tikzset{month label above left/.style={%
+  execute before day scope={%
+    \ifdate{day of month=1}{%
+      {
+        \pgftransformxshift{-3.25ex}%
+        \pgfmathsetlength{\pgf@y}{\tikz@lib@cal@yshift}%
+        \pgftransformyshift{1.25\pgf@y}
+        \tikzmonthcode%
+      }
+    }{}},
+  every month/.append style={anchor=base west}
+}}
+
+
+
+\tikzset{month label above right/.style={%
+  execute before day scope={%
+    \ifdate{day of month=1}{%
+      {
+        \pgfmathsetlength{\pgf@xa}{\tikz@lib@cal@xshift}%
+        \pgf@xb=\tikz@lib@cal@width\pgf@xa%
+        \advance\pgf@xb by-\pgf@xa%
+        \pgftransformxshift{\pgf@xb}%
+        \pgfmathsetlength{\pgf@y}{\tikz@lib@cal@yshift}%
+        \pgftransformyshift{1.25\pgf@y}
+        \tikzmonthcode%
+      }
+    }{}},
+  every month/.append style={anchor=base east}
+}}
+
+\tikzset{month label below centered/.style={%
+  execute before day scope={%
+    \ifdate{day of month=1}{%
+      {
+        \pgfmathsetlength{\pgf@xa}{\tikz@lib@cal@xshift}%
+        \pgf@xb=\tikz@lib@cal@width\pgf@xa%
+        \advance\pgf@xb by-\pgf@xa%
+        \pgf@xb=.5\pgf@xb%
+        \pgftransformxshift{\pgf@xb}%
+        \pgftransformxshift{-1.5ex}%
+        \pgfmathsetlength{\pgf@y}{\tikz@lib@cal@yshift}%
+        \pgftransformyshift{-1.25\pgf@y}
+        \tikzmonthcode%
+      }
+    }{}},
+  every month/.append style={anchor=base}
+}}
+
+\tikzset{month label below left/.style={%
+  execute before day scope={%
+    \ifdate{day of month=1}{%
+      {
+        \pgftransformxshift{-3.25ex}%
+        \pgfmathsetlength{\pgf@y}{\tikz@lib@cal@yshift}%
+        \pgftransformyshift{-1.25\pgf@y}
+        \tikzmonthcode%
+      }
+    }{}},
+  every month/.append style={anchor=base west}
+}}
+
+
+
+
+\def\tikz@lib@cal@calendar{%
+  \begingroup%
+    \let\tikz@lib@cal@ifs=\pgfutil@empty%
+    \tikz@resetexpandcount
+    \tikzset{name=,at={(0,0)}}%
+    \let\%=\pgfcalendarshorthand%
+    \tikzset{every calendar/.try}%
+    \tikz@lib@cal@scanner%
+}
+
+\def\tikz@lib@cal@scanner{%
+  \afterassignment\tikz@lib@cal@handle\let\pgf@let@token=%
+}
+
+\def\tikz@lib@cal@handle{%
+  \pgfutil@switch\pgfutil@ifx\pgf@let@token{%
+    {;}{\let\pgfutil@next\tikz@lib@cal@stop}%
+    {(}{\let\pgfutil@next\tikz@lib@cal@name}%
+    {a}{\let\pgfutil@next\tikz@lib@cal@at}%
+    {[}{\let\pgfutil@next\tikz@lib@cal@option}%
+    {i}{\let\pgfutil@next\tikz@lib@cal@if}%
+  }{\tikz@resetexpandcount\pgfutil@next}{\tikz@lib@cal@expand}%
+}
+\def\tikz@lib@cal@expand{%
+  \advance\tikz@expandcount by -1
+  \ifnum\tikz@expandcount<0\relax%
+    \tikzerror{Giving up on this calendar}%
+    \let\pgfutil@next=\tikz@lib@cal@end%
+  \else%
+    \let\pgfutil@next=\tikz@lib@cal@@expand
+  \fi%
+  \pgfutil@next}
+
+\def\tikz@lib@cal@@expand{\expandafter\tikz@lib@cal@scanner\pgf@let@token}
+
+
+\def\tikz@lib@cal@name#1){%
+  \tikzset{name=#1}%
+  \tikz@lib@cal@scanner%
+}
+\def\tikz@lib@cal@at t#1(#2){%
+  \tikzset{at={(#2)}}%
+  \tikz@lib@cal@scanner%
+}
+\def\tikz@lib@cal@option#1]{%
+  \tikzset{#1}%
+  \tikz@lib@cal@scanner%
+}
+\def\tikz@lib@cal@if f#1(#2){%
+  \pgfutil@ifnextchar[{\tikz@lib@cal@if@opt{#2}}{\tikz@lib@cal@if@code{#2}}}%
+
+\def\tikz@lib@cal@if@opt#1[#2]{\tikz@lib@cal@if@code{#1}{\tikzset{#2}}}
+\def\tikz@lib@cal@if@code#1#2{%
+  \pgfutil@ifnextchar e{\tikz@lib@cal@if@else{#1}{#2}}{\tikz@lib@cal@if@else{#1}{#2}else{}}}
+
+\def\tikz@lib@cal@if@else#1#2else{%
+  \pgfutil@ifnextchar[{\tikz@lib@cal@if@else@opt{#1}{#2}}{\tikz@lib@cal@if@else@code{#1}{#2}}}%
+\def\tikz@lib@cal@if@else@opt#1#2[#3]{\tikz@lib@cal@if@else@code{#1}{#2}{\tikzset{#3}}}
+\def\tikz@lib@cal@if@else@code#1#2#3{%
+  \expandafter\def\expandafter\tikz@lib@cal@ifs\expandafter{\tikz@lib@cal@ifs\ifdate{#1}{#2}{#3}}%
+  \tikz@lib@cal@scanner%
+}
+\def\tikz@lib@cal@stop{%
+    \pgftransformshift{\tikz@node@at}%
+    \expandafter\pgfcalendar\expandafter{\tikz@fig@name}{\tikz@lib@cal@start}{\tikz@lib@cal@end}%
+    {%
+      \tikz@before@day%
+      \scope%
+        \tikz@atbegin@day%
+        \tikz@lib@cal@ifs%
+        \tikzdaycode%
+        \tikz@atend@day%
+      \endscope%
+      \tikz@after@day%
+    }%
+  \endgroup%
+}
+
+\tikzoption{if}{%
+  \let\tikz@lib@cal@scanner@orig=\tikz@lib@cal@scanner%
+  \let\tikz@lib@cal@scanner=\relax%
+  \tikz@lib@cal@if f#1\relax%
+  \let\tikz@lib@cal@scanner=\tikz@lib@cal@scanner@orig}
+
+
+
+\endinput

preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibrarychains.code.tex

@@ -0,0 +1,198 @@
+
+\ProvidesFileRCS{tikzlibrarychains.code.tex}
+
+\usetikzlibrary{positioning}%
+
+\tikzset{start chain/.default=,
+         start chain/.code={%
+    \tikz@lib@chain@parse{#1}%
+    \ifx\tikz@lib@chain@name\pgfutil@empty%
+      \def\tikz@lib@chain@name{chain}%
+    \fi%
+    \ifx\tikz@lib@chain@direction\relax%
+      \let\tikz@lib@chain@direction=\tikz@lib@chain@default@direction%
+    \fi%
+    \expandafter\ifx\csname tikz@lib@chain@active@\tikz@lib@chain@name\endcsname\relax%
+      \expandafter\let\csname tikz@lib@chain@active@\tikz@lib@chain@name\endcsname=\pgfutil@empty%
+      \expandafter\global\expandafter\let\csname tikz@lib@chain@exists@\tikz@lib@chain@name\endcsname=\pgfutil@empty%
+      \expandafter\gdef\csname tikz@lib@chain@count@\tikz@lib@chain@name\endcsname{0}%
+      \expandafter\global\expandafter\let\csname tikz@lib@chain@dir@\tikz@lib@chain@name\endcsname\tikz@lib@chain@direction%
+      \let\tikz@lib@current@chain=\tikz@lib@chain@name%
+      \let\chainin=\tikz@lib@chainin%
+    \else%
+      \tikzerror{Chain ``\tikz@lib@chain@name'' is already active}%
+    \fi%
+  },
+  continue chain/.default=,
+  continue chain/.code={%
+    \tikz@lib@chain@parse{#1}%
+    \ifx\tikz@lib@chain@name\pgfutil@empty%
+      \let\tikz@lib@chain@name\tikz@lib@current@chain%
+    \fi%
+    \expandafter\ifx\csname tikz@lib@chain@exists@\tikz@lib@chain@name\endcsname\relax%
+      \tikzerror{Unknown chain ``#1''}%
+    \else%
+      \let\tikz@lib@current@chain=\tikz@lib@chain@name%
+      \expandafter\let\csname tikz@lib@chain@active@\tikz@lib@chain@name\endcsname=\pgfutil@empty%
+      \ifx\tikz@lib@chain@direction\relax%
+      \else%
+        \expandafter\global\expandafter\let\csname tikz@lib@chain@dir@\tikz@lib@chain@name\endcsname\tikz@lib@chain@direction%
+      \fi%
+    \fi%
+  },
+  join/.code=\tikz@lib@parse@join{#1},
+  join/.default={}%
+}%
+
+\def\tikz@lib@chain@parse#1{%
+  \pgfutil@in@{going }{#1}%
+  \ifpgfutil@in@%
+    \tikz@lib@chain@going#1\pgf@stop%
+  \else%
+    \pgfutil@in@{placed }{#1}%
+    \ifpgfutil@in@%
+      \tikz@lib@chain@positioning#1\pgf@stop%
+    \else%
+      \def\tikz@lib@chain@name{#1}%
+      \let\tikz@lib@chain@direction\relax%
+    \fi%
+  \fi%
+}%
+
+\def\tikz@lib@chain@going#1going #2\pgf@stop{%
+  \def\tikz@lib@chain@name{#1}%
+  \ifx\tikz@lib@chain@name\pgfutil@empty%
+  \else%
+    \tikz@lib@chain@strip#1\pgf@stop%
+  \fi%
+  \tikz@lib@chain@is@goingtrue%
+  \def\tikz@lib@chain@direction{%
+    \ifx\tikzchainprevious\pgfutil@empty%
+    \else%
+      \tikz@lib@chain@place{#2}%
+    \fi%
+  }%
+}%
+
+\def\tikz@lib@chain@positioning#1placed #2\pgf@stop{%
+  \def\tikz@lib@chain@name{#1}%
+  \ifx\tikz@lib@chain@name\pgfutil@empty%
+  \else%
+    \tikz@lib@chain@strip#1\pgf@stop%
+  \fi%
+  \tikz@lib@chain@is@goingfalse%
+  \def\tikz@lib@chain@direction{\tikz@lib@chain@place{#2}}%
+}%
+\newif\iftikz@lib@chain@is@going
+
+
+\tikzset{/tikz/chain default direction/.code=%
+  {%
+    \tikz@lib@chain@parse{#1}%
+    \let\tikz@lib@chain@default@direction=\tikz@lib@chain@direction%
+  },%
+  /tikz/chain default direction=going right
+}%
+
+\def\tikz@lib@current@chain{chain}%
+
+\pgfutil@g@addto@macro\tikz@node@reset@hook{\let\tikz@lib@chain@caller=\relax}%
+\pgfutil@g@addto@macro\tikz@node@begin@hook{\tikz@lib@chain@caller}%
+
+\tikzset{
+  on chain/.default=,
+  on chain/.code=\tikz@lib@on@chain{#1}%
+}%
+\def\tikz@lib@on@chain#1{%
+  \tikz@lib@chain@parse{#1}%
+  \ifx\tikz@lib@chain@name\pgfutil@empty%
+    \let\tikz@lib@chain@name\tikz@lib@current@chain%
+  \fi%
+  \expandafter\ifx\csname tikz@lib@chain@exists@\tikz@lib@chain@name\endcsname\relax%
+    \tikzerror{Unknown chain ``\tikz@lib@chain@name''}%
+  \else%
+    \c@pgf@counta\csname tikz@lib@chain@count@\tikz@lib@chain@name\endcsname\relax%
+    \ifnum\c@pgf@counta=0\relax%
+      \global\let\tikzchainprevious=\pgfutil@empty%
+    \else
+      \xdef\tikzchainprevious{\tikz@lib@chain@name-\the\c@pgf@counta}%
+    \fi%
+    \advance\c@pgf@counta by1\relax%
+    \xdef\tikzchaincount{\the\c@pgf@counta}%
+    \ifx\tikz@lib@chain@direction\relax%
+      \csname tikz@lib@chain@dir@\tikz@lib@chain@name\endcsname%
+    \else%
+      \tikz@lib@chain@direction%
+    \fi%
+    \edef\tikz@lib@chain@caller{\noexpand\tikz@lib@chain@last@found{\tikz@lib@chain@name}}%
+  \fi%
+}%
+\def\tikz@lib@chain@last@found#1{%
+  \c@pgf@counta\csname tikz@lib@chain@count@#1\endcsname\relax%
+  \advance\c@pgf@counta by1\relax%
+  \xdef\tikzchaincurrent{#1-\the\c@pgf@counta}%
+  \expandafter\xdef\csname tikz@lib@chain@count@#1\endcsname{\the\c@pgf@counta}%
+  \ifnum\c@pgf@counta=1\relax%
+    \tikzset{alias/.expanded={#1-begin}} %
+  \fi%
+  \tikzset{alias/.expanded={#1-end}} %
+  \tikzset{alias/.expanded={#1-\the\c@pgf@counta}} %
+  \tikz@lib@chain@direction%
+  \tikzset{every on chain/.try}%
+}%
+
+
+\def\tikz@lib@chain@place#1{%
+  \pgfutil@in@{=}{#1}%
+  \ifpgfutil@in@%
+    \tikzset{#1}%
+  \else%
+    \tikzset{#1=of \tikzchainprevious}%
+  \fi%
+}%
+
+\def\tikz@lib@chain@strip#1 \pgf@stop{%
+  \def\tikz@lib@chain@name{#1}%
+}%
+
+\def\tikz@lib@parse@join#1{%
+  \def\tikz@temp{#1}%
+  \ifx\tikz@temp\pgfutil@empty%
+    \tikz@lib@parse@join@by by \pgf@stop%
+  \else%
+    \pgfutil@in@{with }{#1}%
+    \ifpgfutil@in@%
+      \pgfutil@in@{by }{#1}%
+      \ifpgfutil@in@%
+        \tikz@lib@parse@join@with@by#1\pgf@stop%
+      \else%
+        \tikz@lib@parse@join@with@by#1 by \pgf@stop%
+      \fi%
+    \else%
+      \tikz@lib@parse@join@by#1\pgf@stop%
+    \fi%
+  \fi%
+}%
+\def\tikz@lib@parse@join@with@by with #1 by #2\pgf@stop{%
+  \tikzset{after node path={(#1)edge[every join,#2](\tikzchaincurrent)}}%
+}%
+\def\tikz@lib@parse@join@by by #1\pgf@stop{%
+  \tikzset{after node path={\ifx\tikzchainprevious\pgfutil@empty\else (\tikzchainprevious)edge[every join,#1](\tikzchaincurrent)\fi}}%
+}%
+\tikzset{every join/.style=}%
+
+
+\def\tikz@lib@chainin#1(#2){\pgfutil@ifnextchar[{\tikz@lib@chainin@{#2}}{\tikz@lib@chainin@{#2}[]}}%
+\def\tikz@lib@chainin@#1[#2]{\path[late options={name=#1,on chain,every chain in/.try,#2}]}%
+
+
+
+\tikzset{start branch/.code={%
+    \let\tikz@lib@save@current\tikz@lib@current@chain%
+    \pgfkeysalso{/tikz/start chain/.expand once=\tikz@lib@current@chain/#1}%
+    \path[late options={name=\tikz@lib@save@current-end,on chain}];%
+  }%
+}%
+\tikzset{continue branch/.style={continue chain/.expand once=\tikz@lib@current@chain/#1}}%
+
+\endinput

preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibrarydecorations.code.tex

@@ -0,0 +1,173 @@
+
+\usepgfmodule{decorations}%
+
+
+\tikzset{decorate/.is if=tikz@decoratepath,
+  /pgf/decoration/name/.store in=\tikz@decoration@name,
+  /pgf/decoration/.unknown/.code=%
+    \pgfifdecoration{\pgfkeyscurrentname}{\edef\tikz@decoration@name{\pgfkeyscurrentname}}
+    {\pgfifmetadecoration{\pgfkeyscurrentname}{\edef\tikz@decoration@name{\pgfkeyscurrentname}}
+    {\pgfkeys{/errors/unknown
+        key/.expanded={/pgf/decoration/\pgfkeyscurrentname}{\pgfutil@unexpanded{#1}}}}},%
+  /pgf/decoration/raise/.code={\def\tikz@dec@shift{\pgftransformyshift{#1}}\tikz@dec@trans},
+  /pgf/decoration/mirror/.code={%
+    \csname if#1\endcsname
+      \def\tikz@dec@mirror{\pgftransformyscale{-1}}%
+    \else%
+      \let\tikz@dec@mirror=\relax%
+    \fi%
+    \tikz@dec@trans%
+  },
+  /pgf/decoration/mirror/.default=true,
+  /pgf/decoration/transform/.code={%
+    {%
+      \pgftransformreset%
+      \def\tikz@transform{}%
+      \pgfkeysalso{/tikz/.cd, #1}%
+      \expandafter\gdef\expandafter\tikz@g@temptransform\expandafter{\tikz@transform}%
+    }%
+    \let\tikz@dec@user@transform=\tikz@g@temptransform%
+    \tikz@dec@trans%
+  },%
+  /pgf/decoration/pre/.initial=lineto,
+  /pgf/decoration/post/.initial=lineto,
+  /pgf/decoration/pre length/.initial=0pt,
+  /pgf/decoration/post length/.initial=0pt,
+}%
+
+\let\tikz@decoration@name=\tikz@nonetext
+
+\def\tikz@dec@trans{\pgfsetdecorationsegmenttransformation{\tikz@dec@user@transform\tikz@dec@mirror\tikz@dec@shift}}%
+\let\tikz@dec@user@transform=\relax
+\let\tikz@dec@shift=\relax
+\let\tikz@dec@mirror=\relax
+
+\pgfdeclaremetadecoration{tikz@internal}{pre}{%
+  \state{pre}[width=\pgfkeysvalueof{/pgf/decoration/pre length}, next state=main]
+  {
+    \tikz@dec@trans
+    \decoration{\pgfkeysvalueof{/pgf/decoration/pre}}
+  }%
+  \state{main}[width=\pgfmetadecoratedremainingdistance-\pgfkeysvalueof{/pgf/decoration/post length}, next state=final]
+  {
+    \tikz@dec@trans
+    \decoration{\tikz@decoration@name}
+  }%
+  \state{final}
+  {
+    \tikz@dec@trans
+    \decoration{\pgfkeysvalueof{/pgf/decoration/post}}
+  }%
+}%
+
+
+\newif\iftikz@metadecoration
+
+\def\tikz@lib@dec@addtomacro#1#2{\expandafter\def\expandafter#1\expandafter{#1#2}}%
+
+\def\tikz@lib@decoration[#1]{%
+  \begingroup%
+    \tikzset{#1}%
+    \ifx\tikz@decoration@name\tikz@nonetext%
+    \else
+      \expandafter\tikz@lib@do@dec%
+    \fi%
+      \pgfutil@ifnextchar\bgroup{%
+        \begingroup%
+          \tikz@auto@end@pathfalse%
+          \aftergroup\tikz@enddecoration%
+          \afterassignment\tikz@scan@next@command%
+          \let\tikz@lib@next%
+      }%
+      {%
+        \tikzerror{A decoration must begin with a brace}%
+        \tikz@enddecoration%
+      }%
+}%
+\def\tikz@lib@do@dec{%
+  \pgfifmetadecoration{\tikz@decoration@name}%
+  {\expandafter\pgfmetadecoration\expandafter{\tikz@decoration@name}}%
+  {%
+    \pgfifdecoration{\tikz@decoration@name}%
+    {\tikz@lib@dec@startdecoration}%
+    {\tikzerror{Unknown (meta-)decoration '\tikz@decoration@name'. Perhaps you
+        misspelled it?}}%
+  }%
+  \ifx\pgfdecorateexistingpath\pgfutil@empty%
+    \pgfpathmoveto{\pgfqpoint{\the\tikz@lastxsaved}{\the\tikz@lastysaved}}%
+  \fi%
+}%
+\newbox\tikz@lib@dec@box
+\def\tikz@enddecoration{%
+    \global\setbox\tikz@lib@dec@box=\box\tikz@tempbox%
+    \ifx\tikz@decoration@name\tikz@nonetext%
+    \else
+      \iftikz@metadecoration%
+        \endpgfmetadecoration%
+      \else%
+        \tikz@lib@dec@stopdecoration%
+      \fi%
+    \fi
+  \endgroup%
+  \setbox\tikz@tempbox=\box\tikz@lib@dec@box%
+}%
+
+
+\def\tikz@lib@dec@decorate@path{%
+  \ifx\tikz@decoration@name\tikz@nonetext%
+  \else%
+    \pgfgetpath\tikz@lib@dec@currentpath%
+    \pgfsetpath\pgfutil@empty%
+    \pgfifmetadecoration{\tikz@decoration@name}
+    {
+      \expandafter\pgfmetadecoration\expandafter{\tikz@decoration@name}%
+        \pgfsetpath\tikz@lib@dec@currentpath%
+      \endpgfmetadecoration%
+    }
+    {
+      \pgfifdecoration{\tikz@decoration@name}
+      {
+        \tikz@lib@dec@startdecoration%
+          \pgfsetpath\tikz@lib@dec@currentpath%
+        \tikz@lib@dec@stopdecoration%
+      }
+      {
+        \tikzerror{Unknown (meta-)decoration '\tikz@decoration@name'. Perhaps
+          you misspelled it?}
+      }
+    }
+  \fi%
+}%
+
+\def\tikz@lib@dec@zpttext{0pt}%
+
+\newif\iftikz@lib@dec@temp
+\def\tikz@lib@dec@startdecoration{%
+  \pgfkeysgetvalue{/pgf/decoration/pre length}{\tikz@lib@pre}%
+  \pgfkeysgetvalue{/pgf/decoration/post length}{\tikz@lib@post}%
+  \tikz@lib@dec@tempfalse%
+  \ifx\tikz@lib@pre\tikz@lib@dec@zpttext%
+    \ifx\tikz@lib@post\tikz@lib@dec@zpttext%
+    \else%
+      \tikz@lib@dec@temptrue%
+    \fi%
+  \else%
+    \tikz@lib@dec@temptrue%
+  \fi%
+  \iftikz@lib@dec@temp%
+    \pgfmetadecoration{tikz@internal}%
+  \else%
+    \expandafter\pgfdecoration\expandafter{\expandafter{\tikz@decoration@name}{\pgfdecoratedpathlength}{}{}}%
+  \fi%
+}%
+
+\def\tikz@lib@dec@stopdecoration{%
+  \iftikz@lib@dec@temp%
+    \endpgfmetadecoration%
+  \else%
+    \endpgfdecoration%
+  \fi%
+}%
+
+
+\endinput

preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibrarydecorations.footprints.code.tex

@@ -0,0 +1,5 @@
+
+\usetikzlibrary{decorations}%
+\usepgflibrary{decorations.footprints}%
+
+\endinput

preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibrarydecorations.fractals.code.tex

@@ -0,0 +1,5 @@
+
+\usetikzlibrary{decorations}%
+\usepgflibrary{decorations.fractals}%
+
+\endinput

preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibrarydecorations.markings.code.tex

@@ -0,0 +1,22 @@
+
+\usetikzlibrary{decorations}%
+\usepgflibrary{decorations.markings}%
+
+\def\pgf@lib@dec@doarrowhead{%
+  \pgfutil@ifnextchar[{\tikz@lib@dec@doarrowhead}{\tikz@lib@dec@doarrowhead[]}%
+}%
+\def\tikz@lib@dec@doarrowhead[#1]#2{%
+  \scope[#1]
+    \pgf@lib@dec@arrowhead{1}{#2}%
+  \endscope
+}%
+\def\pgf@lib@dec@doarrowheadrev{%
+  \pgfutil@ifnextchar[{\tikz@lib@dec@doarrowheadrev}{\tikz@lib@dec@doarrowheadrev[]}%
+}%
+\def\tikz@lib@dec@doarrowheadrev[#1]#2{%
+  \scope[#1]
+    \pgf@lib@dec@arrowhead{-1}{#2}%
+  \endscope
+}%
+
+\endinput

preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibrarydecorations.pathmorphing.code.tex

@@ -0,0 +1,5 @@
+
+\usetikzlibrary{decorations}%
+\usepgflibrary{decorations.pathmorphing}%
+
+\endinput