From 39f69b5fa3db2024fbb837598be1249b3a35c3fd Mon Sep 17 00:00:00 2001
From: Jaron Kent-Dobias <jaron@kent-dobias.com>
Date: Thu, 28 Oct 2021 17:37:30 +0200
Subject: Spell check and added a reference.

---
 ising_scaling.tex | 10 ++++++----
 1 file changed, 6 insertions(+), 4 deletions(-)

(limited to 'ising_scaling.tex')

diff --git a/ising_scaling.tex b/ising_scaling.tex
index 8488f9d..2b1fb62 100644
--- a/ising_scaling.tex
+++ b/ising_scaling.tex
@@ -171,7 +171,7 @@ use $\xi=u_h|u_t|^{-\Delta}$ and $\eta=u_t|u_h|^{-1/\Delta}$.
 The analyticity of the free energy at places away from the critical point
 implies that the functions $\mathcal F_\pm$ and $\mathcal F_0$ have power-law
 expansions of their arguments about zero, the result of so-called Griffiths
-analyticity. For instance, when $u_t$ goes to zero for nonzero $u_h$ there is
+analyticity \cite{Griffiths_1967_Thermodynamic}. For instance, when $u_t$ goes to zero for nonzero $u_h$ there is
 no phase transition, and the free energy must be an analytic function of its
 arguments. It follows that $\mathcal F_0$ is analytic about zero. This is not
 the case at infinity: since
@@ -896,7 +896,7 @@ values of both are plotted.
     Free parameters in the fit of the parametric coordinate transformation and
     scaling form to known values of the scaling function series coefficients
     for $\mathcal F_\pm$. The fit at stage $n$ matches those coefficients up to
-    and including order $n$. Error estimates are difficult to quantify directly.
+    and including order $n$. Uncertainty estimates are difficult to quantify directly.
   } \label{tab:fits}
 \end{table}
 
@@ -1013,7 +1013,7 @@ Fig.~\ref{fig:phi.series}.
     The series coefficients for the scaling function $\mathcal F_-$ as a
     function of polynomial order $m$. The numeric values are from Table
     \ref{tab:data}, and those of Caselle \textit{et al.} are from the most
-    accurate scaling function listed in \cite{Caselle_2001_The}. The deviation at high polynomial order illustrates the lack of the essential singularity in Caselle's form.
+    accurate scaling function listed in \cite{Caselle_2001_The}. The deviation at high polynomial order illustrates the lack of the essential singularity in the form of Caselle \textit{et al.}.
   } \label{fig:glow.series}
 \end{figure}
 
@@ -1186,7 +1186,9 @@ the ratio.
     Sequential ratios of the series coefficients of the scaling function
     $\mathcal F_-$ as a function of inverse polynomial order $m$. The
     extrapolated $y$-intercept of this plot gives the radius of convergence of
-    the series, which should be zero due to the essential singularity (as seen in the known numeric values and in this work). Cassel {\em et al} do not incorporate the essential singularity.
+    the series, which should be zero due to the essential singularity (as seen
+    in the known numeric values and in this work). Caselle \textit{et al.} do
+    not incorporate the essential singularity.
   } \label{fig:glow.radius}
 \end{figure}
 
-- 
cgit v1.2.3-70-g09d2


From e10a0bf22228557aab3b7c797ae40083498faaa9 Mon Sep 17 00:00:00 2001
From: Jaron Kent-Dobias <jaron@kent-dobias.com>
Date: Sat, 27 May 2023 16:37:05 +0200
Subject: Move some more figures into the root directory for APS.

---
 F_higher_singularities.eps      | 343 +++++++++++++++++++++++++++++++
 F_lower_singularities.eps       | 270 ++++++++++++++++++++++++
 F_theta_singularities.eps       | 374 ++++++++++++++++++++++++++++++++++
 contour_path.eps                | 440 ++++++++++++++++++++++++++++++++++++++++
 figs/F_higher_singularities.eps | 343 -------------------------------
 figs/F_lower_singularities.eps  | 270 ------------------------
 figs/F_theta_singularities.eps  | 374 ----------------------------------
 figs/contour_path.eps           | 440 ----------------------------------------
 ising_scaling.tex               |   8 +-
 9 files changed, 1431 insertions(+), 1431 deletions(-)
 create mode 100644 F_higher_singularities.eps
 create mode 100644 F_lower_singularities.eps
 create mode 100644 F_theta_singularities.eps
 create mode 100644 contour_path.eps
 delete mode 100644 figs/F_higher_singularities.eps
 delete mode 100644 figs/F_lower_singularities.eps
 delete mode 100644 figs/F_theta_singularities.eps
 delete mode 100644 figs/contour_path.eps

(limited to 'ising_scaling.tex')

diff --git a/F_higher_singularities.eps b/F_higher_singularities.eps
new file mode 100644
index 0000000..e3d6a7e
--- /dev/null
+++ b/F_higher_singularities.eps
@@ -0,0 +1,343 @@
+%!PS-Adobe-3.0 EPSF-3.0
+%%Creator: cairo 1.15.4 (http://cairographics.org)
+%%CreationDate: Wed Jan 19 13:55:17 2022
+%%Pages: 1
+%%DocumentData: Clean7Bit
+%%LanguageLevel: 2
+%%Creator: Wolfram Mathematica 13.0.0.0 for Linux x86 (64-bit) (December 2, 2021)
+%%BoundingBox: 0 0 360 221
+%%EndComments
+%%BeginProlog
+save
+50 dict begin
+/q { gsave } bind def
+/Q { grestore } bind def
+/cm { 6 array astore concat } bind def
+/w { setlinewidth } bind def
+/J { setlinecap } bind def
+/j { setlinejoin } bind def
+/M { setmiterlimit } bind def
+/d { setdash } bind def
+/m { moveto } bind def
+/l { lineto } bind def
+/c { curveto } bind def
+/h { closepath } bind def
+/re { exch dup neg 3 1 roll 5 3 roll moveto 0 rlineto
+      0 exch rlineto 0 rlineto closepath } bind def
+/S { stroke } bind def
+/f { fill } bind def
+/f* { eofill } bind def
+/n { newpath } bind def
+/W { clip } bind def
+/W* { eoclip } bind def
+/BT { } bind def
+/ET { } bind def
+/pdfmark where { pop globaldict /?pdfmark /exec load put }
+    { globaldict begin /?pdfmark /pop load def /pdfmark
+    /cleartomark load def end } ifelse
+/BDC { mark 3 1 roll /BDC pdfmark } bind def
+/EMC { mark /EMC pdfmark } bind def
+/cairo_store_point { /cairo_point_y exch def /cairo_point_x exch def } def
+/Tj { show currentpoint cairo_store_point } bind def
+/TJ {
+  {
+    dup
+    type /stringtype eq
+    { show } { -0.001 mul 0 cairo_font_matrix dtransform rmoveto } ifelse
+  } forall
+  currentpoint cairo_store_point
+} bind def
+/cairo_selectfont { cairo_font_matrix aload pop pop pop 0 0 6 array astore
+    cairo_font exch selectfont cairo_point_x cairo_point_y moveto } bind def
+/Tf { pop /cairo_font exch def /cairo_font_matrix where
+      { pop cairo_selectfont } if } bind def
+/Td { matrix translate cairo_font_matrix matrix concatmatrix dup
+      /cairo_font_matrix exch def dup 4 get exch 5 get cairo_store_point
+      /cairo_font where { pop cairo_selectfont } if } bind def
+/Tm { 2 copy 8 2 roll 6 array astore /cairo_font_matrix exch def
+      cairo_store_point /cairo_font where { pop cairo_selectfont } if } bind def
+/g { setgray } bind def
+/rg { setrgbcolor } bind def
+/d1 { setcachedevice } bind def
+/cairo_flush_ascii85_file { cairo_ascii85_file status { cairo_ascii85_file flushfile } if } def
+/cairo_image { image cairo_flush_ascii85_file } def
+/cairo_imagemask { imagemask cairo_flush_ascii85_file } def
+%%EndProlog
+%%BeginSetup
+%%BeginResource: font f-0-0
+%!FontType1-1.1 f-0-0 1.0
+11 dict begin
+/FontName /f-0-0 def
+/PaintType 0 def
+/FontType 1 def
+/FontMatrix [0.001 0 0 0.001 0 0] readonly def
+/FontBBox {-12 -14 908 692                                   } readonly def
+/Encoding 256 array
+0 1 255 {1 index exch /.notdef put} for
+dup 73 /I put
+dup 76 /L put
+dup 82 /R put
+dup 89 /Y put
+dup 101 /e put
+dup 109 /m put
+readonly def
+currentdict end
+currentfile eexec
+f983ef0097ece636fb4a96c74d26ab84185f6dfa4a16a7a1c27bbe3f1156aea698df336d20b467
+b10e7f33846656653c5ac6962759d3056cbdb3190bac614b984bf5a132dc418192443014ba63de
+800d392b6fea026574bb2535fd7bb5338f35bf15a88ea328fdaa49670c7852e3d060f3c5d6b07f
+2ef6d0f22646c5d18e19a2ae3ee120390f6dd96f76dcf1e127de5e9299077a00c17c0d71e36e5b
+9d5ec58fceda57739a6a4214d4b79d6c48d2784b60c320323c7acddddf34db833cac0cf109f799
+69d114a330d372e5c978a66acc84e3fe5557f6240856a013ffaa0199444e5c5036f775eba4a5c5
+8cde66cf604b9aca2178431127b8a1ff7ed633a65c04600af5f573483112251ca5d188dea508ed
+e1b2455317d2f89946db9171817b252ef4aed3b4d1e2d956531eb1466794df0a360608df9ddca3
+31d2d2e2835dae9cd39f88612df7540cb9134838f4d1d7d0f988815e63e88d14438a2ae43b6c64
+be2dc4f7b2e0c6a08fddad8746441fd5ac6854ff0c5ab7f7aca25cf081d4002f9811a93d3cdd0e
+00461c900c9e0c4f58969c6373636df5e12ca751b7e06a02b752e460d25a56e1b33dc0411ddd9e
+7b458fb4ff92195044e45a4c4f7904a7044d8d7f650b213d98f76e83b77a688cc939916088b4f9
+316351e48f38913000572d64d4afabc0ac17fd4b7223a755f8b481993158b33f9a2524016d7477
+18ddb89457c416c0db81b77356fff18507f286362ac9e87ca0429ff2f1acf7da2c47c6bdeb8d3c
+dc85780c28d652b255ed19df2c7f1c293e2b4bdf5edf4f16ac3e63826fc81a6bcebd904dbea152
+fd3b2185df087937c972d9c4a501a4c7f0991d1033d353df360f862b6d64d19957837efab9f754
+4b76f75fd04448d93f7ab3efdcd67a3b9b75470a0a773a7ddfec9008c973d8c459fcfc82947e61
+7c5140a933df404ce0206a24d9b6b6eed01d8b7eeee44aa93da77f3fbb1c99652e49426f7553c1
+13eb226edbfa600fb6ce98480d508f341eb46fe90bdc9e935d369104cf68e1435eef393cbe5a6a
+efd5a9d8c610237e51e66ed3de56b37a7c59f9e3642aa04a2c3feb1b5abb201b93dea4435b152a
+462dc36f44e1bfcf3ba187d9a9f70fa6beaf5d86c022ba6ebae51edaa5c2342996c0ddae2272de
+8bac4e6ccd4c78fbec53c96b34f4331c65a2f71190129f4416757fb1c470e976533e1f06441616
+b5ff7a78767d4b03f77127ef23a399515d6872fbe8977e3964bec1cb24c25fec9b6cba05a3bf46
+be9af306047fabbb331681b6c868e4a4ee1deab5eb4b85a8eb6e1bfdf21879963c943083af8e41
+e8c6ff780f855a21a161365d196069e0ae48e5d0b919fc7739a8486c2c7a3d7e5e577d94444a88
+f74814b026e2daa92fff0388fb5daaa8ef72bd44483204465071e60635f799dd2db005d99abd51
+13861f361f8d668fe4096a495b88e511086498864a23f931cd6043a33d3d09682f051d001b3f95
+dbcfb6ad9568d4ccf870fe2b242b09cd5e0365dec74bc5b4ac844ca0f5d994762e9918c422741d
+e6babf3da5b45853b89197b1b305b8842ba7a257615aa19d73450044339f90a351f4ee83288330
+7286c63001122838f16c75a11d404ea26e4ae1f27bc81979767804594b2bc71814cc25658dd8a0
+0709c062e5fb4f4478cb108f13bb74d8db95907f94a16b2953129862c3cae5b4643a42e99893a6
+d95b8d4f8ae8f8f287e7b822a9bd0f9c7a59b283baa4c396d52e6d4144261d6f79d9ba824c235d
+60f9b23849684b89f610e3eb3d642f9113269e3639e1c69e19572609e94ad0bcc0e60000000000000000000000000000000000000000000000000000000000000000
+0000000000000000000000000000000000000000000000000000000000000000
+0000000000000000000000000000000000000000000000000000000000000000
+0000000000000000000000000000000000000000000000000000000000000000
+0000000000000000000000000000000000000000000000000000000000000000
+0000000000000000000000000000000000000000000000000000000000000000
+0000000000000000000000000000000000000000000000000000000000000000
+0000000000000000000000000000000000000000000000000000000000000000
+cleartomark
+%%EndResource
+%%BeginResource: font f-1-0
+%!FontType1-1.1 f-1-0 1.0
+11 dict begin
+/FontName /f-1-0 def
+/PaintType 0 def
+/FontType 1 def
+/FontMatrix [0.001 0 0 0.001 0 0] readonly def
+/FontBBox {29 -169 437 799                                   } readonly def
+/Encoding 256 array
+0 1 255 {1 index exch /.notdef put} for
+dup 40 /parenleft put
+dup 41 /parenright put
+readonly def
+currentdict end
+currentfile eexec
+f983ef0097ece636fb4a96c74d26ab84185f6dfa4a16a7a1c27bbe3f1156aea698df336d20b467
+b10e7f33846656653c5ac6962759d3056cbdb3190bac614b984bf5a132dc418192443014ba63de
+800d392b6fea026574bb2535fd7bb5338f35bf15a88ea328fdaa49670c7852e3d060f3c5d6b07f
+2ef6d0f22646c5d18e19a2ae3ee120390f6dd96f76dcf1e127de5e9299077a00c17c0d71e36e5b
+9d5ec58fceda57739a6a4214d4b79d6c48d2784b60c320323c7acddddf34db833cac0cf109f799
+69d114a330d372e5c978a66acc84e3fe5557f6240856a013ffaa0199444e5c5036f775eba4a5c5
+8cde66cf604b9aca2178431127b8a1ff7ed633a65c04600af5f573483112251ca90bc9cf8825c7
+41412dda705317b7cb229dd377ff3d18e94daa9ba3bbd4ccd2ecde18a1c220179cca13293a42f7
+1d167cd6ac624b8f8573fc281c165eeb093c7705f0c9d1ce383c8701d14fcde12ac700699f81e8
+412c2e7e4c95c1440662af1652abdb4ce6be4b5f976724c26d20f166e17532da87ef8b24e90d2b
+ca09313d345112c202c1d9528e8c8e15bdfd68385cef36d711b99ee54d324b8778dae18d9af490
+41fbe748f7910913a3460e4af7353d7952f1fa9fde2bb171a7717e297425e0c08ca9800b01b2f5
+d645e0dbbc3a76bdfc773c19f4917354ed597d131dcc12985dd83ff833cc665a3ed3f11ec3814b
+3a8be6d7aef97d0b12b552d8da18f6cea65a8e284355941aae2da895a0fee8c8c2d4c22664f827
+5fb1ca0fbda2da6ff7fee9a610c58ec5d0c82dbb9b890d86f03ce85b69a56821a477e957df28b4
+b7afc889cbe637525896dc572b943c7f55648deb0894a36d8a1f7cfe05e48b6abb21a9949c7070
+43ecfa2c9ed9ed591f98e5fb1581bfb12e97b35bab44504370459fd28ca0c151ded5634089598c
+3d20720000000000000000000000000000000000000000000000000000000000000000
+0000000000000000000000000000000000000000000000000000000000000000
+0000000000000000000000000000000000000000000000000000000000000000
+0000000000000000000000000000000000000000000000000000000000000000
+0000000000000000000000000000000000000000000000000000000000000000
+0000000000000000000000000000000000000000000000000000000000000000
+0000000000000000000000000000000000000000000000000000000000000000
+0000000000000000000000000000000000000000000000000000000000000000
+cleartomark
+%%EndResource
+%%BeginResource: font f-1-1
+%!FontType1-1.1 f-1-1 1.0
+11 dict begin
+/FontName /f-1-1 def
+/PaintType 0 def
+/FontType 1 def
+/FontMatrix [0.001 0 0 0.001 0 0] readonly def
+/FontBBox {-6 -207 465 799                                   } readonly def
+/Encoding 256 array
+0 1 255 {1 index exch /.notdef put} for
+dup 1 /uni03BE put
+readonly def
+currentdict end
+currentfile eexec
+f983ef0097ece636fb4a96c74d26ab84185f6dfa4a16a7a1c27bbe3f1156aea698df336d20b467
+b10e7f33846656653c5ac6962759d3056cbdb3190bac614b984bf5a132dc418192443014ba63de
+800d392b6fea026574bb2535fd7bb5338f35bf15a88ea328fdaa49670c7852e3d060f3c5d6b07f
+2ef6d0f22646c5d18e19a2ae3ee120390f6dd96f76dcf1e127de5e9299077a00c17c0d71e36e5b
+9d5ec58fceda57739a6a4214d4b79d6c48d2784b60c320323c7acddddf34db833cac0cf109f799
+69d114a330d372e5c978a66acc84e3fe5557f6240856a013ffaa0199444e5c5036f775eba4a5c5
+8cde66cf604b9aca2178431127b8a1ff7ed633a65c04600af5f573483112251cae134058d6a192
+3c6b565d778d9618b31789d664bb543a0e576f202df308890d53425311c0df16d70e7088bc233c
+2aeafd23aed96e18251b90593258f09f68b68c844c8e5bf170e06e331e14147fa538f8473eeb1e
+c84dbfec93c34173c11f0744da9bfa7cf6a3d8c4eb2a75eb71b49d69da4ade018689e722cfab11
+be4351efa968308dff1933cdf6da74c1d45ce31ed30cfd322f1554cf02839075c2488a6e43b89a
+f24d9bd7595d4fc4c07d5aa69574f2b45a692e0305a31ca8496286dde55759bacec2cf519a550c
+fc581758620e692c3d1f29b52b360ab757e8a4ed621b3b2c5ce883b037b9fd1b119dba66319bb2
+4706b3eb74ba54dfb209979bff3f44781327e8d4e7b20328f58cdea3284522496934f1cd89a9ab
+8f825cc46c51daa2ea8f85719a90e312bb07457ba2739fe15e7f59e27a646521ff053df21c2edf
+9d96735ee9d39d251bcf0113dc96ad03208d1ae62db8141146cfd99f59fcb8a10bdbf341def129
+fd5b55b7fe37f31eae75b5caf35814db82b954eeb9ce040e42be770590adeaa9a03b85f5c8e344
+bef5c97285dc20e725e2b0ecaea95a78cc672f11240e0fed510f9027f695fe53aecf49f9bdd51c
+949743af735f932804173c4d9584652fc9184b875b8cf21b4af33bdcf8580ca4ce84b48a0a40b1
+9771faa53eb86add0076d818c9d10927b64117ce25af360fa0ef5061787ff063349478ead89981
+4641ebef5cebc2b444f7497c0f9638073d57ef29982e7efcd5421544ba5a737b3527d24db03842
+aa24c1f0c002b36b8656951b8f835f2dfd1d419cdcd2e490cc73162e9163805e9cf101f7d336ea
+d0caa5b458789b0f625cc937389ec0a67f90c3c2640000000000000000000000000000000000000000000000000000000000000000
+0000000000000000000000000000000000000000000000000000000000000000
+0000000000000000000000000000000000000000000000000000000000000000
+0000000000000000000000000000000000000000000000000000000000000000
+0000000000000000000000000000000000000000000000000000000000000000
+0000000000000000000000000000000000000000000000000000000000000000
+0000000000000000000000000000000000000000000000000000000000000000
+0000000000000000000000000000000000000000000000000000000000000000
+cleartomark
+%%EndResource
+%%BeginResource: font f-2-0
+%!FontType1-1.1 f-2-0 1.0
+11 dict begin
+/FontName /f-2-0 def
+/PaintType 0 def
+/FontType 1 def
+/FontMatrix [0.001 0 0 0.001 0 0] readonly def
+/FontBBox {0 -12 363 715                                     } readonly def
+/Encoding 256 array
+0 1 255 {1 index exch /.notdef put} for
+dup 105 /i put
+readonly def
+currentdict end
+currentfile eexec
+f983ef0097ece636fb4a96c74d26ab84185f6dfa4a16a7a1c27bbe3f1156aea698df336d20b467
+b10e7f33846656653c5ac6962759d3056cbdb3190bac614b984bf5a132dc418192443014ba63de
+800d392b6fea026574bb2535fd7bb5338f35bf15a88ea328fdaa49670c7852e3d060f3c5d6b07f
+2ef6d0f22646c5d18e19a2ae3ee120390f6dd96f76dcf1e127de5e9299077a00c17c0d71e36e5b
+9d5ec58fceda57739a6a4214d4b79d6c48d2784b60c320323c7acddddf34db833cac0cf109f799
+69d114a330d372e5c978a66acc84e3fe5557f6240856a013ffaa0199444e5c5036f775eba4a5c5
+8cde66cf604b9aca2178431127b8a1ff7ed633a65c04600af5f573483112251cae134058d6a192
+3c6b565d778d9618b31789d664bb543a0e576f252e8520c2d0698c337b75c663f61d3deead2935
+71dc9621dfa39dc5f30363291678a7d9dfdeaa2de43d090fdf9945858d9b5b3a5df2a5865b3028
+dc4b7ac7fe8270eda10a09d5669f164eb5fa6e4ca848129c7f59349ba575bbdf02dfbd8f5ed330
+d9554dd1eb8b856cdef62fe801b421cc107aa678dbf1124aab4cbde909fd8611cafc587bb34560
+f3428a01d0fd050e1c1ae785787bd5c142500e345326b240d6d37c6801da6061e4be60b75cc4a0
+06ffe4ca26e456a9313b7f02bd60218dde34c309130b9ee274c413f042863100acb2ad54244397
+b1ccf64df275ba901ee414216a2d7c659e80f9eb06bcb6f8d4b9e005690000000000000000000000000000000000000000000000000000000000000000
+0000000000000000000000000000000000000000000000000000000000000000
+0000000000000000000000000000000000000000000000000000000000000000
+0000000000000000000000000000000000000000000000000000000000000000
+0000000000000000000000000000000000000000000000000000000000000000
+0000000000000000000000000000000000000000000000000000000000000000
+0000000000000000000000000000000000000000000000000000000000000000
+0000000000000000000000000000000000000000000000000000000000000000
+cleartomark
+%%EndResource
+%%EndSetup
+%%Page: 1 1
+%%BeginPageSetup
+%%PageBoundingBox: 0 0 360 221
+%%EndPageSetup
+q 0 0 360 221 rectclip
+1 0 0 -1 0 222 cm q
+0 g
+0.36 w
+0 J
+0 j
+[ 2.88 2.88] 0 d
+3.25 M 0.18 119.551 m 330.613 119.551 l S
+BT
+10.08 0 0 -10.08 336.375 122.110031 Tm
+/f-0-0 1 Tf
+(Re)Tj
+10.8 0 0 -10.8 348.045 122.110031 Tm
+/f-1-0 1 Tf
+(\()Tj
+/f-1-1 1 Tf
+<01>Tj
+/f-1-0 1 Tf
+[()-29(\))]TJ
+ET
+Q q
+165 17 1 204.762 re W n
+0 g
+0.36 w
+0 J
+0 j
+[ 2.88 2.88] 0 d
+3.25 M 165.398 221.66 m 165.398 17.441 l S
+Q q
+0 g
+BT
+10.08 0 0 -10.08 153.009375 9.12 Tm
+/f-0-0 1 Tf
+(Im)Tj
+10.8 0 0 -10.8 165.830625 9.12 Tm
+/f-1-0 1 Tf
+(\()Tj
+/f-1-1 1 Tf
+<01>Tj
+/f-1-0 1 Tf
+[()-29(\))]TJ
+ET
+Q q
+164 17 3 53 re W n
+0 g
+1.44 w
+2 J
+0 j
+[] 0.0 d
+3.25 M 165.398 68.496 m 165.398 -45.668 l S
+Q q
+164 169 3 52.762 re W n
+0 g
+1.44 w
+2 J
+0 j
+[] 0.0 d
+3.25 M 165.398 170.605 m 165.398 284.766 l S
+Q q
+0 g
+162.477 65.574 5.84 5.84 re f
+1.44 w
+2 J
+0 j
+[] 0.0 d
+3.25 M 162.477 65.574 5.84 5.84 re S
+162.477 167.684 5.84 5.844 re f
+162.477 167.684 5.84 5.844 re S
+0.36 w
+165.398 68.496 m 173.66 68.496 l S
+BT
+10.08 0 0 -10.08 177.659063 71.055015 Tm
+/f-2-0 1 Tf
+(i)Tj
+10.8 0 0 -10.8 181.319063 71.055015 Tm
+/f-1-1 1 Tf
+<01>Tj
+7.2 0 0 -7.2 186.036563 72.761265 Tm
+/f-0-0 1 Tf
+(YL)Tj
+ET
+Q Q
+showpage
+%%Trailer
+end restore
+%%EOF
diff --git a/F_lower_singularities.eps b/F_lower_singularities.eps
new file mode 100644
index 0000000..ae7d570
--- /dev/null
+++ b/F_lower_singularities.eps
@@ -0,0 +1,270 @@
+%!PS-Adobe-3.0 EPSF-3.0
+%%Creator: cairo 1.15.4 (http://cairographics.org)
+%%CreationDate: Wed Jan 19 13:55:11 2022
+%%Pages: 1
+%%DocumentData: Clean7Bit
+%%LanguageLevel: 2
+%%Creator: Wolfram Mathematica 13.0.0.0 for Linux x86 (64-bit) (December 2, 2021)
+%%BoundingBox: 0 0 360 221
+%%EndComments
+%%BeginProlog
+save
+50 dict begin
+/q { gsave } bind def
+/Q { grestore } bind def
+/cm { 6 array astore concat } bind def
+/w { setlinewidth } bind def
+/J { setlinecap } bind def
+/j { setlinejoin } bind def
+/M { setmiterlimit } bind def
+/d { setdash } bind def
+/m { moveto } bind def
+/l { lineto } bind def
+/c { curveto } bind def
+/h { closepath } bind def
+/re { exch dup neg 3 1 roll 5 3 roll moveto 0 rlineto
+      0 exch rlineto 0 rlineto closepath } bind def
+/S { stroke } bind def
+/f { fill } bind def
+/f* { eofill } bind def
+/n { newpath } bind def
+/W { clip } bind def
+/W* { eoclip } bind def
+/BT { } bind def
+/ET { } bind def
+/pdfmark where { pop globaldict /?pdfmark /exec load put }
+    { globaldict begin /?pdfmark /pop load def /pdfmark
+    /cleartomark load def end } ifelse
+/BDC { mark 3 1 roll /BDC pdfmark } bind def
+/EMC { mark /EMC pdfmark } bind def
+/cairo_store_point { /cairo_point_y exch def /cairo_point_x exch def } def
+/Tj { show currentpoint cairo_store_point } bind def
+/TJ {
+  {
+    dup
+    type /stringtype eq
+    { show } { -0.001 mul 0 cairo_font_matrix dtransform rmoveto } ifelse
+  } forall
+  currentpoint cairo_store_point
+} bind def
+/cairo_selectfont { cairo_font_matrix aload pop pop pop 0 0 6 array astore
+    cairo_font exch selectfont cairo_point_x cairo_point_y moveto } bind def
+/Tf { pop /cairo_font exch def /cairo_font_matrix where
+      { pop cairo_selectfont } if } bind def
+/Td { matrix translate cairo_font_matrix matrix concatmatrix dup
+      /cairo_font_matrix exch def dup 4 get exch 5 get cairo_store_point
+      /cairo_font where { pop cairo_selectfont } if } bind def
+/Tm { 2 copy 8 2 roll 6 array astore /cairo_font_matrix exch def
+      cairo_store_point /cairo_font where { pop cairo_selectfont } if } bind def
+/g { setgray } bind def
+/rg { setrgbcolor } bind def
+/d1 { setcachedevice } bind def
+/cairo_flush_ascii85_file { cairo_ascii85_file status { cairo_ascii85_file flushfile } if } def
+/cairo_image { image cairo_flush_ascii85_file } def
+/cairo_imagemask { imagemask cairo_flush_ascii85_file } def
+%%EndProlog
+%%BeginSetup
+%%BeginResource: font f-0-0
+%!FontType1-1.1 f-0-0 1.0
+11 dict begin
+/FontName /f-0-0 def
+/PaintType 0 def
+/FontType 1 def
+/FontMatrix [0.001 0 0 0.001 0 0] readonly def
+/FontBBox {0 -14 908 692                                     } readonly def
+/Encoding 256 array
+0 1 255 {1 index exch /.notdef put} for
+dup 73 /I put
+dup 82 /R put
+dup 101 /e put
+dup 109 /m put
+readonly def
+currentdict end
+currentfile eexec
+f983ef0097ece636fb4a96c74d26ab84185f6dfa4a16a7a1c27bbe3f1156aea698df336d20b467
+b10e7f33846656653c5ac6962759d3056cbdb3190bac614b984bf5a132dc418192443014ba63de
+800d392b6fea026574bb2535fd7bb5338f35bf15a88ea328fdaa49670c7852e3d060f3c5d6b07f
+2ef6d0f22646c5d18e19a2ae3ee120390f6dd96f76dcf1e127de5e9299077a00c17c0d71e36e5b
+9d5ec58fceda57739a6a4214d4b79d6c48d2784b60c320323c7acddddf34db833cac0cf109f799
+69d114a330d372e5c978a66acc84e3fe5557f6240856a013ffaa0199444e5c5036f775eba4a5c5
+8cde66cf604b9aca2178431127b8a1ff7ed633a65c04600af5f573483112251cabe8722c0ba224
+7e4445af50cf2457d0f320e3c97746456087766b4bf11115560ce328711eca3bd110d9edf8f723
+7690411035c2d2a4529eceb3758e9dfdf69937c82634682ddec349213e6cdca1236ff1e59fd7ad
+c509a9f3c257841b8053a86b38d617d963b24dfb3767bfc9b4af0288c9b0b8e2572d16601fc539
+50419b779278a6ee6aa2c6f6e88f16020db6e348845fd5b2cd9ac2bb9cc9caa74bac30ab845da5
+f651fffe8b245f374569b60b2520d5b091c2895daa06f7cacffa423bc29ca3a939660aef03f4ba
+db6c051bab9e97aa6f8b3423aee96ff61f682293fdb336288dbb885c46c5c6d7ca5c5a0cf84a99
+4b1ef4f098cdceee4559f76b71375ac1e48de97bc26d04e944bd8f7723aaca9bdeb0a55b4d8e30
+b9169a69c8b151f7e913240de4e7614c0ce99885f8de5ae8d0c7602bdba359c79247126be04fa0
+4837a74d4b1829aba24a81ace9429198af5c03ce00c992b95216dab9619da47da7550eca0ff6cd
+0ebc575021f16decb7f0d945e2c73764f06e1781806305825422f0f7ad20cee7de432128300693
+599dbdafc575e2f472140a927b4552e1cd714bd09871feab74613bf38b4117e1b2c870998d1584
+50ae3c9c1b184d5529d7092e102d713e1e4a8d02eb0fb3edc7ef054b7fbe323e488fbcf700dac6
+058c3eeb18d59888e42247d792f3cff694e14a0b69965054b8e811dc8ae391c9be575648546fef
+0365caa0b5334da60343169e20c6b1b8d51c5fbe17cfca3ec7f3bd1c61d09838b717c08ccfcbda
+2a43ce0a730162c3285d5185e5fa3f8c6aaa204a403cdae550e565dcaf3816e4f19a66fee5bb4d
+e532d49827c5c811b8c6effa17be7f7f897390f48ca0d11588bc17af153bec904639fcce603e9a
+fb7417deeba06beb6901c0fba586004121e1aa2dcab890d83326fd7ffca74c35e64a22c9434ef6
+7d7496180137f9c8705089856e54a802d541062de40941e37319ed189b6dd27b69783befae9725
+88dacdb39bfe000a0789e90bfdcc7a2187dbff723ba8a74bb2ececfee0a9ea34b01434890000000000000000000000000000000000000000000000000000000000000000
+0000000000000000000000000000000000000000000000000000000000000000
+0000000000000000000000000000000000000000000000000000000000000000
+0000000000000000000000000000000000000000000000000000000000000000
+0000000000000000000000000000000000000000000000000000000000000000
+0000000000000000000000000000000000000000000000000000000000000000
+0000000000000000000000000000000000000000000000000000000000000000
+0000000000000000000000000000000000000000000000000000000000000000
+cleartomark
+%%EndResource
+%%BeginResource: font f-1-0
+%!FontType1-1.1 f-1-0 1.0
+11 dict begin
+/FontName /f-1-0 def
+/PaintType 0 def
+/FontType 1 def
+/FontMatrix [0.001 0 0 0.001 0 0] readonly def
+/FontBBox {29 -169 437 799                                   } readonly def
+/Encoding 256 array
+0 1 255 {1 index exch /.notdef put} for
+dup 40 /parenleft put
+dup 41 /parenright put
+readonly def
+currentdict end
+currentfile eexec
+f983ef0097ece636fb4a96c74d26ab84185f6dfa4a16a7a1c27bbe3f1156aea698df336d20b467
+b10e7f33846656653c5ac6962759d3056cbdb3190bac614b984bf5a132dc418192443014ba63de
+800d392b6fea026574bb2535fd7bb5338f35bf15a88ea328fdaa49670c7852e3d060f3c5d6b07f
+2ef6d0f22646c5d18e19a2ae3ee120390f6dd96f76dcf1e127de5e9299077a00c17c0d71e36e5b
+9d5ec58fceda57739a6a4214d4b79d6c48d2784b60c320323c7acddddf34db833cac0cf109f799
+69d114a330d372e5c978a66acc84e3fe5557f6240856a013ffaa0199444e5c5036f775eba4a5c5
+8cde66cf604b9aca2178431127b8a1ff7ed633a65c04600af5f573483112251ca90bc9cf8825c7
+41412dda705317b7cb229dd377ff3d18e94daa9ba3bbd4ccd2ecde18a1c220179cca13293a42f7
+1d167cd6ac624b8f8573fc281c165eeb093c7705f0c9d1ce383c8701d14fcde12ac700699f81e8
+412c2e7e4c95c1440662af1652abdb4ce6be4b5f976724c26d20f166e17532da87ef8b24e90d2b
+ca09313d345112c202c1d9528e8c8e15bdfd68385cef36d711b99ee54d324b8778dae18d9af490
+41fbe748f7910913a3460e4af7353d7952f1fa9fde2bb171a7717e297425e0c08ca9800b01b2f5
+d645e0dbbc3a76bdfc773c19f4917354ed597d131dcc12985dd83ff833cc665a3ed3f11ec3814b
+3a8be6d7aef97d0b12b552d8da18f6cea65a8e284355941aae2da895a0fee8c8c2d4c22664f827
+5fb1ca0fbda2da6ff7fee9a610c58ec5d0c82dbb9b890d86f03ce85b69a56821a477e957df28b4
+b7afc889cbe637525896dc572b943c7f55648deb0894a36d8a1f7cfe05e48b6abb21a9949c7070
+43ecfa2c9ed9ed591f98e5fb1581bfb12e97b35bab44504370459fd28ca0c151ded5634089598c
+3d20720000000000000000000000000000000000000000000000000000000000000000
+0000000000000000000000000000000000000000000000000000000000000000
+0000000000000000000000000000000000000000000000000000000000000000
+0000000000000000000000000000000000000000000000000000000000000000
+0000000000000000000000000000000000000000000000000000000000000000
+0000000000000000000000000000000000000000000000000000000000000000
+0000000000000000000000000000000000000000000000000000000000000000
+0000000000000000000000000000000000000000000000000000000000000000
+cleartomark
+%%EndResource
+%%BeginResource: font f-1-1
+%!FontType1-1.1 f-1-1 1.0
+11 dict begin
+/FontName /f-1-1 def
+/PaintType 0 def
+/FontType 1 def
+/FontMatrix [0.001 0 0 0.001 0 0] readonly def
+/FontBBox {-6 -207 465 799                                   } readonly def
+/Encoding 256 array
+0 1 255 {1 index exch /.notdef put} for
+dup 1 /uni03BE put
+readonly def
+currentdict end
+currentfile eexec
+f983ef0097ece636fb4a96c74d26ab84185f6dfa4a16a7a1c27bbe3f1156aea698df336d20b467
+b10e7f33846656653c5ac6962759d3056cbdb3190bac614b984bf5a132dc418192443014ba63de
+800d392b6fea026574bb2535fd7bb5338f35bf15a88ea328fdaa49670c7852e3d060f3c5d6b07f
+2ef6d0f22646c5d18e19a2ae3ee120390f6dd96f76dcf1e127de5e9299077a00c17c0d71e36e5b
+9d5ec58fceda57739a6a4214d4b79d6c48d2784b60c320323c7acddddf34db833cac0cf109f799
+69d114a330d372e5c978a66acc84e3fe5557f6240856a013ffaa0199444e5c5036f775eba4a5c5
+8cde66cf604b9aca2178431127b8a1ff7ed633a65c04600af5f573483112251cae134058d6a192
+3c6b565d778d9618b31789d664bb543a0e576f202df308890d53425311c0df16d70e7088bc233c
+2aeafd23aed96e18251b90593258f09f68b68c844c8e5bf170e06e331e14147fa538f8473eeb1e
+c84dbfec93c34173c11f0744da9bfa7cf6a3d8c4eb2a75eb71b49d69da4ade018689e722cfab11
+be4351efa968308dff1933cdf6da74c1d45ce31ed30cfd322f1554cf02839075c2488a6e43b89a
+f24d9bd7595d4fc4c07d5aa69574f2b45a692e0305a31ca8496286dde55759bacec2cf519a550c
+fc581758620e692c3d1f29b52b360ab757e8a4ed621b3b2c5ce883b037b9fd1b119dba66319bb2
+4706b3eb74ba54dfb209979bff3f44781327e8d4e7b20328f58cdea3284522496934f1cd89a9ab
+8f825cc46c51daa2ea8f85719a90e312bb07457ba2739fe15e7f59e27a646521ff053df21c2edf
+9d96735ee9d39d251bcf0113dc96ad03208d1ae62db8141146cfd99f59fcb8a10bdbf341def129
+fd5b55b7fe37f31eae75b5caf35814db82b954eeb9ce040e42be770590adeaa9a03b85f5c8e344
+bef5c97285dc20e725e2b0ecaea95a78cc672f11240e0fed510f9027f695fe53aecf49f9bdd51c
+949743af735f932804173c4d9584652fc9184b875b8cf21b4af33bdcf8580ca4ce84b48a0a40b1
+9771faa53eb86add0076d818c9d10927b64117ce25af360fa0ef5061787ff063349478ead89981
+4641ebef5cebc2b444f7497c0f9638073d57ef29982e7efcd5421544ba5a737b3527d24db03842
+aa24c1f0c002b36b8656951b8f835f2dfd1d419cdcd2e490cc73162e9163805e9cf101f7d336ea
+d0caa5b458789b0f625cc937389ec0a67f90c3c2640000000000000000000000000000000000000000000000000000000000000000
+0000000000000000000000000000000000000000000000000000000000000000
+0000000000000000000000000000000000000000000000000000000000000000
+0000000000000000000000000000000000000000000000000000000000000000
+0000000000000000000000000000000000000000000000000000000000000000
+0000000000000000000000000000000000000000000000000000000000000000
+0000000000000000000000000000000000000000000000000000000000000000
+0000000000000000000000000000000000000000000000000000000000000000
+cleartomark
+%%EndResource
+%%EndSetup
+%%Page: 1 1
+%%BeginPageSetup
+%%PageBoundingBox: 0 0 360 221
+%%EndPageSetup
+q 0 0 360 221 rectclip
+1 0 0 -1 0 222 cm q
+0 g
+0.36 w
+0 J
+0 j
+[ 2.88 2.88] 0 d
+3.25 M 0.18 119.551 m 330.613 119.551 l S
+BT
+10.08 0 0 -10.08 336.375 122.110031 Tm
+/f-0-0 1 Tf
+(Re)Tj
+10.8 0 0 -10.8 348.045 122.110031 Tm
+/f-1-0 1 Tf
+(\()Tj
+/f-1-1 1 Tf
+<01>Tj
+/f-1-0 1 Tf
+[()-29(\))]TJ
+ET
+Q q
+165 17 1 204.762 re W n
+0 g
+0.36 w
+0 J
+0 j
+[ 2.88 2.88] 0 d
+3.25 M 165.398 221.66 m 165.398 17.441 l S
+Q q
+0 g
+BT
+10.08 0 0 -10.08 153.009375 9.12 Tm
+/f-0-0 1 Tf
+(Im)Tj
+10.8 0 0 -10.8 165.830625 9.12 Tm
+/f-1-0 1 Tf
+(\()Tj
+/f-1-1 1 Tf
+<01>Tj
+/f-1-0 1 Tf
+[()-29(\))]TJ
+ET
+1.44 w
+2 J
+0 j
+[] 0.0 d
+3.25 M 0.18 119.551 m 165.398 119.551 l S
+169.527 119.551 m 169.527 118.453 169.094 117.402 168.316 116.629 c 167.543
+ 115.855 166.492 115.418 165.398 115.418 c 164.301 115.418 163.25 115.855
+ 162.477 116.629 c 161.703 117.402 161.266 118.453 161.266 119.551 c 161.266
+ 120.645 161.703 121.695 162.477 122.469 c 163.25 123.246 164.301 123.68
+ 165.398 123.68 c 166.492 123.68 167.543 123.246 168.316 122.469 c 169.094
+ 121.695 169.527 120.645 169.527 119.551 c h
+169.527 119.551 m f*
+Q Q
+showpage
+%%Trailer
+end restore
+%%EOF
diff --git a/F_theta_singularities.eps b/F_theta_singularities.eps
new file mode 100644
index 0000000..cba0e16
--- /dev/null
+++ b/F_theta_singularities.eps
@@ -0,0 +1,374 @@
+%!PS-Adobe-3.0 EPSF-3.0
+%%Creator: cairo 1.15.4 (http://cairographics.org)
+%%CreationDate: Tue May 16 17:20:36 2023
+%%Pages: 1
+%%DocumentData: Clean7Bit
+%%LanguageLevel: 2
+%%Creator: Wolfram Mathematica 13.2.1.0 for Linux x86 (64-bit) (January 31, 2023)
+%%BoundingBox: 0 0 360 220
+%%EndComments
+%%BeginProlog
+save
+50 dict begin
+/q { gsave } bind def
+/Q { grestore } bind def
+/cm { 6 array astore concat } bind def
+/w { setlinewidth } bind def
+/J { setlinecap } bind def
+/j { setlinejoin } bind def
+/M { setmiterlimit } bind def
+/d { setdash } bind def
+/m { moveto } bind def
+/l { lineto } bind def
+/c { curveto } bind def
+/h { closepath } bind def
+/re { exch dup neg 3 1 roll 5 3 roll moveto 0 rlineto
+      0 exch rlineto 0 rlineto closepath } bind def
+/S { stroke } bind def
+/f { fill } bind def
+/f* { eofill } bind def
+/n { newpath } bind def
+/W { clip } bind def
+/W* { eoclip } bind def
+/BT { } bind def
+/ET { } bind def
+/pdfmark where { pop globaldict /?pdfmark /exec load put }
+    { globaldict begin /?pdfmark /pop load def /pdfmark
+    /cleartomark load def end } ifelse
+/BDC { mark 3 1 roll /BDC pdfmark } bind def
+/EMC { mark /EMC pdfmark } bind def
+/cairo_store_point { /cairo_point_y exch def /cairo_point_x exch def } def
+/Tj { show currentpoint cairo_store_point } bind def
+/TJ {
+  {
+    dup
+    type /stringtype eq
+    { show } { -0.001 mul 0 cairo_font_matrix dtransform rmoveto } ifelse
+  } forall
+  currentpoint cairo_store_point
+} bind def
+/cairo_selectfont { cairo_font_matrix aload pop pop pop 0 0 6 array astore
+    cairo_font exch selectfont cairo_point_x cairo_point_y moveto } bind def
+/Tf { pop /cairo_font exch def /cairo_font_matrix where
+      { pop cairo_selectfont } if } bind def
+/Td { matrix translate cairo_font_matrix matrix concatmatrix dup
+      /cairo_font_matrix exch def dup 4 get exch 5 get cairo_store_point
+      /cairo_font where { pop cairo_selectfont } if } bind def
+/Tm { 2 copy 8 2 roll 6 array astore /cairo_font_matrix exch def
+      cairo_store_point /cairo_font where { pop cairo_selectfont } if } bind def
+/g { setgray } bind def
+/rg { setrgbcolor } bind def
+/d1 { setcachedevice } bind def
+/cairo_flush_ascii85_file { cairo_ascii85_file status { cairo_ascii85_file flushfile } if } def
+/cairo_image { image cairo_flush_ascii85_file } def
+/cairo_imagemask { imagemask cairo_flush_ascii85_file } def
+%%EndProlog
+%%BeginSetup
+%%BeginResource: font f-0-0
+%!FontType1-1.1 f-0-0 1.0
+11 dict begin
+/FontName /f-0-0 def
+/PaintType 0 def
+/FontType 1 def
+/FontMatrix [0.001 0 0 0.001 0 0] readonly def
+/FontBBox {-12 -14 908 692                                   } readonly def
+/Encoding 256 array
+0 1 255 {1 index exch /.notdef put} for
+dup 48 /zero put
+dup 73 /I put
+dup 76 /L put
+dup 82 /R put
+dup 89 /Y put
+dup 101 /e put
+dup 109 /m put
+readonly def
+currentdict end
+currentfile eexec
+f983ef0097ece636fb4a96c74d26ab84185f6dfa4a16a7a1c27bbe3f1156aea698df336d20b467
+b10e7f33846656653c5ac6962759d3056cbdb3190bac614b984bf5a132dc418192443014ba63de
+800d392b6fea026574bb2535fd7bb5338f35bf15a88ea328fdaa49670c7852e3d060f3c5d6b07f
+2ef6d0f22646c5d18e19a2ae3ee120390f6dd96f76dcf1e127de5e9299077a00c17c0d71e36e5b
+9d5ec58fceda57739a6a4214d4b79d6c48d2784b60c320323c7acddddf34db833cac0cf109f799
+69d114a330d372e5c978a66acc84e3fe5557f6240856a013ffaa0199444e5c5036f775eba4a5c5
+8cde66cf604b9aca2178431127b8a1ff7ed633a65c04600af5f573483112251ca40352c6e2284e
+344947523a70f7b109147467f7576cb1df156dca2f25ccb577c1669626620a113ccdc0d69bb530
+dcedcb09d669e42789d3d1f1eb2fba73343f65132cb03065d412c4d987b79778555f98cbc72ab7
+18a72c35e371bf684a718b599d9f12c1a856afb05fa3bd876d6a55dcc6279feec01485b499c3da
+d50b200814e31ce340178663202f0a0324b15a23d545a665ada375c999b9af688f6f64738c2b03
+3fad0ff51c135ab5fc976cac8f6ee6fd117af76aede659c3d7c3ef848e783a3d7fc2ffd6dfb65d
+6fec08c4a48386ae22093696e4a4149206687406201494f7c92d83695ede02da0ec2efc745388b
+d4e96b9bf02196c1313f7b64670b3012e1b26b62b4c4398f62988c452011a3012866807ac3e958
+f6a33e22de6dad25663512af2f744cb4b2bccf96491c7dabfa4a6f3809714ce5e12c0ec56411de
+8d2d1ce34f9869137188615c0f4fbdfbea4b6aa825293167df8a44ecd5367cc0d134374c602f68
+cb24646d0a40cd42b9eaaa594b27274ae56eca9966b295b52c551e9431db92a8490105b9fca3cf
+abf2e646e6178f99068ffc46e80d0e6b91f6f7753ef194c42e47f2e32cfdbeff85b184ae87b96c
+ba03c00d2bb80c124412d6eac22d919a886efaafd1e1f0539f0b2277d7a3a570c352d18e8b9098
+262a6012482668a2836e6c631e98f1ffdfbd7e6a8327c434da366e42b10b3a04e6020dbad97dbf
+44a4eeb858298517e1b653d5719207f977d26cb9faf9285db28ec7bb55ecdf88173ed6a7542538
+75b780cffa546283ca777009c8bde4c70cd590dd3eca81b89e295c43771d95b90337e38f8f9d62
+501c3f0250ee10607517107eb9b8686aa2b2e73618e6ec508658efdfd4a9fbeff0a5f794ecb851
+81b07fb69e57d0ba45b34b1ddf3985403bf1ddbe9e24e73214cb9e3417f1569784c7585e54ce17
+993a0b1834c6e8641e48f9d2ed82931b358ce1638f893f198549802d03b5f77c30cdb701565094
+9cbc86327e59767775ffe0232e8fb09d9a865d66031371a7c4f279e83b7bbd2a9d3d5c04b876de
+303044b11569247c0a341892b60d49bf5a3d90cff8ecb498d5221203b27e9f7a0e2a0f5c83b803
+141289b187e0e40330f366ffe1889280fe6e24c8fe248cdd7b505c38a12f9aea4e0604d3a39b85
+dfa73f752e4deea83932b5b06717fe4ff53bc029968c48bf2eb97e7a4e0e462e6524fa833c2544
+99918cfc9b5c58f63e8bafb50d95ca777708fb85e9fd4babeb223ba13b0d5325efaf7813ead314
+ba40c2317c875af7430deaab519f75944b416da03bc21b407842090e3499d799ed64c606ae45cc
+de54f08502d814e5cd8cb51c31d0c7c591ea9e77342183be87d82d0bdbccf16c8edef1c1499d14
+4bff2d5ba6173f20939c2f5662bdb688061117662e55fa0d8aa7080bdc88b7a24b462ccffc833e
+1e75fd5537be5f7e7079349eacdec1709dd1889595a5092327dbbce7a3a8fca00d74fce608e932
+9721f45d89f7ccc9ee55a8f4082b95ef9fe1787ce123cdddbb83af12376b602e43b5a8cfcf4550
+0e418a92789eea9e01719ad69ffd7ed668660165e0d959ec6695fac6f428d6d777d8610000000000000000000000000000000000000000000000000000000000000000
+0000000000000000000000000000000000000000000000000000000000000000
+0000000000000000000000000000000000000000000000000000000000000000
+0000000000000000000000000000000000000000000000000000000000000000
+0000000000000000000000000000000000000000000000000000000000000000
+0000000000000000000000000000000000000000000000000000000000000000
+0000000000000000000000000000000000000000000000000000000000000000
+0000000000000000000000000000000000000000000000000000000000000000
+cleartomark
+%%EndResource
+%%BeginResource: font f-1-0
+%!FontType1-1.1 f-1-0 1.0
+11 dict begin
+/FontName /f-1-0 def
+/PaintType 0 def
+/FontType 1 def
+/FontMatrix [0.001 0 0 0.001 0 0] readonly def
+/FontBBox {29 -169 437 799                                   } readonly def
+/Encoding 256 array
+0 1 255 {1 index exch /.notdef put} for
+dup 40 /parenleft put
+dup 41 /parenright put
+readonly def
+currentdict end
+currentfile eexec
+f983ef0097ece636fb4a96c74d26ab84185f6dfa4a16a7a1c27bbe3f1156aea698df336d20b467
+b10e7f33846656653c5ac6962759d3056cbdb3190bac614b984bf5a132dc418192443014ba63de
+800d392b6fea026574bb2535fd7bb5338f35bf15a88ea328fdaa49670c7852e3d060f3c5d6b07f
+2ef6d0f22646c5d18e19a2ae3ee120390f6dd96f76dcf1e127de5e9299077a00c17c0d71e36e5b
+9d5ec58fceda57739a6a4214d4b79d6c48d2784b60c320323c7acddddf34db833cac0cf109f799
+69d114a330d372e5c978a66acc84e3fe5557f6240856a013ffaa0199444e5c5036f775eba4a5c5
+8cde66cf604b9aca2178431127b8a1ff7ed633a65c04600af5f573483112251ca90bc9cf8825c7
+41412dda705317b7cb229dd377ff3d18e94daa9ba3bbd4ccd2ecde18a1c220179cca13293a42f7
+1d167cd6ac624b8f8573fc281c165eeb093c7705f0c9d1ce383c8701d14fcde12ac700699f81e8
+412c2e7e4c95c1440662af1652abdb4ce6be4b5f976724c26d20f166e17532da87ef8b24e90d2b
+ca09313d345112c202c1d9528e8c8e15bdfd68385cef36d711b99ee54d324b8778dae18d9af490
+41fbe748f7910913a3460e4af7353d7952f1fa9fde2bb171a7717e297425e0c08ca9800b01b2f5
+d645e0dbbc3a76bdfc773c19f4917354ed597d131dcc12985dd83ff833cc665a3ed3f11ec3814b
+3a8be6d7aef97d0b12b552d8da18f6cea65a8e284355941aae2da895a0fee8c8c2d4c22664f827
+5fb1ca0fbda2da6ff7fee9a610c58ec5d0c82dbb9b890d86f03ce85b69a56821a477e957df28b4
+b7afc889cbe637525896dc572b943c7f55648deb0894a36d8a1f7cfe05e48b6abb21a9949c7070
+43ecfa2c9ed9ed591f98e5fb1581bfb12e97b35bab44504370459fd28ca0c151ded5634089598c
+3d20720000000000000000000000000000000000000000000000000000000000000000
+0000000000000000000000000000000000000000000000000000000000000000
+0000000000000000000000000000000000000000000000000000000000000000
+0000000000000000000000000000000000000000000000000000000000000000
+0000000000000000000000000000000000000000000000000000000000000000
+0000000000000000000000000000000000000000000000000000000000000000
+0000000000000000000000000000000000000000000000000000000000000000
+0000000000000000000000000000000000000000000000000000000000000000
+cleartomark
+%%EndResource
+%%BeginResource: font f-1-1
+%!FontType1-1.1 f-1-1 1.0
+11 dict begin
+/FontName /f-1-1 def
+/PaintType 0 def
+/FontType 1 def
+/FontMatrix [0.001 0 0 0.001 0 0] readonly def
+/FontBBox {28 -13 453 799                                    } readonly def
+/Encoding 256 array
+0 1 255 {1 index exch /.notdef put} for
+dup 1 /uni03B8 put
+readonly def
+currentdict end
+currentfile eexec
+f983ef0097ece636fb4a96c74d26ab84185f6dfa4a16a7a1c27bbe3f1156aea698df336d20b467
+b10e7f33846656653c5ac6962759d3056cbdb3190bac614b984bf5a132dc418192443014ba63de
+800d392b6fea026574bb2535fd7bb5338f35bf15a88ea328fdaa49670c7852e3d060f3c5d6b07f
+2ef6d0f22646c5d18e19a2ae3ee120390f6dd96f76dcf1e127de5e9299077a00c17c0d71e36e5b
+9d5ec58fceda57739a6a4214d4b79d6c48d2784b60c320323c7acddddf34db833cac0cf109f799
+69d114a330d372e5c978a66acc84e3fe5557f6240856a013ffaa0199444e5c5036f775eba4a5c5
+8cde66cf604b9aca2178431127b8a1ff7ed633a65c04600af5f573483112251cae134058d6a192
+3c6b565d778d9618b31789d664bb543a0e576f202df308890d53425311c0df16d70e7088bc233c
+2aeafd23aed96e18251b90593258f09f68b68c844c8e5bf170e06e331e14147fa538f8473eeb1e
+c84dbfec93c3410e50135635b99de6891224a561e7c815e270995932d4ca76c8cc14b02767bb66
+7e6acad1ab52cbc965dc9fc5d35b7f55bd68178f09c7128011331eb172346c01b77767a131365b
+3cb1e76bf2ef8772818a52fde15db663b8b91d9d22148c044c1f17c084466eee12d35401b0d206
+447bd9cb8b6e927f74a828d01e7ce0e8504701d21d52e83a0f908b3eaf18af033d7fdc4519160d
+a1f3998dc14198ecb66970ab1422655946606979ebc3920ec6406caae936b284318ce59d7fd021
+6da6916dccf7cddaa08c95fe84fe0a36eff860ec858faee6eae9b234fd7f6b7922b6407fe66548
+4ee8a12cf4b24800049489170c1c089065cfd05e7611f514854ffb249e79b19db4e86d95818819
+599eccc923f9ec10ebcf73f55e7828ba032aff285278971bd99c0a3ddf0000000000000000000000000000000000000000000000000000000000000000
+0000000000000000000000000000000000000000000000000000000000000000
+0000000000000000000000000000000000000000000000000000000000000000
+0000000000000000000000000000000000000000000000000000000000000000
+0000000000000000000000000000000000000000000000000000000000000000
+0000000000000000000000000000000000000000000000000000000000000000
+0000000000000000000000000000000000000000000000000000000000000000
+0000000000000000000000000000000000000000000000000000000000000000
+cleartomark
+%%EndResource
+%%BeginResource: font f-2-0
+%!FontType1-1.1 f-2-0 1.0
+11 dict begin
+/FontName /f-2-0 def
+/PaintType 0 def
+/FontType 1 def
+/FontMatrix [0.001 0 0 0.001 0 0] readonly def
+/FontBBox {0 -12 363 715                                     } readonly def
+/Encoding 256 array
+0 1 255 {1 index exch /.notdef put} for
+dup 105 /i put
+readonly def
+currentdict end
+currentfile eexec
+f983ef0097ece636fb4a96c74d26ab84185f6dfa4a16a7a1c27bbe3f1156aea698df336d20b467
+b10e7f33846656653c5ac6962759d3056cbdb3190bac614b984bf5a132dc418192443014ba63de
+800d392b6fea026574bb2535fd7bb5338f35bf15a88ea328fdaa49670c7852e3d060f3c5d6b07f
+2ef6d0f22646c5d18e19a2ae3ee120390f6dd96f76dcf1e127de5e9299077a00c17c0d71e36e5b
+9d5ec58fceda57739a6a4214d4b79d6c48d2784b60c320323c7acddddf34db833cac0cf109f799
+69d114a330d372e5c978a66acc84e3fe5557f6240856a013ffaa0199444e5c5036f775eba4a5c5
+8cde66cf604b9aca2178431127b8a1ff7ed633a65c04600af5f573483112251cae134058d6a192
+3c6b565d778d9618b31789d664bb543a0e576f252e8520c2d0698c337b75c663f61d3deead2935
+71dc9621dfa39dc5f30363291678a7d9dfdeaa2de43d090fdf9945858d9b5b3a5df2a5865b3028
+dc4b7ac7fe8270eda10a09d5669f164eb5fa6e4ca848129c7f59349ba575bbdf02dfbd8f5ed330
+d9554dd1eb8b856cdef62fe801b421cc107aa678dbf1124aab4cbde909fd8611cafc587bb34560
+f3428a01d0fd050e1c1ae785787bd5c142500e345326b240d6d37c6801da6061e4be60b75cc4a0
+06ffe4ca26e456a9313b7f02bd60218dde34c309130b9ee274c413f042863100acb2ad54244397
+b1ccf64df275ba901ee414216a2d7c659e80f9eb06bcb6f8d4b9e005690000000000000000000000000000000000000000000000000000000000000000
+0000000000000000000000000000000000000000000000000000000000000000
+0000000000000000000000000000000000000000000000000000000000000000
+0000000000000000000000000000000000000000000000000000000000000000
+0000000000000000000000000000000000000000000000000000000000000000
+0000000000000000000000000000000000000000000000000000000000000000
+0000000000000000000000000000000000000000000000000000000000000000
+0000000000000000000000000000000000000000000000000000000000000000
+cleartomark
+%%EndResource
+%%EndSetup
+%%Page: 1 1
+%%BeginPageSetup
+%%PageBoundingBox: 0 0 360 220
+%%EndPageSetup
+q 0 0 360 220 rectclip
+1 0 0 -1 0 221 cm q
+0 g
+0.36 w
+0 J
+0 j
+[ 2.88 2.88] 0 d
+3.25 M 0.18 118.234 m 330.754 118.234 l S
+BT
+10.08 0 0 -10.08 336.51375 121.472907 Tm
+/f-0-0 1 Tf
+(Re)Tj
+10.8 0 0 -10.8 348.18375 121.472907 Tm
+/f-1-0 1 Tf
+(\()Tj
+/f-1-1 1 Tf
+<01>Tj
+/f-1-0 1 Tf
+[()-14(\))]TJ
+ET
+Q q
+165 16 1 204.801 re W n
+0 g
+0.36 w
+0 J
+0 j
+[ 2.88 2.88] 0 d
+3.25 M 165.469 220.387 m 165.469 16.078 l S
+Q q
+0 g
+BT
+10.08 0 0 -10.08 153.148125 9.12 Tm
+/f-0-0 1 Tf
+(Im)Tj
+10.8 0 0 -10.8 165.969375 9.12 Tm
+/f-1-0 1 Tf
+(\()Tj
+/f-1-1 1 Tf
+<01>Tj
+/f-1-0 1 Tf
+[()-14(\))]TJ
+ET
+Q q
+164 16 3 52 re W n
+0 g
+1.44 w
+2 J
+0 j
+[] 0.0 d
+3.25 M 165.469 67.156 m 165.469 -47.055 l S
+Q q
+164 168 3 52.801 re W n
+0 g
+1.44 w
+2 J
+0 j
+[] 0.0 d
+3.25 M 165.469 169.309 m 165.469 283.52 l S
+Q q
+0 g
+162.547 64.234 5.844 5.844 re f
+162.547 166.387 5.844 5.844 re f
+1.44 w
+2 J
+0 j
+[] 0.0 d
+3.25 M 0.18 118.234 m 41.5 118.234 l S
+45.633 118.234 m 45.633 117.137 45.199 116.086 44.422 115.312 c 43.648 
+114.535 42.598 114.102 41.5 114.102 c 40.406 114.102 39.355 114.535 38.578
+ 115.312 c 37.805 116.086 37.371 117.137 37.371 118.234 c 37.371 119.328
+ 37.805 120.379 38.578 121.156 c 39.355 121.93 40.406 122.363 41.5 122.363
+ c 42.598 122.363 43.648 121.93 44.422 121.156 c 45.199 120.379 45.633 119.328
+ 45.633 118.234 c h
+45.633 118.234 m f*
+Q q
+288 117 43 2 re W n
+0 g
+1.44 w
+2 J
+0 j
+[] 0.0 d
+3.25 M 330.754 118.234 m 289.434 118.234 l S
+Q q
+0 g
+293.562 118.234 m 293.562 117.137 293.129 116.086 292.355 115.312 c 291.578
+ 114.535 290.527 114.102 289.434 114.102 c 288.336 114.102 287.285 114.535
+ 286.512 115.312 c 285.734 116.086 285.301 117.137 285.301 118.234 c 285.301
+ 119.328 285.734 120.379 286.512 121.156 c 287.285 121.93 288.336 122.363
+ 289.434 122.363 c 290.527 122.363 291.578 121.93 292.355 121.156 c 293.129
+ 120.379 293.562 119.328 293.562 118.234 c h
+293.562 118.234 m f*
+0.36 w
+2 J
+0 j
+[] 0.0 d
+3.25 M 289.434 118.234 m 289.434 109.969 l S
+165.469 67.156 m 173.73 67.156 l S
+BT
+10.08 0 0 -10.08 177.725859 70.396453 Tm
+/f-2-0 1 Tf
+(i)Tj
+10.8 0 0 -10.8 181.385859 70.396453 Tm
+/f-1-1 1 Tf
+<01>Tj
+7.2 0 0 -7.2 186.125859 72.102703 Tm
+/f-0-0 1 Tf
+(YL)Tj
+10.8 0 0 -10.8 285.038906 104.944219 Tm
+/f-1-1 1 Tf
+<01>Tj
+7.2 0 0 -7.2 289.778906 106.650469 Tm
+/f-0-0 1 Tf
+(0)Tj
+ET
+Q Q
+showpage
+%%Trailer
+end restore
+%%EOF
diff --git a/contour_path.eps b/contour_path.eps
new file mode 100644
index 0000000..cb65b3c
--- /dev/null
+++ b/contour_path.eps
@@ -0,0 +1,440 @@
+%!PS-Adobe-3.0 EPSF-3.0
+%%Creator: cairo 1.15.4 (http://cairographics.org)
+%%CreationDate: Wed Jan 19 13:55:29 2022
+%%Pages: 1
+%%DocumentData: Clean7Bit
+%%LanguageLevel: 2
+%%Creator: Wolfram Mathematica 13.0.0.0 for Linux x86 (64-bit) (December 2, 2021)
+%%BoundingBox: 0 0 360 218
+%%EndComments
+%%BeginProlog
+save
+50 dict begin
+/q { gsave } bind def
+/Q { grestore } bind def
+/cm { 6 array astore concat } bind def
+/w { setlinewidth } bind def
+/J { setlinecap } bind def
+/j { setlinejoin } bind def
+/M { setmiterlimit } bind def
+/d { setdash } bind def
+/m { moveto } bind def
+/l { lineto } bind def
+/c { curveto } bind def
+/h { closepath } bind def
+/re { exch dup neg 3 1 roll 5 3 roll moveto 0 rlineto
+      0 exch rlineto 0 rlineto closepath } bind def
+/S { stroke } bind def
+/f { fill } bind def
+/f* { eofill } bind def
+/n { newpath } bind def
+/W { clip } bind def
+/W* { eoclip } bind def
+/BT { } bind def
+/ET { } bind def
+/pdfmark where { pop globaldict /?pdfmark /exec load put }
+    { globaldict begin /?pdfmark /pop load def /pdfmark
+    /cleartomark load def end } ifelse
+/BDC { mark 3 1 roll /BDC pdfmark } bind def
+/EMC { mark /EMC pdfmark } bind def
+/cairo_store_point { /cairo_point_y exch def /cairo_point_x exch def } def
+/Tj { show currentpoint cairo_store_point } bind def
+/TJ {
+  {
+    dup
+    type /stringtype eq
+    { show } { -0.001 mul 0 cairo_font_matrix dtransform rmoveto } ifelse
+  } forall
+  currentpoint cairo_store_point
+} bind def
+/cairo_selectfont { cairo_font_matrix aload pop pop pop 0 0 6 array astore
+    cairo_font exch selectfont cairo_point_x cairo_point_y moveto } bind def
+/Tf { pop /cairo_font exch def /cairo_font_matrix where
+      { pop cairo_selectfont } if } bind def
+/Td { matrix translate cairo_font_matrix matrix concatmatrix dup
+      /cairo_font_matrix exch def dup 4 get exch 5 get cairo_store_point
+      /cairo_font where { pop cairo_selectfont } if } bind def
+/Tm { 2 copy 8 2 roll 6 array astore /cairo_font_matrix exch def
+      cairo_store_point /cairo_font where { pop cairo_selectfont } if } bind def
+/g { setgray } bind def
+/rg { setrgbcolor } bind def
+/d1 { setcachedevice } bind def
+/cairo_flush_ascii85_file { cairo_ascii85_file status { cairo_ascii85_file flushfile } if } def
+/cairo_image { image cairo_flush_ascii85_file } def
+/cairo_imagemask { imagemask cairo_flush_ascii85_file } def
+%%EndProlog
+%%BeginSetup
+%%BeginResource: font f-0-0
+%!FontType1-1.1 f-0-0 1.0
+11 dict begin
+/FontName /f-0-0 def
+/PaintType 0 def
+/FontType 1 def
+/FontMatrix [0.001 0 0 0.001 0 0] readonly def
+/FontBBox {29 -169 437 799                                   } readonly def
+/Encoding 256 array
+0 1 255 {1 index exch /.notdef put} for
+dup 40 /parenleft put
+dup 41 /parenright put
+readonly def
+currentdict end
+currentfile eexec
+f983ef0097ece636fb4a96c74d26ab84185f6dfa4a16a7a1c27bbe3f1156aea698df336d20b467
+b10e7f33846656653c5ac6962759d3056cbdb3190bac614b984bf5a132dc418192443014ba63de
+800d392b6fea026574bb2535fd7bb5338f35bf15a88ea328fdaa49670c7852e3d060f3c5d6b07f
+2ef6d0f22646c5d18e19a2ae3ee120390f6dd96f76dcf1e127de5e9299077a00c17c0d71e36e5b
+9d5ec58fceda57739a6a4214d4b79d6c48d2784b60c320323c7acddddf34db833cac0cf109f799
+69d114a330d372e5c978a66acc84e3fe5557f6240856a013ffaa0199444e5c5036f775eba4a5c5
+8cde66cf604b9aca2178431127b8a1ff7ed633a65c04600af5f573483112251ca90bc9cf8825c7
+41412dda705317b7cb229dd377ff3d18e94daa9ba3bbd4ccd2ecde18a1c220179cca13293a42f7
+1d167cd6ac624b8f8573fc281c165eeb093c7705f0c9d1ce383c8701d14fcde12ac700699f81e8
+412c2e7e4c95c1440662af1652abdb4ce6be4b5f976724c26d20f166e17532da87ef8b24e90d2b
+ca09313d345112c202c1d9528e8c8e15bdfd68385cef36d711b99ee54d324b8778dae18d9af490
+41fbe748f7910913a3460e4af7353d7952f1fa9fde2bb171a7717e297425e0c08ca9800b01b2f5
+d645e0dbbc3a76bdfc773c19f4917354ed597d131dcc12985dd83ff833cc665a3ed3f11ec3814b
+3a8be6d7aef97d0b12b552d8da18f6cea65a8e284355941aae2da895a0fee8c8c2d4c22664f827
+5fb1ca0fbda2da6ff7fee9a610c58ec5d0c82dbb9b890d86f03ce85b69a56821a477e957df28b4
+b7afc889cbe637525896dc572b943c7f55648deb0894a36d8a1f7cfe05e48b6abb21a9949c7070
+43ecfa2c9ed9ed591f98e5fb1581bfb12e97b35bab44504370459fd28ca0c151ded5634089598c
+3d20720000000000000000000000000000000000000000000000000000000000000000
+0000000000000000000000000000000000000000000000000000000000000000
+0000000000000000000000000000000000000000000000000000000000000000
+0000000000000000000000000000000000000000000000000000000000000000
+0000000000000000000000000000000000000000000000000000000000000000
+0000000000000000000000000000000000000000000000000000000000000000
+0000000000000000000000000000000000000000000000000000000000000000
+0000000000000000000000000000000000000000000000000000000000000000
+cleartomark
+%%EndResource
+%%BeginResource: font f-0-1
+%!FontType1-1.1 f-0-1 1.0
+11 dict begin
+/FontName /f-0-1 def
+/PaintType 0 def
+/FontType 1 def
+/FontMatrix [0.001 0 0 0.001 0 0] readonly def
+/FontBBox {28 -13 453 799                                    } readonly def
+/Encoding 256 array
+0 1 255 {1 index exch /.notdef put} for
+dup 1 /uni03B8 put
+dup 2 /uni2032 put
+readonly def
+currentdict end
+currentfile eexec
+f983ef0097ece636fb4a96c74d26ab84185f6dfa4a16a7a1c27bbe3f1156aea698df336d20b467
+b10e7f33846656653c5ac6962759d3056cbdb3190bac614b984bf5a132dc418192443014ba63de
+800d392b6fea026574bb2535fd7bb5338f35bf15a88ea328fdaa49670c7852e3d060f3c5d6b07f
+2ef6d0f22646c5d18e19a2ae3ee120390f6dd96f76dcf1e127de5e9299077a00c17c0d71e36e5b
+9d5ec58fceda57739a6a4214d4b79d6c48d2784b60c320323c7acddddf34db833cac0cf109f799
+69d114a330d372e5c978a66acc84e3fe5557f6240856a013ffaa0199444e5c5036f775eba4a5c5
+8cde66cf604b9aca2178431127b8a1ff7ed633a65c04600af5f573483112251ca90bc9cf8825c7
+41412dda705317b7cb229dd377ff3d18e94daa9ba3bbd4ccd2ecde18a1c220179cca13293a42f7
+1d167cd6ac624b8f8573fc281c165eeb093c7705f0c9d1ce383c8701d14fcde12ac700699f81e8
+41298a056fbf05326bc567de0a0b26ab9bb8bf1c727fffe1a769e825cf16eef0e80b165c6bf01f
+c921bca94f4af777d97a2f19e0a6ba590a7e6bb59956c28a9e498787adbe3de7e6d3fc47ff7726
+4b0c3148d711961ef450730e7d9c2a0f9a8a8f7848739b2b8d2d56196d23d6b0a070f7ac34e28f
+1949b3d9933bd71bf994c695728647fe1cf6384f74801dd45d812cb26587dcf820b46a68885bcd
+be76f7a022b91b2856413f8b472c291f6323e69460888d3cf8b748160f2e465f470393d943268b
+e792e635a8fd6619217c82809f6c96a1c9f9d29ad32faaaebfee0f7caa41b8bd0cb26e12ae0006
+88ed16f82ca7c86fa6dfcd1624fb95587b3f4af99d73d037e596049ed240cfc364725448a51776
+ac6f8704995692b4cfb620640c12fafe8bda7ad95960cba96348a26386586f689b88045f9d5c17
+e43924d6e512c17db975287c04f45268e5a9a97237ed2fbf40344d73de6125e201a21057af59b0
+2ebd555ff2f2a4fec3352b5f2224db9c832d06cce2408ec8547633e84867b3a73065ab9671a46f
+925533c889164deafa20f00ef1f3f3a6639bc9333208014faba60b13c7b07b41e98c88d797eeaf
+1109a75b204ee60000000000000000000000000000000000000000000000000000000000000000
+0000000000000000000000000000000000000000000000000000000000000000
+0000000000000000000000000000000000000000000000000000000000000000
+0000000000000000000000000000000000000000000000000000000000000000
+0000000000000000000000000000000000000000000000000000000000000000
+0000000000000000000000000000000000000000000000000000000000000000
+0000000000000000000000000000000000000000000000000000000000000000
+0000000000000000000000000000000000000000000000000000000000000000
+cleartomark
+%%EndResource
+%%BeginResource: font f-1-0
+%!FontType1-1.1 f-1-0 1.0
+11 dict begin
+/FontName /f-1-0 def
+/PaintType 0 def
+/FontType 1 def
+/FontMatrix [0.001 0 0 0.001 0 0] readonly def
+/FontBBox {0 -14 908 692                                     } readonly def
+/Encoding 256 array
+0 1 255 {1 index exch /.notdef put} for
+dup 73 /I put
+dup 82 /R put
+dup 101 /e put
+dup 109 /m put
+readonly def
+currentdict end
+currentfile eexec
+f983ef0097ece636fb4a96c74d26ab84185f6dfa4a16a7a1c27bbe3f1156aea698df336d20b467
+b10e7f33846656653c5ac6962759d3056cbdb3190bac614b984bf5a132dc418192443014ba63de
+800d392b6fea026574bb2535fd7bb5338f35bf15a88ea328fdaa49670c7852e3d060f3c5d6b07f
+2ef6d0f22646c5d18e19a2ae3ee120390f6dd96f76dcf1e127de5e9299077a00c17c0d71e36e5b
+9d5ec58fceda57739a6a4214d4b79d6c48d2784b60c320323c7acddddf34db833cac0cf109f799
+69d114a330d372e5c978a66acc84e3fe5557f6240856a013ffaa0199444e5c5036f775eba4a5c5
+8cde66cf604b9aca2178431127b8a1ff7ed633a65c04600af5f573483112251cabe8722c0ba224
+7e4445af50cf2457d0f320e3c97746456087766b4bf11115560ce328711eca3bd110d9edf8f723
+7690411035c2d2a4529eceb3758e9dfdf69937c82634682ddec349213e6cdca1236ff1e59fd7ad
+c509a9f3c257841b8053a86b38d617d963b24dfb3767bfc9b4af0288c9b0b8e2572d16601fc539
+50419b779278a6ee6aa2c6f6e88f16020db6e348845fd5b2cd9ac2bb9cc9caa74bac30ab845da5
+f651fffe8b245f374569b60b2520d5b091c2895daa06f7cacffa423bc29ca3a939660aef03f4ba
+db6c051bab9e97aa6f8b3423aee96ff61f682293fdb336288dbb885c46c5c6d7ca5c5a0cf84a99
+4b1ef4f098cdceee4559f76b71375ac1e48de97bc26d04e944bd8f7723aaca9bdeb0a55b4d8e30
+b9169a69c8b151f7e913240de4e7614c0ce99885f8de5ae8d0c7602bdba359c79247126be04fa0
+4837a74d4b1829aba24a81ace9429198af5c03ce00c992b95216dab9619da47da7550eca0ff6cd
+0ebc575021f16decb7f0d945e2c73764f06e1781806305825422f0f7ad20cee7de432128300693
+599dbdafc575e2f472140a927b4552e1cd714bd09871feab74613bf38b4117e1b2c870998d1584
+50ae3c9c1b184d5529d7092e102d713e1e4a8d02eb0fb3edc7ef054b7fbe323e488fbcf700dac6
+058c3eeb18d59888e42247d792f3cff694e14a0b69965054b8e811dc8ae391c9be575648546fef
+0365caa0b5334da60343169e20c6b1b8d51c5fbe17cfca3ec7f3bd1c61d09838b717c08ccfcbda
+2a43ce0a730162c3285d5185e5fa3f8c6aaa204a403cdae550e565dcaf3816e4f19a66fee5bb4d
+e532d49827c5c811b8c6effa17be7f7f897390f48ca0d11588bc17af153bec904639fcce603e9a
+fb7417deeba06beb6901c0fba586004121e1aa2dcab890d83326fd7ffca74c35e64a22c9434ef6
+7d7496180137f9c8705089856e54a802d541062de40941e37319ed189b6dd27b69783befae9725
+88dacdb39bfe000a0789e90bfdcc7a2187dbff723ba8a74bb2ececfee0a9ea34b01434890000000000000000000000000000000000000000000000000000000000000000
+0000000000000000000000000000000000000000000000000000000000000000
+0000000000000000000000000000000000000000000000000000000000000000
+0000000000000000000000000000000000000000000000000000000000000000
+0000000000000000000000000000000000000000000000000000000000000000
+0000000000000000000000000000000000000000000000000000000000000000
+0000000000000000000000000000000000000000000000000000000000000000
+0000000000000000000000000000000000000000000000000000000000000000
+cleartomark
+%%EndResource
+%%EndSetup
+%%Page: 1 1
+%%BeginPageSetup
+%%PageBoundingBox: 0 0 360 218
+%%EndPageSetup
+q 0 0 360 218 rectclip
+1 0 0 -1 0 219 cm q
+0.999985 0 0 rg
+1.310865 w
+2 J
+0 j
+[] 0.0 d
+3.25 M 8.371 116.121 m 32.953 116.121 l S
+49.336 117.352 m 49.336 115.176 48.473 113.094 46.938 111.555 c 45.402 
+110.02 43.316 109.156 41.145 109.156 c 38.973 109.156 36.887 110.02 35.352
+ 111.555 c 33.816 113.094 32.953 115.176 32.953 117.352 c S
+295.125 116.121 m 319.703 116.121 l S
+295.125 117.352 m 295.125 115.176 294.262 113.094 292.727 111.555 c 291.188
+ 110.02 289.105 109.156 286.934 109.156 c 284.758 109.156 282.676 110.02
+ 281.137 111.555 c 279.602 113.094 278.738 115.176 278.738 117.352 c S
+49.336 117.352 m 155.844 117.352 l S
+172.23 117.352 m 172.23 115.176 171.367 113.094 169.832 111.555 c 168.293
+ 110.02 166.211 109.156 164.039 109.156 c 161.863 109.156 159.781 110.02
+ 158.246 111.555 c 156.707 113.094 155.844 115.176 155.844 117.352 c S
+172.23 117.352 m 205.004 117.352 l S
+221.387 117.352 m 221.387 115.176 220.523 113.094 218.988 111.555 c 217.453
+ 110.02 215.367 109.156 213.195 109.156 c 211.023 109.156 208.938 110.02
+ 207.402 111.555 c 205.867 113.094 205.004 115.176 205.004 117.352 c S
+221.387 117.352 m 278.738 117.352 l S
+165.266 21.145 m 165.266 58.523 l S
+162.809 21.145 m 162.809 58.523 l S
+172.23 66.715 m 172.23 64.543 171.367 62.457 169.832 60.922 c 168.293 59.387
+ 166.211 58.523 164.039 58.523 c 161.863 58.523 159.781 59.387 158.246 60.922
+ c 156.707 62.457 155.844 64.543 155.844 66.715 c 155.844 68.887 156.707
+ 70.973 158.246 72.508 c 159.781 74.043 161.863 74.906 164.039 74.906 c 
+166.211 74.906 168.293 74.043 169.832 72.508 c 171.367 70.973 172.23 68.887
+ 172.23 66.715 c h
+172.23 66.715 m S
+0 g
+0.36 w
+213.195 117.352 m 213.195 125.543 l S
+BT
+10.8 0 0 -10.8 210.748688 136.975703 Tm
+/f-0-1 1 Tf
+<01>Tj
+ET
+0.999985 0 0 rg
+1.152 w
+8.379 116.582 m 8.465 114.039 l 8.574 112.461 l 8.684 111.281 l 8.793 110.297
+ l 8.902 109.434 l 9.012 108.656 l 9.117 107.941 l 9.227 107.281 l 9.336
+ 106.66 l 9.445 106.074 l 9.664 104.988 l 9.773 104.477 l 9.883 103.988 
+l 10.098 103.062 l 10.207 102.621 l 10.316 102.191 l 10.535 101.371 l 10.973
+ 99.844 l 11.082 99.484 l 11.188 99.133 l 11.406 98.449 l 11.844 97.148 
+l 12.062 96.531 l 12.277 95.934 l 12.715 94.785 l 13.586 92.66 l 13.789 
+92.191 l 13.992 91.73 l 14.398 90.84 l 15.215 89.141 l 16.844 86.051 l 16.945
+ 85.867 l 17.25 85.328 l 17.656 84.625 l 18.469 83.266 l 20.098 80.719 l
+ 20.199 80.57 l 20.297 80.422 l 20.496 80.125 l 20.895 79.543 l 21.695 78.41
+ l 23.289 76.254 l 26.48 72.312 l 26.699 72.062 l 26.914 71.812 l 27.348
+ 71.32 l 28.215 70.352 l 29.945 68.488 l 33.406 65.027 l 33.508 64.934 l
+ 33.609 64.836 l 33.812 64.645 l 34.215 64.266 l 35.023 63.52 l 36.637 62.066
+ l 39.871 59.328 l 46.875 54.008 l 53.75 49.457 l 60.164 45.695 l 67.117
+ 42.066 l 73.613 39.039 l 79.977 36.379 l 86.883 33.793 l 93.328 31.641 
+l 100.312 29.574 l 107.168 27.793 l 113.566 26.34 l 120.5 24.984 l 120.703
+ 24.945 l 121.312 24.84 l 122.121 24.695 l 123.738 24.422 l 126.977 23.91
+ l 127.195 23.879 l 127.414 23.844 l 127.852 23.777 l 128.73 23.652 l 130.484
+ 23.406 l 130.703 23.375 l 130.922 23.348 l 131.359 23.289 l 132.238 23.172
+ l 133.992 22.953 l 134.098 22.941 l 134.207 22.926 l 134.422 22.902 l 134.852
+ 22.848 l 135.715 22.75 l 137.434 22.559 l 137.543 22.547 l 137.648 22.535
+ l 137.867 22.512 l 138.297 22.469 l 139.156 22.379 l 140.879 22.215 l 140.98
+ 22.203 l 141.078 22.195 l 141.281 22.176 l 141.684 22.141 l 142.484 22.07
+ l 144.09 21.938 l 144.293 21.922 l 144.492 21.906 l 145.699 21.812 l 147.305
+ 21.699 l 147.414 21.695 l 147.523 21.688 l 147.738 21.672 l 148.176 21.645
+ l 149.047 21.59 l 149.156 21.586 l 149.266 21.578 l 149.48 21.566 l 149.918
+ 21.539 l 150.789 21.492 l 150.895 21.488 l 151.004 21.48 l 151.223 21.469
+ l 151.66 21.449 l 152.527 21.406 l 154.27 21.332 l 154.676 21.316 l 155.082
+ 21.305 l 155.898 21.273 l 156 21.273 l 156.305 21.262 l 157.523 21.227 
+l 157.625 21.227 l 157.727 21.223 l 157.93 21.219 l 158.336 21.207 l 158.438
+ 21.207 l 158.539 21.203 l 159.148 21.191 l 159.25 21.188 l 159.352 21.188
+ l 159.961 21.176 l 160.062 21.176 l 160.164 21.172 l 160.367 21.172 l 160.773
+ 21.164 l 160.977 21.164 l 161.176 21.16 l 161.273 21.16 l 161.375 21.156
+ l 161.672 21.156 l 161.773 21.152 l 162.172 21.152 l 162.371 21.148 l 162.77
+ 21.148 l 162.867 21.145 l 165.258 21.145 l 165.359 21.148 l 165.758 21.148
+ l 165.957 21.152 l 166.355 21.152 l 166.453 21.156 l 166.754 21.156 l 167.152
+ 21.164 l 167.367 21.164 l 167.586 21.168 l 168.016 21.176 l 168.125 21.176
+ l 168.234 21.18 l 168.449 21.184 l 168.883 21.191 l 168.988 21.191 l 169.098
+ 21.195 l 169.312 21.199 l 169.746 21.207 l 170.609 21.23 l 170.719 21.23
+ l 170.828 21.234 l 171.043 21.242 l 171.477 21.254 l 172.34 21.281 l 172.449
+ 21.285 l 172.555 21.289 l 172.773 21.297 l 173.207 21.309 l 174.07 21.344
+ l 174.273 21.352 l 174.473 21.359 l 174.875 21.379 l 175.684 21.414 l 175.887
+ 21.422 l 176.086 21.434 l 176.492 21.453 l 177.297 21.492 l 177.398 21.5
+ l 177.5 21.504 l 177.703 21.516 l 178.105 21.535 l 178.91 21.582 l 180.527
+ 21.684 l 180.746 21.699 l 180.961 21.715 l 181.398 21.742 l 182.273 21.805
+ l 184.023 21.941 l 184.242 21.957 l 184.461 21.977 l 184.898 22.012 l 185.773
+ 22.086 l 187.523 22.246 l 187.629 22.254 l 187.738 22.266 l 187.953 22.285
+ l 188.383 22.328 l 189.238 22.414 l 190.957 22.594 l 194.391 22.988 l 194.492
+ 23.004 l 194.59 23.016 l 194.793 23.039 l 195.191 23.09 l 195.992 23.191
+ l 197.594 23.406 l 200.797 23.863 l 200.906 23.879 l 201.016 23.898 l 201.23
+ 23.93 l 201.668 23.996 l 202.535 24.133 l 204.273 24.414 l 207.746 25.016
+ l 214.23 26.281 l 220.59 27.715 l 227.488 29.5 l 233.926 31.383 l 240.902
+ 33.691 l 247.422 36.109 l 253.809 38.754 l 260.738 41.957 l 267.203 45.305
+ l 274.215 49.387 l 281.094 53.93 l 287.512 58.766 l 294.473 64.84 l 294.574
+ 64.938 l 294.676 65.031 l 295.285 65.617 l 296.098 66.414 l 297.719 68.059
+ l 300.969 71.594 l 301.07 71.707 l 301.168 71.82 l 301.367 72.051 l 301.766
+ 72.516 l 302.562 73.461 l 304.152 75.438 l 304.254 75.562 l 304.352 75.691
+ l 304.551 75.949 l 304.949 76.469 l 305.746 77.535 l 307.34 79.773 l 307.445
+ 79.93 l 307.555 80.09 l 307.77 80.41 l 308.203 81.059 l 309.066 82.398 
+l 310.793 85.27 l 310.902 85.457 l 311.012 85.648 l 311.227 86.035 l 311.656
+ 86.82 l 312.523 88.465 l 314.25 92.105 l 314.352 92.336 l 314.449 92.57
+ l 314.652 93.043 l 315.055 94.016 l 315.156 94.266 l 315.258 94.52 l 315.457
+ 95.035 l 315.863 96.105 l 315.961 96.383 l 316.062 96.664 l 316.266 97.238
+ l 316.668 98.441 l 316.77 98.754 l 316.867 99.074 l 317.07 99.73 l 317.473
+ 101.125 l 317.574 101.492 l 317.676 101.871 l 317.875 102.652 l 317.977
+ 103.062 l 318.078 103.484 l 318.281 104.367 l 318.379 104.832 l 318.48 
+105.316 l 318.684 106.352 l 318.785 106.906 l 318.883 107.492 l 319.086 
+108.789 l 319.188 109.516 l 319.289 110.32 l 319.387 111.227 l 319.488 112.297
+ l 319.59 113.668 l 319.691 116.098 l 319.699 116.742 l S
+0 g
+0.36 w
+0 J
+[ 2.88 2.88] 0 d
+0.18 117.352 m 327.895 117.352 l S
+BT
+10.08 0 0 -10.08 333.65625 120.589891 Tm
+/f-1-0 1 Tf
+(Re)Tj
+10.8 0 0 -10.8 345.32625 120.589891 Tm
+/f-0-0 1 Tf
+(\()Tj
+/f-0-1 1 Tf
+<01>Tj
+7.2 0 0 -7.2 353.68125 116.145016 Tm
+<02>Tj
+10.8 0 0 -10.8 356.53875 120.589891 Tm
+/f-0-0 1 Tf
+(\))Tj
+ET
+Q q
+163 16 2 202.641 re W n
+0 g
+0.36 w
+0 J
+0 j
+[ 2.88 2.88] 0 d
+3.25 M 164.039 218.621 m 164.039 16.078 l S
+Q q
+0 g
+BT
+10.08 0 0 -10.08 150.290625 9.12 Tm
+/f-1-0 1 Tf
+(Im)Tj
+10.8 0 0 -10.8 163.111875 9.12 Tm
+/f-0-0 1 Tf
+(\()Tj
+/f-0-1 1 Tf
+<01>Tj
+7.2 0 0 -7.2 171.466875 4.675125 Tm
+<02>Tj
+10.8 0 0 -10.8 174.324375 9.12 Tm
+/f-0-0 1 Tf
+(\))Tj
+ET
+Q q
+163 16 2 52 re W n
+0 g
+1.44 w
+2 J
+0 j
+[] 0.0 d
+3.25 M 164.039 66.715 m 164.039 -46.508 l S
+Q q
+163 167 2 51.641 re W n
+0 g
+1.44 w
+2 J
+0 j
+[] 0.0 d
+3.25 M 164.039 167.984 m 164.039 281.207 l S
+Q q
+0 g
+161.141 63.816 5.793 5.797 re f
+1.44 w
+2 J
+0 j
+[] 0.0 d
+3.25 M 161.141 63.816 5.793 5.797 re S
+168.133 117.352 m 164.039 113.254 l 159.941 117.352 l 164.039 121.445 l
+ h
+168.133 117.352 m f
+168.133 117.352 m 164.039 113.254 l 159.941 117.352 l 164.039 121.445 l
+ h
+168.133 117.352 m S
+161.141 165.09 5.793 5.793 re f
+161.141 165.09 5.793 5.793 re S
+0.18 117.352 m 41.145 117.352 l S
+45.242 117.352 m 45.242 116.262 44.809 115.223 44.043 114.453 c 43.273 
+113.684 42.23 113.254 41.145 113.254 c 40.059 113.254 39.016 113.684 38.246
+ 114.453 c 37.48 115.223 37.047 116.262 37.047 117.352 c 37.047 118.438 
+37.48 119.477 38.246 120.246 c 39.016 121.016 40.059 121.445 41.145 121.445
+ c 42.23 121.445 43.273 121.016 44.043 120.246 c 44.809 119.477 45.242 118.438
+ 45.242 117.352 c h
+45.242 117.352 m f*
+Q q
+286 116 42 3 re W n
+0 g
+1.44 w
+2 J
+0 j
+[] 0.0 d
+3.25 M 327.895 117.352 m 286.934 117.352 l S
+Q q
+0 g
+291.027 117.352 m 291.027 116.262 290.598 115.223 289.828 114.453 c 289.059
+ 113.684 288.02 113.254 286.934 113.254 c 285.844 113.254 284.805 113.684
+ 284.035 114.453 c 283.266 115.223 282.836 116.262 282.836 117.352 c 282.836
+ 118.438 283.266 119.477 284.035 120.246 c 284.805 121.016 285.844 121.445
+ 286.934 121.445 c 288.02 121.445 289.059 121.016 289.828 120.246 c 290.598
+ 119.477 291.027 118.438 291.027 117.352 c h
+291.027 117.352 m f*
+211.898 117.773 m 211.59 119.559 l 213.195 118.715 l 214.801 119.559 l 
+214.496 117.773 l 215.793 116.508 l 214 116.246 l 213.195 114.617 l 212.395
+ 116.246 l 210.598 116.508 l h
+211.898 117.773 m f
+1.44 w
+2 J
+0 j
+[] 0.0 d
+3.25 M 211.898 117.773 m 211.59 119.559 l 213.195 118.715 l 214.801 119.559 l 
+214.496 117.773 l 215.793 116.508 l 214 116.246 l 213.195 114.617 l 212.395
+ 116.246 l 210.598 116.508 l h
+211.898 117.773 m S
+Q Q
+showpage
+%%Trailer
+end restore
+%%EOF
diff --git a/figs/F_higher_singularities.eps b/figs/F_higher_singularities.eps
deleted file mode 100644
index e3d6a7e..0000000
--- a/figs/F_higher_singularities.eps
+++ /dev/null
@@ -1,343 +0,0 @@
-%!PS-Adobe-3.0 EPSF-3.0
-%%Creator: cairo 1.15.4 (http://cairographics.org)
-%%CreationDate: Wed Jan 19 13:55:17 2022
-%%Pages: 1
-%%DocumentData: Clean7Bit
-%%LanguageLevel: 2
-%%Creator: Wolfram Mathematica 13.0.0.0 for Linux x86 (64-bit) (December 2, 2021)
-%%BoundingBox: 0 0 360 221
-%%EndComments
-%%BeginProlog
-save
-50 dict begin
-/q { gsave } bind def
-/Q { grestore } bind def
-/cm { 6 array astore concat } bind def
-/w { setlinewidth } bind def
-/J { setlinecap } bind def
-/j { setlinejoin } bind def
-/M { setmiterlimit } bind def
-/d { setdash } bind def
-/m { moveto } bind def
-/l { lineto } bind def
-/c { curveto } bind def
-/h { closepath } bind def
-/re { exch dup neg 3 1 roll 5 3 roll moveto 0 rlineto
-      0 exch rlineto 0 rlineto closepath } bind def
-/S { stroke } bind def
-/f { fill } bind def
-/f* { eofill } bind def
-/n { newpath } bind def
-/W { clip } bind def
-/W* { eoclip } bind def
-/BT { } bind def
-/ET { } bind def
-/pdfmark where { pop globaldict /?pdfmark /exec load put }
-    { globaldict begin /?pdfmark /pop load def /pdfmark
-    /cleartomark load def end } ifelse
-/BDC { mark 3 1 roll /BDC pdfmark } bind def
-/EMC { mark /EMC pdfmark } bind def
-/cairo_store_point { /cairo_point_y exch def /cairo_point_x exch def } def
-/Tj { show currentpoint cairo_store_point } bind def
-/TJ {
-  {
-    dup
-    type /stringtype eq
-    { show } { -0.001 mul 0 cairo_font_matrix dtransform rmoveto } ifelse
-  } forall
-  currentpoint cairo_store_point
-} bind def
-/cairo_selectfont { cairo_font_matrix aload pop pop pop 0 0 6 array astore
-    cairo_font exch selectfont cairo_point_x cairo_point_y moveto } bind def
-/Tf { pop /cairo_font exch def /cairo_font_matrix where
-      { pop cairo_selectfont } if } bind def
-/Td { matrix translate cairo_font_matrix matrix concatmatrix dup
-      /cairo_font_matrix exch def dup 4 get exch 5 get cairo_store_point
-      /cairo_font where { pop cairo_selectfont } if } bind def
-/Tm { 2 copy 8 2 roll 6 array astore /cairo_font_matrix exch def
-      cairo_store_point /cairo_font where { pop cairo_selectfont } if } bind def
-/g { setgray } bind def
-/rg { setrgbcolor } bind def
-/d1 { setcachedevice } bind def
-/cairo_flush_ascii85_file { cairo_ascii85_file status { cairo_ascii85_file flushfile } if } def
-/cairo_image { image cairo_flush_ascii85_file } def
-/cairo_imagemask { imagemask cairo_flush_ascii85_file } def
-%%EndProlog
-%%BeginSetup
-%%BeginResource: font f-0-0
-%!FontType1-1.1 f-0-0 1.0
-11 dict begin
-/FontName /f-0-0 def
-/PaintType 0 def
-/FontType 1 def
-/FontMatrix [0.001 0 0 0.001 0 0] readonly def
-/FontBBox {-12 -14 908 692                                   } readonly def
-/Encoding 256 array
-0 1 255 {1 index exch /.notdef put} for
-dup 73 /I put
-dup 76 /L put
-dup 82 /R put
-dup 89 /Y put
-dup 101 /e put
-dup 109 /m put
-readonly def
-currentdict end
-currentfile eexec
-f983ef0097ece636fb4a96c74d26ab84185f6dfa4a16a7a1c27bbe3f1156aea698df336d20b467
-b10e7f33846656653c5ac6962759d3056cbdb3190bac614b984bf5a132dc418192443014ba63de
-800d392b6fea026574bb2535fd7bb5338f35bf15a88ea328fdaa49670c7852e3d060f3c5d6b07f
-2ef6d0f22646c5d18e19a2ae3ee120390f6dd96f76dcf1e127de5e9299077a00c17c0d71e36e5b
-9d5ec58fceda57739a6a4214d4b79d6c48d2784b60c320323c7acddddf34db833cac0cf109f799
-69d114a330d372e5c978a66acc84e3fe5557f6240856a013ffaa0199444e5c5036f775eba4a5c5
-8cde66cf604b9aca2178431127b8a1ff7ed633a65c04600af5f573483112251ca5d188dea508ed
-e1b2455317d2f89946db9171817b252ef4aed3b4d1e2d956531eb1466794df0a360608df9ddca3
-31d2d2e2835dae9cd39f88612df7540cb9134838f4d1d7d0f988815e63e88d14438a2ae43b6c64
-be2dc4f7b2e0c6a08fddad8746441fd5ac6854ff0c5ab7f7aca25cf081d4002f9811a93d3cdd0e
-00461c900c9e0c4f58969c6373636df5e12ca751b7e06a02b752e460d25a56e1b33dc0411ddd9e
-7b458fb4ff92195044e45a4c4f7904a7044d8d7f650b213d98f76e83b77a688cc939916088b4f9
-316351e48f38913000572d64d4afabc0ac17fd4b7223a755f8b481993158b33f9a2524016d7477
-18ddb89457c416c0db81b77356fff18507f286362ac9e87ca0429ff2f1acf7da2c47c6bdeb8d3c
-dc85780c28d652b255ed19df2c7f1c293e2b4bdf5edf4f16ac3e63826fc81a6bcebd904dbea152
-fd3b2185df087937c972d9c4a501a4c7f0991d1033d353df360f862b6d64d19957837efab9f754
-4b76f75fd04448d93f7ab3efdcd67a3b9b75470a0a773a7ddfec9008c973d8c459fcfc82947e61
-7c5140a933df404ce0206a24d9b6b6eed01d8b7eeee44aa93da77f3fbb1c99652e49426f7553c1
-13eb226edbfa600fb6ce98480d508f341eb46fe90bdc9e935d369104cf68e1435eef393cbe5a6a
-efd5a9d8c610237e51e66ed3de56b37a7c59f9e3642aa04a2c3feb1b5abb201b93dea4435b152a
-462dc36f44e1bfcf3ba187d9a9f70fa6beaf5d86c022ba6ebae51edaa5c2342996c0ddae2272de
-8bac4e6ccd4c78fbec53c96b34f4331c65a2f71190129f4416757fb1c470e976533e1f06441616
-b5ff7a78767d4b03f77127ef23a399515d6872fbe8977e3964bec1cb24c25fec9b6cba05a3bf46
-be9af306047fabbb331681b6c868e4a4ee1deab5eb4b85a8eb6e1bfdf21879963c943083af8e41
-e8c6ff780f855a21a161365d196069e0ae48e5d0b919fc7739a8486c2c7a3d7e5e577d94444a88
-f74814b026e2daa92fff0388fb5daaa8ef72bd44483204465071e60635f799dd2db005d99abd51
-13861f361f8d668fe4096a495b88e511086498864a23f931cd6043a33d3d09682f051d001b3f95
-dbcfb6ad9568d4ccf870fe2b242b09cd5e0365dec74bc5b4ac844ca0f5d994762e9918c422741d
-e6babf3da5b45853b89197b1b305b8842ba7a257615aa19d73450044339f90a351f4ee83288330
-7286c63001122838f16c75a11d404ea26e4ae1f27bc81979767804594b2bc71814cc25658dd8a0
-0709c062e5fb4f4478cb108f13bb74d8db95907f94a16b2953129862c3cae5b4643a42e99893a6
-d95b8d4f8ae8f8f287e7b822a9bd0f9c7a59b283baa4c396d52e6d4144261d6f79d9ba824c235d
-60f9b23849684b89f610e3eb3d642f9113269e3639e1c69e19572609e94ad0bcc0e60000000000000000000000000000000000000000000000000000000000000000
-0000000000000000000000000000000000000000000000000000000000000000
-0000000000000000000000000000000000000000000000000000000000000000
-0000000000000000000000000000000000000000000000000000000000000000
-0000000000000000000000000000000000000000000000000000000000000000
-0000000000000000000000000000000000000000000000000000000000000000
-0000000000000000000000000000000000000000000000000000000000000000
-0000000000000000000000000000000000000000000000000000000000000000
-cleartomark
-%%EndResource
-%%BeginResource: font f-1-0
-%!FontType1-1.1 f-1-0 1.0
-11 dict begin
-/FontName /f-1-0 def
-/PaintType 0 def
-/FontType 1 def
-/FontMatrix [0.001 0 0 0.001 0 0] readonly def
-/FontBBox {29 -169 437 799                                   } readonly def
-/Encoding 256 array
-0 1 255 {1 index exch /.notdef put} for
-dup 40 /parenleft put
-dup 41 /parenright put
-readonly def
-currentdict end
-currentfile eexec
-f983ef0097ece636fb4a96c74d26ab84185f6dfa4a16a7a1c27bbe3f1156aea698df336d20b467
-b10e7f33846656653c5ac6962759d3056cbdb3190bac614b984bf5a132dc418192443014ba63de
-800d392b6fea026574bb2535fd7bb5338f35bf15a88ea328fdaa49670c7852e3d060f3c5d6b07f
-2ef6d0f22646c5d18e19a2ae3ee120390f6dd96f76dcf1e127de5e9299077a00c17c0d71e36e5b
-9d5ec58fceda57739a6a4214d4b79d6c48d2784b60c320323c7acddddf34db833cac0cf109f799
-69d114a330d372e5c978a66acc84e3fe5557f6240856a013ffaa0199444e5c5036f775eba4a5c5
-8cde66cf604b9aca2178431127b8a1ff7ed633a65c04600af5f573483112251ca90bc9cf8825c7
-41412dda705317b7cb229dd377ff3d18e94daa9ba3bbd4ccd2ecde18a1c220179cca13293a42f7
-1d167cd6ac624b8f8573fc281c165eeb093c7705f0c9d1ce383c8701d14fcde12ac700699f81e8
-412c2e7e4c95c1440662af1652abdb4ce6be4b5f976724c26d20f166e17532da87ef8b24e90d2b
-ca09313d345112c202c1d9528e8c8e15bdfd68385cef36d711b99ee54d324b8778dae18d9af490
-41fbe748f7910913a3460e4af7353d7952f1fa9fde2bb171a7717e297425e0c08ca9800b01b2f5
-d645e0dbbc3a76bdfc773c19f4917354ed597d131dcc12985dd83ff833cc665a3ed3f11ec3814b
-3a8be6d7aef97d0b12b552d8da18f6cea65a8e284355941aae2da895a0fee8c8c2d4c22664f827
-5fb1ca0fbda2da6ff7fee9a610c58ec5d0c82dbb9b890d86f03ce85b69a56821a477e957df28b4
-b7afc889cbe637525896dc572b943c7f55648deb0894a36d8a1f7cfe05e48b6abb21a9949c7070
-43ecfa2c9ed9ed591f98e5fb1581bfb12e97b35bab44504370459fd28ca0c151ded5634089598c
-3d20720000000000000000000000000000000000000000000000000000000000000000
-0000000000000000000000000000000000000000000000000000000000000000
-0000000000000000000000000000000000000000000000000000000000000000
-0000000000000000000000000000000000000000000000000000000000000000
-0000000000000000000000000000000000000000000000000000000000000000
-0000000000000000000000000000000000000000000000000000000000000000
-0000000000000000000000000000000000000000000000000000000000000000
-0000000000000000000000000000000000000000000000000000000000000000
-cleartomark
-%%EndResource
-%%BeginResource: font f-1-1
-%!FontType1-1.1 f-1-1 1.0
-11 dict begin
-/FontName /f-1-1 def
-/PaintType 0 def
-/FontType 1 def
-/FontMatrix [0.001 0 0 0.001 0 0] readonly def
-/FontBBox {-6 -207 465 799                                   } readonly def
-/Encoding 256 array
-0 1 255 {1 index exch /.notdef put} for
-dup 1 /uni03BE put
-readonly def
-currentdict end
-currentfile eexec
-f983ef0097ece636fb4a96c74d26ab84185f6dfa4a16a7a1c27bbe3f1156aea698df336d20b467
-b10e7f33846656653c5ac6962759d3056cbdb3190bac614b984bf5a132dc418192443014ba63de
-800d392b6fea026574bb2535fd7bb5338f35bf15a88ea328fdaa49670c7852e3d060f3c5d6b07f
-2ef6d0f22646c5d18e19a2ae3ee120390f6dd96f76dcf1e127de5e9299077a00c17c0d71e36e5b
-9d5ec58fceda57739a6a4214d4b79d6c48d2784b60c320323c7acddddf34db833cac0cf109f799
-69d114a330d372e5c978a66acc84e3fe5557f6240856a013ffaa0199444e5c5036f775eba4a5c5
-8cde66cf604b9aca2178431127b8a1ff7ed633a65c04600af5f573483112251cae134058d6a192
-3c6b565d778d9618b31789d664bb543a0e576f202df308890d53425311c0df16d70e7088bc233c
-2aeafd23aed96e18251b90593258f09f68b68c844c8e5bf170e06e331e14147fa538f8473eeb1e
-c84dbfec93c34173c11f0744da9bfa7cf6a3d8c4eb2a75eb71b49d69da4ade018689e722cfab11
-be4351efa968308dff1933cdf6da74c1d45ce31ed30cfd322f1554cf02839075c2488a6e43b89a
-f24d9bd7595d4fc4c07d5aa69574f2b45a692e0305a31ca8496286dde55759bacec2cf519a550c
-fc581758620e692c3d1f29b52b360ab757e8a4ed621b3b2c5ce883b037b9fd1b119dba66319bb2
-4706b3eb74ba54dfb209979bff3f44781327e8d4e7b20328f58cdea3284522496934f1cd89a9ab
-8f825cc46c51daa2ea8f85719a90e312bb07457ba2739fe15e7f59e27a646521ff053df21c2edf
-9d96735ee9d39d251bcf0113dc96ad03208d1ae62db8141146cfd99f59fcb8a10bdbf341def129
-fd5b55b7fe37f31eae75b5caf35814db82b954eeb9ce040e42be770590adeaa9a03b85f5c8e344
-bef5c97285dc20e725e2b0ecaea95a78cc672f11240e0fed510f9027f695fe53aecf49f9bdd51c
-949743af735f932804173c4d9584652fc9184b875b8cf21b4af33bdcf8580ca4ce84b48a0a40b1
-9771faa53eb86add0076d818c9d10927b64117ce25af360fa0ef5061787ff063349478ead89981
-4641ebef5cebc2b444f7497c0f9638073d57ef29982e7efcd5421544ba5a737b3527d24db03842
-aa24c1f0c002b36b8656951b8f835f2dfd1d419cdcd2e490cc73162e9163805e9cf101f7d336ea
-d0caa5b458789b0f625cc937389ec0a67f90c3c2640000000000000000000000000000000000000000000000000000000000000000
-0000000000000000000000000000000000000000000000000000000000000000
-0000000000000000000000000000000000000000000000000000000000000000
-0000000000000000000000000000000000000000000000000000000000000000
-0000000000000000000000000000000000000000000000000000000000000000
-0000000000000000000000000000000000000000000000000000000000000000
-0000000000000000000000000000000000000000000000000000000000000000
-0000000000000000000000000000000000000000000000000000000000000000
-cleartomark
-%%EndResource
-%%BeginResource: font f-2-0
-%!FontType1-1.1 f-2-0 1.0
-11 dict begin
-/FontName /f-2-0 def
-/PaintType 0 def
-/FontType 1 def
-/FontMatrix [0.001 0 0 0.001 0 0] readonly def
-/FontBBox {0 -12 363 715                                     } readonly def
-/Encoding 256 array
-0 1 255 {1 index exch /.notdef put} for
-dup 105 /i put
-readonly def
-currentdict end
-currentfile eexec
-f983ef0097ece636fb4a96c74d26ab84185f6dfa4a16a7a1c27bbe3f1156aea698df336d20b467
-b10e7f33846656653c5ac6962759d3056cbdb3190bac614b984bf5a132dc418192443014ba63de
-800d392b6fea026574bb2535fd7bb5338f35bf15a88ea328fdaa49670c7852e3d060f3c5d6b07f
-2ef6d0f22646c5d18e19a2ae3ee120390f6dd96f76dcf1e127de5e9299077a00c17c0d71e36e5b
-9d5ec58fceda57739a6a4214d4b79d6c48d2784b60c320323c7acddddf34db833cac0cf109f799
-69d114a330d372e5c978a66acc84e3fe5557f6240856a013ffaa0199444e5c5036f775eba4a5c5
-8cde66cf604b9aca2178431127b8a1ff7ed633a65c04600af5f573483112251cae134058d6a192
-3c6b565d778d9618b31789d664bb543a0e576f252e8520c2d0698c337b75c663f61d3deead2935
-71dc9621dfa39dc5f30363291678a7d9dfdeaa2de43d090fdf9945858d9b5b3a5df2a5865b3028
-dc4b7ac7fe8270eda10a09d5669f164eb5fa6e4ca848129c7f59349ba575bbdf02dfbd8f5ed330
-d9554dd1eb8b856cdef62fe801b421cc107aa678dbf1124aab4cbde909fd8611cafc587bb34560
-f3428a01d0fd050e1c1ae785787bd5c142500e345326b240d6d37c6801da6061e4be60b75cc4a0
-06ffe4ca26e456a9313b7f02bd60218dde34c309130b9ee274c413f042863100acb2ad54244397
-b1ccf64df275ba901ee414216a2d7c659e80f9eb06bcb6f8d4b9e005690000000000000000000000000000000000000000000000000000000000000000
-0000000000000000000000000000000000000000000000000000000000000000
-0000000000000000000000000000000000000000000000000000000000000000
-0000000000000000000000000000000000000000000000000000000000000000
-0000000000000000000000000000000000000000000000000000000000000000
-0000000000000000000000000000000000000000000000000000000000000000
-0000000000000000000000000000000000000000000000000000000000000000
-0000000000000000000000000000000000000000000000000000000000000000
-cleartomark
-%%EndResource
-%%EndSetup
-%%Page: 1 1
-%%BeginPageSetup
-%%PageBoundingBox: 0 0 360 221
-%%EndPageSetup
-q 0 0 360 221 rectclip
-1 0 0 -1 0 222 cm q
-0 g
-0.36 w
-0 J
-0 j
-[ 2.88 2.88] 0 d
-3.25 M 0.18 119.551 m 330.613 119.551 l S
-BT
-10.08 0 0 -10.08 336.375 122.110031 Tm
-/f-0-0 1 Tf
-(Re)Tj
-10.8 0 0 -10.8 348.045 122.110031 Tm
-/f-1-0 1 Tf
-(\()Tj
-/f-1-1 1 Tf
-<01>Tj
-/f-1-0 1 Tf
-[()-29(\))]TJ
-ET
-Q q
-165 17 1 204.762 re W n
-0 g
-0.36 w
-0 J
-0 j
-[ 2.88 2.88] 0 d
-3.25 M 165.398 221.66 m 165.398 17.441 l S
-Q q
-0 g
-BT
-10.08 0 0 -10.08 153.009375 9.12 Tm
-/f-0-0 1 Tf
-(Im)Tj
-10.8 0 0 -10.8 165.830625 9.12 Tm
-/f-1-0 1 Tf
-(\()Tj
-/f-1-1 1 Tf
-<01>Tj
-/f-1-0 1 Tf
-[()-29(\))]TJ
-ET
-Q q
-164 17 3 53 re W n
-0 g
-1.44 w
-2 J
-0 j
-[] 0.0 d
-3.25 M 165.398 68.496 m 165.398 -45.668 l S
-Q q
-164 169 3 52.762 re W n
-0 g
-1.44 w
-2 J
-0 j
-[] 0.0 d
-3.25 M 165.398 170.605 m 165.398 284.766 l S
-Q q
-0 g
-162.477 65.574 5.84 5.84 re f
-1.44 w
-2 J
-0 j
-[] 0.0 d
-3.25 M 162.477 65.574 5.84 5.84 re S
-162.477 167.684 5.84 5.844 re f
-162.477 167.684 5.84 5.844 re S
-0.36 w
-165.398 68.496 m 173.66 68.496 l S
-BT
-10.08 0 0 -10.08 177.659063 71.055015 Tm
-/f-2-0 1 Tf
-(i)Tj
-10.8 0 0 -10.8 181.319063 71.055015 Tm
-/f-1-1 1 Tf
-<01>Tj
-7.2 0 0 -7.2 186.036563 72.761265 Tm
-/f-0-0 1 Tf
-(YL)Tj
-ET
-Q Q
-showpage
-%%Trailer
-end restore
-%%EOF
diff --git a/figs/F_lower_singularities.eps b/figs/F_lower_singularities.eps
deleted file mode 100644
index ae7d570..0000000
--- a/figs/F_lower_singularities.eps
+++ /dev/null
@@ -1,270 +0,0 @@
-%!PS-Adobe-3.0 EPSF-3.0
-%%Creator: cairo 1.15.4 (http://cairographics.org)
-%%CreationDate: Wed Jan 19 13:55:11 2022
-%%Pages: 1
-%%DocumentData: Clean7Bit
-%%LanguageLevel: 2
-%%Creator: Wolfram Mathematica 13.0.0.0 for Linux x86 (64-bit) (December 2, 2021)
-%%BoundingBox: 0 0 360 221
-%%EndComments
-%%BeginProlog
-save
-50 dict begin
-/q { gsave } bind def
-/Q { grestore } bind def
-/cm { 6 array astore concat } bind def
-/w { setlinewidth } bind def
-/J { setlinecap } bind def
-/j { setlinejoin } bind def
-/M { setmiterlimit } bind def
-/d { setdash } bind def
-/m { moveto } bind def
-/l { lineto } bind def
-/c { curveto } bind def
-/h { closepath } bind def
-/re { exch dup neg 3 1 roll 5 3 roll moveto 0 rlineto
-      0 exch rlineto 0 rlineto closepath } bind def
-/S { stroke } bind def
-/f { fill } bind def
-/f* { eofill } bind def
-/n { newpath } bind def
-/W { clip } bind def
-/W* { eoclip } bind def
-/BT { } bind def
-/ET { } bind def
-/pdfmark where { pop globaldict /?pdfmark /exec load put }
-    { globaldict begin /?pdfmark /pop load def /pdfmark
-    /cleartomark load def end } ifelse
-/BDC { mark 3 1 roll /BDC pdfmark } bind def
-/EMC { mark /EMC pdfmark } bind def
-/cairo_store_point { /cairo_point_y exch def /cairo_point_x exch def } def
-/Tj { show currentpoint cairo_store_point } bind def
-/TJ {
-  {
-    dup
-    type /stringtype eq
-    { show } { -0.001 mul 0 cairo_font_matrix dtransform rmoveto } ifelse
-  } forall
-  currentpoint cairo_store_point
-} bind def
-/cairo_selectfont { cairo_font_matrix aload pop pop pop 0 0 6 array astore
-    cairo_font exch selectfont cairo_point_x cairo_point_y moveto } bind def
-/Tf { pop /cairo_font exch def /cairo_font_matrix where
-      { pop cairo_selectfont } if } bind def
-/Td { matrix translate cairo_font_matrix matrix concatmatrix dup
-      /cairo_font_matrix exch def dup 4 get exch 5 get cairo_store_point
-      /cairo_font where { pop cairo_selectfont } if } bind def
-/Tm { 2 copy 8 2 roll 6 array astore /cairo_font_matrix exch def
-      cairo_store_point /cairo_font where { pop cairo_selectfont } if } bind def
-/g { setgray } bind def
-/rg { setrgbcolor } bind def
-/d1 { setcachedevice } bind def
-/cairo_flush_ascii85_file { cairo_ascii85_file status { cairo_ascii85_file flushfile } if } def
-/cairo_image { image cairo_flush_ascii85_file } def
-/cairo_imagemask { imagemask cairo_flush_ascii85_file } def
-%%EndProlog
-%%BeginSetup
-%%BeginResource: font f-0-0
-%!FontType1-1.1 f-0-0 1.0
-11 dict begin
-/FontName /f-0-0 def
-/PaintType 0 def
-/FontType 1 def
-/FontMatrix [0.001 0 0 0.001 0 0] readonly def
-/FontBBox {0 -14 908 692                                     } readonly def
-/Encoding 256 array
-0 1 255 {1 index exch /.notdef put} for
-dup 73 /I put
-dup 82 /R put
-dup 101 /e put
-dup 109 /m put
-readonly def
-currentdict end
-currentfile eexec
-f983ef0097ece636fb4a96c74d26ab84185f6dfa4a16a7a1c27bbe3f1156aea698df336d20b467
-b10e7f33846656653c5ac6962759d3056cbdb3190bac614b984bf5a132dc418192443014ba63de
-800d392b6fea026574bb2535fd7bb5338f35bf15a88ea328fdaa49670c7852e3d060f3c5d6b07f
-2ef6d0f22646c5d18e19a2ae3ee120390f6dd96f76dcf1e127de5e9299077a00c17c0d71e36e5b
-9d5ec58fceda57739a6a4214d4b79d6c48d2784b60c320323c7acddddf34db833cac0cf109f799
-69d114a330d372e5c978a66acc84e3fe5557f6240856a013ffaa0199444e5c5036f775eba4a5c5
-8cde66cf604b9aca2178431127b8a1ff7ed633a65c04600af5f573483112251cabe8722c0ba224
-7e4445af50cf2457d0f320e3c97746456087766b4bf11115560ce328711eca3bd110d9edf8f723
-7690411035c2d2a4529eceb3758e9dfdf69937c82634682ddec349213e6cdca1236ff1e59fd7ad
-c509a9f3c257841b8053a86b38d617d963b24dfb3767bfc9b4af0288c9b0b8e2572d16601fc539
-50419b779278a6ee6aa2c6f6e88f16020db6e348845fd5b2cd9ac2bb9cc9caa74bac30ab845da5
-f651fffe8b245f374569b60b2520d5b091c2895daa06f7cacffa423bc29ca3a939660aef03f4ba
-db6c051bab9e97aa6f8b3423aee96ff61f682293fdb336288dbb885c46c5c6d7ca5c5a0cf84a99
-4b1ef4f098cdceee4559f76b71375ac1e48de97bc26d04e944bd8f7723aaca9bdeb0a55b4d8e30
-b9169a69c8b151f7e913240de4e7614c0ce99885f8de5ae8d0c7602bdba359c79247126be04fa0
-4837a74d4b1829aba24a81ace9429198af5c03ce00c992b95216dab9619da47da7550eca0ff6cd
-0ebc575021f16decb7f0d945e2c73764f06e1781806305825422f0f7ad20cee7de432128300693
-599dbdafc575e2f472140a927b4552e1cd714bd09871feab74613bf38b4117e1b2c870998d1584
-50ae3c9c1b184d5529d7092e102d713e1e4a8d02eb0fb3edc7ef054b7fbe323e488fbcf700dac6
-058c3eeb18d59888e42247d792f3cff694e14a0b69965054b8e811dc8ae391c9be575648546fef
-0365caa0b5334da60343169e20c6b1b8d51c5fbe17cfca3ec7f3bd1c61d09838b717c08ccfcbda
-2a43ce0a730162c3285d5185e5fa3f8c6aaa204a403cdae550e565dcaf3816e4f19a66fee5bb4d
-e532d49827c5c811b8c6effa17be7f7f897390f48ca0d11588bc17af153bec904639fcce603e9a
-fb7417deeba06beb6901c0fba586004121e1aa2dcab890d83326fd7ffca74c35e64a22c9434ef6
-7d7496180137f9c8705089856e54a802d541062de40941e37319ed189b6dd27b69783befae9725
-88dacdb39bfe000a0789e90bfdcc7a2187dbff723ba8a74bb2ececfee0a9ea34b01434890000000000000000000000000000000000000000000000000000000000000000
-0000000000000000000000000000000000000000000000000000000000000000
-0000000000000000000000000000000000000000000000000000000000000000
-0000000000000000000000000000000000000000000000000000000000000000
-0000000000000000000000000000000000000000000000000000000000000000
-0000000000000000000000000000000000000000000000000000000000000000
-0000000000000000000000000000000000000000000000000000000000000000
-0000000000000000000000000000000000000000000000000000000000000000
-cleartomark
-%%EndResource
-%%BeginResource: font f-1-0
-%!FontType1-1.1 f-1-0 1.0
-11 dict begin
-/FontName /f-1-0 def
-/PaintType 0 def
-/FontType 1 def
-/FontMatrix [0.001 0 0 0.001 0 0] readonly def
-/FontBBox {29 -169 437 799                                   } readonly def
-/Encoding 256 array
-0 1 255 {1 index exch /.notdef put} for
-dup 40 /parenleft put
-dup 41 /parenright put
-readonly def
-currentdict end
-currentfile eexec
-f983ef0097ece636fb4a96c74d26ab84185f6dfa4a16a7a1c27bbe3f1156aea698df336d20b467
-b10e7f33846656653c5ac6962759d3056cbdb3190bac614b984bf5a132dc418192443014ba63de
-800d392b6fea026574bb2535fd7bb5338f35bf15a88ea328fdaa49670c7852e3d060f3c5d6b07f
-2ef6d0f22646c5d18e19a2ae3ee120390f6dd96f76dcf1e127de5e9299077a00c17c0d71e36e5b
-9d5ec58fceda57739a6a4214d4b79d6c48d2784b60c320323c7acddddf34db833cac0cf109f799
-69d114a330d372e5c978a66acc84e3fe5557f6240856a013ffaa0199444e5c5036f775eba4a5c5
-8cde66cf604b9aca2178431127b8a1ff7ed633a65c04600af5f573483112251ca90bc9cf8825c7
-41412dda705317b7cb229dd377ff3d18e94daa9ba3bbd4ccd2ecde18a1c220179cca13293a42f7
-1d167cd6ac624b8f8573fc281c165eeb093c7705f0c9d1ce383c8701d14fcde12ac700699f81e8
-412c2e7e4c95c1440662af1652abdb4ce6be4b5f976724c26d20f166e17532da87ef8b24e90d2b
-ca09313d345112c202c1d9528e8c8e15bdfd68385cef36d711b99ee54d324b8778dae18d9af490
-41fbe748f7910913a3460e4af7353d7952f1fa9fde2bb171a7717e297425e0c08ca9800b01b2f5
-d645e0dbbc3a76bdfc773c19f4917354ed597d131dcc12985dd83ff833cc665a3ed3f11ec3814b
-3a8be6d7aef97d0b12b552d8da18f6cea65a8e284355941aae2da895a0fee8c8c2d4c22664f827
-5fb1ca0fbda2da6ff7fee9a610c58ec5d0c82dbb9b890d86f03ce85b69a56821a477e957df28b4
-b7afc889cbe637525896dc572b943c7f55648deb0894a36d8a1f7cfe05e48b6abb21a9949c7070
-43ecfa2c9ed9ed591f98e5fb1581bfb12e97b35bab44504370459fd28ca0c151ded5634089598c
-3d20720000000000000000000000000000000000000000000000000000000000000000
-0000000000000000000000000000000000000000000000000000000000000000
-0000000000000000000000000000000000000000000000000000000000000000
-0000000000000000000000000000000000000000000000000000000000000000
-0000000000000000000000000000000000000000000000000000000000000000
-0000000000000000000000000000000000000000000000000000000000000000
-0000000000000000000000000000000000000000000000000000000000000000
-0000000000000000000000000000000000000000000000000000000000000000
-cleartomark
-%%EndResource
-%%BeginResource: font f-1-1
-%!FontType1-1.1 f-1-1 1.0
-11 dict begin
-/FontName /f-1-1 def
-/PaintType 0 def
-/FontType 1 def
-/FontMatrix [0.001 0 0 0.001 0 0] readonly def
-/FontBBox {-6 -207 465 799                                   } readonly def
-/Encoding 256 array
-0 1 255 {1 index exch /.notdef put} for
-dup 1 /uni03BE put
-readonly def
-currentdict end
-currentfile eexec
-f983ef0097ece636fb4a96c74d26ab84185f6dfa4a16a7a1c27bbe3f1156aea698df336d20b467
-b10e7f33846656653c5ac6962759d3056cbdb3190bac614b984bf5a132dc418192443014ba63de
-800d392b6fea026574bb2535fd7bb5338f35bf15a88ea328fdaa49670c7852e3d060f3c5d6b07f
-2ef6d0f22646c5d18e19a2ae3ee120390f6dd96f76dcf1e127de5e9299077a00c17c0d71e36e5b
-9d5ec58fceda57739a6a4214d4b79d6c48d2784b60c320323c7acddddf34db833cac0cf109f799
-69d114a330d372e5c978a66acc84e3fe5557f6240856a013ffaa0199444e5c5036f775eba4a5c5
-8cde66cf604b9aca2178431127b8a1ff7ed633a65c04600af5f573483112251cae134058d6a192
-3c6b565d778d9618b31789d664bb543a0e576f202df308890d53425311c0df16d70e7088bc233c
-2aeafd23aed96e18251b90593258f09f68b68c844c8e5bf170e06e331e14147fa538f8473eeb1e
-c84dbfec93c34173c11f0744da9bfa7cf6a3d8c4eb2a75eb71b49d69da4ade018689e722cfab11
-be4351efa968308dff1933cdf6da74c1d45ce31ed30cfd322f1554cf02839075c2488a6e43b89a
-f24d9bd7595d4fc4c07d5aa69574f2b45a692e0305a31ca8496286dde55759bacec2cf519a550c
-fc581758620e692c3d1f29b52b360ab757e8a4ed621b3b2c5ce883b037b9fd1b119dba66319bb2
-4706b3eb74ba54dfb209979bff3f44781327e8d4e7b20328f58cdea3284522496934f1cd89a9ab
-8f825cc46c51daa2ea8f85719a90e312bb07457ba2739fe15e7f59e27a646521ff053df21c2edf
-9d96735ee9d39d251bcf0113dc96ad03208d1ae62db8141146cfd99f59fcb8a10bdbf341def129
-fd5b55b7fe37f31eae75b5caf35814db82b954eeb9ce040e42be770590adeaa9a03b85f5c8e344
-bef5c97285dc20e725e2b0ecaea95a78cc672f11240e0fed510f9027f695fe53aecf49f9bdd51c
-949743af735f932804173c4d9584652fc9184b875b8cf21b4af33bdcf8580ca4ce84b48a0a40b1
-9771faa53eb86add0076d818c9d10927b64117ce25af360fa0ef5061787ff063349478ead89981
-4641ebef5cebc2b444f7497c0f9638073d57ef29982e7efcd5421544ba5a737b3527d24db03842
-aa24c1f0c002b36b8656951b8f835f2dfd1d419cdcd2e490cc73162e9163805e9cf101f7d336ea
-d0caa5b458789b0f625cc937389ec0a67f90c3c2640000000000000000000000000000000000000000000000000000000000000000
-0000000000000000000000000000000000000000000000000000000000000000
-0000000000000000000000000000000000000000000000000000000000000000
-0000000000000000000000000000000000000000000000000000000000000000
-0000000000000000000000000000000000000000000000000000000000000000
-0000000000000000000000000000000000000000000000000000000000000000
-0000000000000000000000000000000000000000000000000000000000000000
-0000000000000000000000000000000000000000000000000000000000000000
-cleartomark
-%%EndResource
-%%EndSetup
-%%Page: 1 1
-%%BeginPageSetup
-%%PageBoundingBox: 0 0 360 221
-%%EndPageSetup
-q 0 0 360 221 rectclip
-1 0 0 -1 0 222 cm q
-0 g
-0.36 w
-0 J
-0 j
-[ 2.88 2.88] 0 d
-3.25 M 0.18 119.551 m 330.613 119.551 l S
-BT
-10.08 0 0 -10.08 336.375 122.110031 Tm
-/f-0-0 1 Tf
-(Re)Tj
-10.8 0 0 -10.8 348.045 122.110031 Tm
-/f-1-0 1 Tf
-(\()Tj
-/f-1-1 1 Tf
-<01>Tj
-/f-1-0 1 Tf
-[()-29(\))]TJ
-ET
-Q q
-165 17 1 204.762 re W n
-0 g
-0.36 w
-0 J
-0 j
-[ 2.88 2.88] 0 d
-3.25 M 165.398 221.66 m 165.398 17.441 l S
-Q q
-0 g
-BT
-10.08 0 0 -10.08 153.009375 9.12 Tm
-/f-0-0 1 Tf
-(Im)Tj
-10.8 0 0 -10.8 165.830625 9.12 Tm
-/f-1-0 1 Tf
-(\()Tj
-/f-1-1 1 Tf
-<01>Tj
-/f-1-0 1 Tf
-[()-29(\))]TJ
-ET
-1.44 w
-2 J
-0 j
-[] 0.0 d
-3.25 M 0.18 119.551 m 165.398 119.551 l S
-169.527 119.551 m 169.527 118.453 169.094 117.402 168.316 116.629 c 167.543
- 115.855 166.492 115.418 165.398 115.418 c 164.301 115.418 163.25 115.855
- 162.477 116.629 c 161.703 117.402 161.266 118.453 161.266 119.551 c 161.266
- 120.645 161.703 121.695 162.477 122.469 c 163.25 123.246 164.301 123.68
- 165.398 123.68 c 166.492 123.68 167.543 123.246 168.316 122.469 c 169.094
- 121.695 169.527 120.645 169.527 119.551 c h
-169.527 119.551 m f*
-Q Q
-showpage
-%%Trailer
-end restore
-%%EOF
diff --git a/figs/F_theta_singularities.eps b/figs/F_theta_singularities.eps
deleted file mode 100644
index cba0e16..0000000
--- a/figs/F_theta_singularities.eps
+++ /dev/null
@@ -1,374 +0,0 @@
-%!PS-Adobe-3.0 EPSF-3.0
-%%Creator: cairo 1.15.4 (http://cairographics.org)
-%%CreationDate: Tue May 16 17:20:36 2023
-%%Pages: 1
-%%DocumentData: Clean7Bit
-%%LanguageLevel: 2
-%%Creator: Wolfram Mathematica 13.2.1.0 for Linux x86 (64-bit) (January 31, 2023)
-%%BoundingBox: 0 0 360 220
-%%EndComments
-%%BeginProlog
-save
-50 dict begin
-/q { gsave } bind def
-/Q { grestore } bind def
-/cm { 6 array astore concat } bind def
-/w { setlinewidth } bind def
-/J { setlinecap } bind def
-/j { setlinejoin } bind def
-/M { setmiterlimit } bind def
-/d { setdash } bind def
-/m { moveto } bind def
-/l { lineto } bind def
-/c { curveto } bind def
-/h { closepath } bind def
-/re { exch dup neg 3 1 roll 5 3 roll moveto 0 rlineto
-      0 exch rlineto 0 rlineto closepath } bind def
-/S { stroke } bind def
-/f { fill } bind def
-/f* { eofill } bind def
-/n { newpath } bind def
-/W { clip } bind def
-/W* { eoclip } bind def
-/BT { } bind def
-/ET { } bind def
-/pdfmark where { pop globaldict /?pdfmark /exec load put }
-    { globaldict begin /?pdfmark /pop load def /pdfmark
-    /cleartomark load def end } ifelse
-/BDC { mark 3 1 roll /BDC pdfmark } bind def
-/EMC { mark /EMC pdfmark } bind def
-/cairo_store_point { /cairo_point_y exch def /cairo_point_x exch def } def
-/Tj { show currentpoint cairo_store_point } bind def
-/TJ {
-  {
-    dup
-    type /stringtype eq
-    { show } { -0.001 mul 0 cairo_font_matrix dtransform rmoveto } ifelse
-  } forall
-  currentpoint cairo_store_point
-} bind def
-/cairo_selectfont { cairo_font_matrix aload pop pop pop 0 0 6 array astore
-    cairo_font exch selectfont cairo_point_x cairo_point_y moveto } bind def
-/Tf { pop /cairo_font exch def /cairo_font_matrix where
-      { pop cairo_selectfont } if } bind def
-/Td { matrix translate cairo_font_matrix matrix concatmatrix dup
-      /cairo_font_matrix exch def dup 4 get exch 5 get cairo_store_point
-      /cairo_font where { pop cairo_selectfont } if } bind def
-/Tm { 2 copy 8 2 roll 6 array astore /cairo_font_matrix exch def
-      cairo_store_point /cairo_font where { pop cairo_selectfont } if } bind def
-/g { setgray } bind def
-/rg { setrgbcolor } bind def
-/d1 { setcachedevice } bind def
-/cairo_flush_ascii85_file { cairo_ascii85_file status { cairo_ascii85_file flushfile } if } def
-/cairo_image { image cairo_flush_ascii85_file } def
-/cairo_imagemask { imagemask cairo_flush_ascii85_file } def
-%%EndProlog
-%%BeginSetup
-%%BeginResource: font f-0-0
-%!FontType1-1.1 f-0-0 1.0
-11 dict begin
-/FontName /f-0-0 def
-/PaintType 0 def
-/FontType 1 def
-/FontMatrix [0.001 0 0 0.001 0 0] readonly def
-/FontBBox {-12 -14 908 692                                   } readonly def
-/Encoding 256 array
-0 1 255 {1 index exch /.notdef put} for
-dup 48 /zero put
-dup 73 /I put
-dup 76 /L put
-dup 82 /R put
-dup 89 /Y put
-dup 101 /e put
-dup 109 /m put
-readonly def
-currentdict end
-currentfile eexec
-f983ef0097ece636fb4a96c74d26ab84185f6dfa4a16a7a1c27bbe3f1156aea698df336d20b467
-b10e7f33846656653c5ac6962759d3056cbdb3190bac614b984bf5a132dc418192443014ba63de
-800d392b6fea026574bb2535fd7bb5338f35bf15a88ea328fdaa49670c7852e3d060f3c5d6b07f
-2ef6d0f22646c5d18e19a2ae3ee120390f6dd96f76dcf1e127de5e9299077a00c17c0d71e36e5b
-9d5ec58fceda57739a6a4214d4b79d6c48d2784b60c320323c7acddddf34db833cac0cf109f799
-69d114a330d372e5c978a66acc84e3fe5557f6240856a013ffaa0199444e5c5036f775eba4a5c5
-8cde66cf604b9aca2178431127b8a1ff7ed633a65c04600af5f573483112251ca40352c6e2284e
-344947523a70f7b109147467f7576cb1df156dca2f25ccb577c1669626620a113ccdc0d69bb530
-dcedcb09d669e42789d3d1f1eb2fba73343f65132cb03065d412c4d987b79778555f98cbc72ab7
-18a72c35e371bf684a718b599d9f12c1a856afb05fa3bd876d6a55dcc6279feec01485b499c3da
-d50b200814e31ce340178663202f0a0324b15a23d545a665ada375c999b9af688f6f64738c2b03
-3fad0ff51c135ab5fc976cac8f6ee6fd117af76aede659c3d7c3ef848e783a3d7fc2ffd6dfb65d
-6fec08c4a48386ae22093696e4a4149206687406201494f7c92d83695ede02da0ec2efc745388b
-d4e96b9bf02196c1313f7b64670b3012e1b26b62b4c4398f62988c452011a3012866807ac3e958
-f6a33e22de6dad25663512af2f744cb4b2bccf96491c7dabfa4a6f3809714ce5e12c0ec56411de
-8d2d1ce34f9869137188615c0f4fbdfbea4b6aa825293167df8a44ecd5367cc0d134374c602f68
-cb24646d0a40cd42b9eaaa594b27274ae56eca9966b295b52c551e9431db92a8490105b9fca3cf
-abf2e646e6178f99068ffc46e80d0e6b91f6f7753ef194c42e47f2e32cfdbeff85b184ae87b96c
-ba03c00d2bb80c124412d6eac22d919a886efaafd1e1f0539f0b2277d7a3a570c352d18e8b9098
-262a6012482668a2836e6c631e98f1ffdfbd7e6a8327c434da366e42b10b3a04e6020dbad97dbf
-44a4eeb858298517e1b653d5719207f977d26cb9faf9285db28ec7bb55ecdf88173ed6a7542538
-75b780cffa546283ca777009c8bde4c70cd590dd3eca81b89e295c43771d95b90337e38f8f9d62
-501c3f0250ee10607517107eb9b8686aa2b2e73618e6ec508658efdfd4a9fbeff0a5f794ecb851
-81b07fb69e57d0ba45b34b1ddf3985403bf1ddbe9e24e73214cb9e3417f1569784c7585e54ce17
-993a0b1834c6e8641e48f9d2ed82931b358ce1638f893f198549802d03b5f77c30cdb701565094
-9cbc86327e59767775ffe0232e8fb09d9a865d66031371a7c4f279e83b7bbd2a9d3d5c04b876de
-303044b11569247c0a341892b60d49bf5a3d90cff8ecb498d5221203b27e9f7a0e2a0f5c83b803
-141289b187e0e40330f366ffe1889280fe6e24c8fe248cdd7b505c38a12f9aea4e0604d3a39b85
-dfa73f752e4deea83932b5b06717fe4ff53bc029968c48bf2eb97e7a4e0e462e6524fa833c2544
-99918cfc9b5c58f63e8bafb50d95ca777708fb85e9fd4babeb223ba13b0d5325efaf7813ead314
-ba40c2317c875af7430deaab519f75944b416da03bc21b407842090e3499d799ed64c606ae45cc
-de54f08502d814e5cd8cb51c31d0c7c591ea9e77342183be87d82d0bdbccf16c8edef1c1499d14
-4bff2d5ba6173f20939c2f5662bdb688061117662e55fa0d8aa7080bdc88b7a24b462ccffc833e
-1e75fd5537be5f7e7079349eacdec1709dd1889595a5092327dbbce7a3a8fca00d74fce608e932
-9721f45d89f7ccc9ee55a8f4082b95ef9fe1787ce123cdddbb83af12376b602e43b5a8cfcf4550
-0e418a92789eea9e01719ad69ffd7ed668660165e0d959ec6695fac6f428d6d777d8610000000000000000000000000000000000000000000000000000000000000000
-0000000000000000000000000000000000000000000000000000000000000000
-0000000000000000000000000000000000000000000000000000000000000000
-0000000000000000000000000000000000000000000000000000000000000000
-0000000000000000000000000000000000000000000000000000000000000000
-0000000000000000000000000000000000000000000000000000000000000000
-0000000000000000000000000000000000000000000000000000000000000000
-0000000000000000000000000000000000000000000000000000000000000000
-cleartomark
-%%EndResource
-%%BeginResource: font f-1-0
-%!FontType1-1.1 f-1-0 1.0
-11 dict begin
-/FontName /f-1-0 def
-/PaintType 0 def
-/FontType 1 def
-/FontMatrix [0.001 0 0 0.001 0 0] readonly def
-/FontBBox {29 -169 437 799                                   } readonly def
-/Encoding 256 array
-0 1 255 {1 index exch /.notdef put} for
-dup 40 /parenleft put
-dup 41 /parenright put
-readonly def
-currentdict end
-currentfile eexec
-f983ef0097ece636fb4a96c74d26ab84185f6dfa4a16a7a1c27bbe3f1156aea698df336d20b467
-b10e7f33846656653c5ac6962759d3056cbdb3190bac614b984bf5a132dc418192443014ba63de
-800d392b6fea026574bb2535fd7bb5338f35bf15a88ea328fdaa49670c7852e3d060f3c5d6b07f
-2ef6d0f22646c5d18e19a2ae3ee120390f6dd96f76dcf1e127de5e9299077a00c17c0d71e36e5b
-9d5ec58fceda57739a6a4214d4b79d6c48d2784b60c320323c7acddddf34db833cac0cf109f799
-69d114a330d372e5c978a66acc84e3fe5557f6240856a013ffaa0199444e5c5036f775eba4a5c5
-8cde66cf604b9aca2178431127b8a1ff7ed633a65c04600af5f573483112251ca90bc9cf8825c7
-41412dda705317b7cb229dd377ff3d18e94daa9ba3bbd4ccd2ecde18a1c220179cca13293a42f7
-1d167cd6ac624b8f8573fc281c165eeb093c7705f0c9d1ce383c8701d14fcde12ac700699f81e8
-412c2e7e4c95c1440662af1652abdb4ce6be4b5f976724c26d20f166e17532da87ef8b24e90d2b
-ca09313d345112c202c1d9528e8c8e15bdfd68385cef36d711b99ee54d324b8778dae18d9af490
-41fbe748f7910913a3460e4af7353d7952f1fa9fde2bb171a7717e297425e0c08ca9800b01b2f5
-d645e0dbbc3a76bdfc773c19f4917354ed597d131dcc12985dd83ff833cc665a3ed3f11ec3814b
-3a8be6d7aef97d0b12b552d8da18f6cea65a8e284355941aae2da895a0fee8c8c2d4c22664f827
-5fb1ca0fbda2da6ff7fee9a610c58ec5d0c82dbb9b890d86f03ce85b69a56821a477e957df28b4
-b7afc889cbe637525896dc572b943c7f55648deb0894a36d8a1f7cfe05e48b6abb21a9949c7070
-43ecfa2c9ed9ed591f98e5fb1581bfb12e97b35bab44504370459fd28ca0c151ded5634089598c
-3d20720000000000000000000000000000000000000000000000000000000000000000
-0000000000000000000000000000000000000000000000000000000000000000
-0000000000000000000000000000000000000000000000000000000000000000
-0000000000000000000000000000000000000000000000000000000000000000
-0000000000000000000000000000000000000000000000000000000000000000
-0000000000000000000000000000000000000000000000000000000000000000
-0000000000000000000000000000000000000000000000000000000000000000
-0000000000000000000000000000000000000000000000000000000000000000
-cleartomark
-%%EndResource
-%%BeginResource: font f-1-1
-%!FontType1-1.1 f-1-1 1.0
-11 dict begin
-/FontName /f-1-1 def
-/PaintType 0 def
-/FontType 1 def
-/FontMatrix [0.001 0 0 0.001 0 0] readonly def
-/FontBBox {28 -13 453 799                                    } readonly def
-/Encoding 256 array
-0 1 255 {1 index exch /.notdef put} for
-dup 1 /uni03B8 put
-readonly def
-currentdict end
-currentfile eexec
-f983ef0097ece636fb4a96c74d26ab84185f6dfa4a16a7a1c27bbe3f1156aea698df336d20b467
-b10e7f33846656653c5ac6962759d3056cbdb3190bac614b984bf5a132dc418192443014ba63de
-800d392b6fea026574bb2535fd7bb5338f35bf15a88ea328fdaa49670c7852e3d060f3c5d6b07f
-2ef6d0f22646c5d18e19a2ae3ee120390f6dd96f76dcf1e127de5e9299077a00c17c0d71e36e5b
-9d5ec58fceda57739a6a4214d4b79d6c48d2784b60c320323c7acddddf34db833cac0cf109f799
-69d114a330d372e5c978a66acc84e3fe5557f6240856a013ffaa0199444e5c5036f775eba4a5c5
-8cde66cf604b9aca2178431127b8a1ff7ed633a65c04600af5f573483112251cae134058d6a192
-3c6b565d778d9618b31789d664bb543a0e576f202df308890d53425311c0df16d70e7088bc233c
-2aeafd23aed96e18251b90593258f09f68b68c844c8e5bf170e06e331e14147fa538f8473eeb1e
-c84dbfec93c3410e50135635b99de6891224a561e7c815e270995932d4ca76c8cc14b02767bb66
-7e6acad1ab52cbc965dc9fc5d35b7f55bd68178f09c7128011331eb172346c01b77767a131365b
-3cb1e76bf2ef8772818a52fde15db663b8b91d9d22148c044c1f17c084466eee12d35401b0d206
-447bd9cb8b6e927f74a828d01e7ce0e8504701d21d52e83a0f908b3eaf18af033d7fdc4519160d
-a1f3998dc14198ecb66970ab1422655946606979ebc3920ec6406caae936b284318ce59d7fd021
-6da6916dccf7cddaa08c95fe84fe0a36eff860ec858faee6eae9b234fd7f6b7922b6407fe66548
-4ee8a12cf4b24800049489170c1c089065cfd05e7611f514854ffb249e79b19db4e86d95818819
-599eccc923f9ec10ebcf73f55e7828ba032aff285278971bd99c0a3ddf0000000000000000000000000000000000000000000000000000000000000000
-0000000000000000000000000000000000000000000000000000000000000000
-0000000000000000000000000000000000000000000000000000000000000000
-0000000000000000000000000000000000000000000000000000000000000000
-0000000000000000000000000000000000000000000000000000000000000000
-0000000000000000000000000000000000000000000000000000000000000000
-0000000000000000000000000000000000000000000000000000000000000000
-0000000000000000000000000000000000000000000000000000000000000000
-cleartomark
-%%EndResource
-%%BeginResource: font f-2-0
-%!FontType1-1.1 f-2-0 1.0
-11 dict begin
-/FontName /f-2-0 def
-/PaintType 0 def
-/FontType 1 def
-/FontMatrix [0.001 0 0 0.001 0 0] readonly def
-/FontBBox {0 -12 363 715                                     } readonly def
-/Encoding 256 array
-0 1 255 {1 index exch /.notdef put} for
-dup 105 /i put
-readonly def
-currentdict end
-currentfile eexec
-f983ef0097ece636fb4a96c74d26ab84185f6dfa4a16a7a1c27bbe3f1156aea698df336d20b467
-b10e7f33846656653c5ac6962759d3056cbdb3190bac614b984bf5a132dc418192443014ba63de
-800d392b6fea026574bb2535fd7bb5338f35bf15a88ea328fdaa49670c7852e3d060f3c5d6b07f
-2ef6d0f22646c5d18e19a2ae3ee120390f6dd96f76dcf1e127de5e9299077a00c17c0d71e36e5b
-9d5ec58fceda57739a6a4214d4b79d6c48d2784b60c320323c7acddddf34db833cac0cf109f799
-69d114a330d372e5c978a66acc84e3fe5557f6240856a013ffaa0199444e5c5036f775eba4a5c5
-8cde66cf604b9aca2178431127b8a1ff7ed633a65c04600af5f573483112251cae134058d6a192
-3c6b565d778d9618b31789d664bb543a0e576f252e8520c2d0698c337b75c663f61d3deead2935
-71dc9621dfa39dc5f30363291678a7d9dfdeaa2de43d090fdf9945858d9b5b3a5df2a5865b3028
-dc4b7ac7fe8270eda10a09d5669f164eb5fa6e4ca848129c7f59349ba575bbdf02dfbd8f5ed330
-d9554dd1eb8b856cdef62fe801b421cc107aa678dbf1124aab4cbde909fd8611cafc587bb34560
-f3428a01d0fd050e1c1ae785787bd5c142500e345326b240d6d37c6801da6061e4be60b75cc4a0
-06ffe4ca26e456a9313b7f02bd60218dde34c309130b9ee274c413f042863100acb2ad54244397
-b1ccf64df275ba901ee414216a2d7c659e80f9eb06bcb6f8d4b9e005690000000000000000000000000000000000000000000000000000000000000000
-0000000000000000000000000000000000000000000000000000000000000000
-0000000000000000000000000000000000000000000000000000000000000000
-0000000000000000000000000000000000000000000000000000000000000000
-0000000000000000000000000000000000000000000000000000000000000000
-0000000000000000000000000000000000000000000000000000000000000000
-0000000000000000000000000000000000000000000000000000000000000000
-0000000000000000000000000000000000000000000000000000000000000000
-cleartomark
-%%EndResource
-%%EndSetup
-%%Page: 1 1
-%%BeginPageSetup
-%%PageBoundingBox: 0 0 360 220
-%%EndPageSetup
-q 0 0 360 220 rectclip
-1 0 0 -1 0 221 cm q
-0 g
-0.36 w
-0 J
-0 j
-[ 2.88 2.88] 0 d
-3.25 M 0.18 118.234 m 330.754 118.234 l S
-BT
-10.08 0 0 -10.08 336.51375 121.472907 Tm
-/f-0-0 1 Tf
-(Re)Tj
-10.8 0 0 -10.8 348.18375 121.472907 Tm
-/f-1-0 1 Tf
-(\()Tj
-/f-1-1 1 Tf
-<01>Tj
-/f-1-0 1 Tf
-[()-14(\))]TJ
-ET
-Q q
-165 16 1 204.801 re W n
-0 g
-0.36 w
-0 J
-0 j
-[ 2.88 2.88] 0 d
-3.25 M 165.469 220.387 m 165.469 16.078 l S
-Q q
-0 g
-BT
-10.08 0 0 -10.08 153.148125 9.12 Tm
-/f-0-0 1 Tf
-(Im)Tj
-10.8 0 0 -10.8 165.969375 9.12 Tm
-/f-1-0 1 Tf
-(\()Tj
-/f-1-1 1 Tf
-<01>Tj
-/f-1-0 1 Tf
-[()-14(\))]TJ
-ET
-Q q
-164 16 3 52 re W n
-0 g
-1.44 w
-2 J
-0 j
-[] 0.0 d
-3.25 M 165.469 67.156 m 165.469 -47.055 l S
-Q q
-164 168 3 52.801 re W n
-0 g
-1.44 w
-2 J
-0 j
-[] 0.0 d
-3.25 M 165.469 169.309 m 165.469 283.52 l S
-Q q
-0 g
-162.547 64.234 5.844 5.844 re f
-162.547 166.387 5.844 5.844 re f
-1.44 w
-2 J
-0 j
-[] 0.0 d
-3.25 M 0.18 118.234 m 41.5 118.234 l S
-45.633 118.234 m 45.633 117.137 45.199 116.086 44.422 115.312 c 43.648 
-114.535 42.598 114.102 41.5 114.102 c 40.406 114.102 39.355 114.535 38.578
- 115.312 c 37.805 116.086 37.371 117.137 37.371 118.234 c 37.371 119.328
- 37.805 120.379 38.578 121.156 c 39.355 121.93 40.406 122.363 41.5 122.363
- c 42.598 122.363 43.648 121.93 44.422 121.156 c 45.199 120.379 45.633 119.328
- 45.633 118.234 c h
-45.633 118.234 m f*
-Q q
-288 117 43 2 re W n
-0 g
-1.44 w
-2 J
-0 j
-[] 0.0 d
-3.25 M 330.754 118.234 m 289.434 118.234 l S
-Q q
-0 g
-293.562 118.234 m 293.562 117.137 293.129 116.086 292.355 115.312 c 291.578
- 114.535 290.527 114.102 289.434 114.102 c 288.336 114.102 287.285 114.535
- 286.512 115.312 c 285.734 116.086 285.301 117.137 285.301 118.234 c 285.301
- 119.328 285.734 120.379 286.512 121.156 c 287.285 121.93 288.336 122.363
- 289.434 122.363 c 290.527 122.363 291.578 121.93 292.355 121.156 c 293.129
- 120.379 293.562 119.328 293.562 118.234 c h
-293.562 118.234 m f*
-0.36 w
-2 J
-0 j
-[] 0.0 d
-3.25 M 289.434 118.234 m 289.434 109.969 l S
-165.469 67.156 m 173.73 67.156 l S
-BT
-10.08 0 0 -10.08 177.725859 70.396453 Tm
-/f-2-0 1 Tf
-(i)Tj
-10.8 0 0 -10.8 181.385859 70.396453 Tm
-/f-1-1 1 Tf
-<01>Tj
-7.2 0 0 -7.2 186.125859 72.102703 Tm
-/f-0-0 1 Tf
-(YL)Tj
-10.8 0 0 -10.8 285.038906 104.944219 Tm
-/f-1-1 1 Tf
-<01>Tj
-7.2 0 0 -7.2 289.778906 106.650469 Tm
-/f-0-0 1 Tf
-(0)Tj
-ET
-Q Q
-showpage
-%%Trailer
-end restore
-%%EOF
diff --git a/figs/contour_path.eps b/figs/contour_path.eps
deleted file mode 100644
index cb65b3c..0000000
--- a/figs/contour_path.eps
+++ /dev/null
@@ -1,440 +0,0 @@
-%!PS-Adobe-3.0 EPSF-3.0
-%%Creator: cairo 1.15.4 (http://cairographics.org)
-%%CreationDate: Wed Jan 19 13:55:29 2022
-%%Pages: 1
-%%DocumentData: Clean7Bit
-%%LanguageLevel: 2
-%%Creator: Wolfram Mathematica 13.0.0.0 for Linux x86 (64-bit) (December 2, 2021)
-%%BoundingBox: 0 0 360 218
-%%EndComments
-%%BeginProlog
-save
-50 dict begin
-/q { gsave } bind def
-/Q { grestore } bind def
-/cm { 6 array astore concat } bind def
-/w { setlinewidth } bind def
-/J { setlinecap } bind def
-/j { setlinejoin } bind def
-/M { setmiterlimit } bind def
-/d { setdash } bind def
-/m { moveto } bind def
-/l { lineto } bind def
-/c { curveto } bind def
-/h { closepath } bind def
-/re { exch dup neg 3 1 roll 5 3 roll moveto 0 rlineto
-      0 exch rlineto 0 rlineto closepath } bind def
-/S { stroke } bind def
-/f { fill } bind def
-/f* { eofill } bind def
-/n { newpath } bind def
-/W { clip } bind def
-/W* { eoclip } bind def
-/BT { } bind def
-/ET { } bind def
-/pdfmark where { pop globaldict /?pdfmark /exec load put }
-    { globaldict begin /?pdfmark /pop load def /pdfmark
-    /cleartomark load def end } ifelse
-/BDC { mark 3 1 roll /BDC pdfmark } bind def
-/EMC { mark /EMC pdfmark } bind def
-/cairo_store_point { /cairo_point_y exch def /cairo_point_x exch def } def
-/Tj { show currentpoint cairo_store_point } bind def
-/TJ {
-  {
-    dup
-    type /stringtype eq
-    { show } { -0.001 mul 0 cairo_font_matrix dtransform rmoveto } ifelse
-  } forall
-  currentpoint cairo_store_point
-} bind def
-/cairo_selectfont { cairo_font_matrix aload pop pop pop 0 0 6 array astore
-    cairo_font exch selectfont cairo_point_x cairo_point_y moveto } bind def
-/Tf { pop /cairo_font exch def /cairo_font_matrix where
-      { pop cairo_selectfont } if } bind def
-/Td { matrix translate cairo_font_matrix matrix concatmatrix dup
-      /cairo_font_matrix exch def dup 4 get exch 5 get cairo_store_point
-      /cairo_font where { pop cairo_selectfont } if } bind def
-/Tm { 2 copy 8 2 roll 6 array astore /cairo_font_matrix exch def
-      cairo_store_point /cairo_font where { pop cairo_selectfont } if } bind def
-/g { setgray } bind def
-/rg { setrgbcolor } bind def
-/d1 { setcachedevice } bind def
-/cairo_flush_ascii85_file { cairo_ascii85_file status { cairo_ascii85_file flushfile } if } def
-/cairo_image { image cairo_flush_ascii85_file } def
-/cairo_imagemask { imagemask cairo_flush_ascii85_file } def
-%%EndProlog
-%%BeginSetup
-%%BeginResource: font f-0-0
-%!FontType1-1.1 f-0-0 1.0
-11 dict begin
-/FontName /f-0-0 def
-/PaintType 0 def
-/FontType 1 def
-/FontMatrix [0.001 0 0 0.001 0 0] readonly def
-/FontBBox {29 -169 437 799                                   } readonly def
-/Encoding 256 array
-0 1 255 {1 index exch /.notdef put} for
-dup 40 /parenleft put
-dup 41 /parenright put
-readonly def
-currentdict end
-currentfile eexec
-f983ef0097ece636fb4a96c74d26ab84185f6dfa4a16a7a1c27bbe3f1156aea698df336d20b467
-b10e7f33846656653c5ac6962759d3056cbdb3190bac614b984bf5a132dc418192443014ba63de
-800d392b6fea026574bb2535fd7bb5338f35bf15a88ea328fdaa49670c7852e3d060f3c5d6b07f
-2ef6d0f22646c5d18e19a2ae3ee120390f6dd96f76dcf1e127de5e9299077a00c17c0d71e36e5b
-9d5ec58fceda57739a6a4214d4b79d6c48d2784b60c320323c7acddddf34db833cac0cf109f799
-69d114a330d372e5c978a66acc84e3fe5557f6240856a013ffaa0199444e5c5036f775eba4a5c5
-8cde66cf604b9aca2178431127b8a1ff7ed633a65c04600af5f573483112251ca90bc9cf8825c7
-41412dda705317b7cb229dd377ff3d18e94daa9ba3bbd4ccd2ecde18a1c220179cca13293a42f7
-1d167cd6ac624b8f8573fc281c165eeb093c7705f0c9d1ce383c8701d14fcde12ac700699f81e8
-412c2e7e4c95c1440662af1652abdb4ce6be4b5f976724c26d20f166e17532da87ef8b24e90d2b
-ca09313d345112c202c1d9528e8c8e15bdfd68385cef36d711b99ee54d324b8778dae18d9af490
-41fbe748f7910913a3460e4af7353d7952f1fa9fde2bb171a7717e297425e0c08ca9800b01b2f5
-d645e0dbbc3a76bdfc773c19f4917354ed597d131dcc12985dd83ff833cc665a3ed3f11ec3814b
-3a8be6d7aef97d0b12b552d8da18f6cea65a8e284355941aae2da895a0fee8c8c2d4c22664f827
-5fb1ca0fbda2da6ff7fee9a610c58ec5d0c82dbb9b890d86f03ce85b69a56821a477e957df28b4
-b7afc889cbe637525896dc572b943c7f55648deb0894a36d8a1f7cfe05e48b6abb21a9949c7070
-43ecfa2c9ed9ed591f98e5fb1581bfb12e97b35bab44504370459fd28ca0c151ded5634089598c
-3d20720000000000000000000000000000000000000000000000000000000000000000
-0000000000000000000000000000000000000000000000000000000000000000
-0000000000000000000000000000000000000000000000000000000000000000
-0000000000000000000000000000000000000000000000000000000000000000
-0000000000000000000000000000000000000000000000000000000000000000
-0000000000000000000000000000000000000000000000000000000000000000
-0000000000000000000000000000000000000000000000000000000000000000
-0000000000000000000000000000000000000000000000000000000000000000
-cleartomark
-%%EndResource
-%%BeginResource: font f-0-1
-%!FontType1-1.1 f-0-1 1.0
-11 dict begin
-/FontName /f-0-1 def
-/PaintType 0 def
-/FontType 1 def
-/FontMatrix [0.001 0 0 0.001 0 0] readonly def
-/FontBBox {28 -13 453 799                                    } readonly def
-/Encoding 256 array
-0 1 255 {1 index exch /.notdef put} for
-dup 1 /uni03B8 put
-dup 2 /uni2032 put
-readonly def
-currentdict end
-currentfile eexec
-f983ef0097ece636fb4a96c74d26ab84185f6dfa4a16a7a1c27bbe3f1156aea698df336d20b467
-b10e7f33846656653c5ac6962759d3056cbdb3190bac614b984bf5a132dc418192443014ba63de
-800d392b6fea026574bb2535fd7bb5338f35bf15a88ea328fdaa49670c7852e3d060f3c5d6b07f
-2ef6d0f22646c5d18e19a2ae3ee120390f6dd96f76dcf1e127de5e9299077a00c17c0d71e36e5b
-9d5ec58fceda57739a6a4214d4b79d6c48d2784b60c320323c7acddddf34db833cac0cf109f799
-69d114a330d372e5c978a66acc84e3fe5557f6240856a013ffaa0199444e5c5036f775eba4a5c5
-8cde66cf604b9aca2178431127b8a1ff7ed633a65c04600af5f573483112251ca90bc9cf8825c7
-41412dda705317b7cb229dd377ff3d18e94daa9ba3bbd4ccd2ecde18a1c220179cca13293a42f7
-1d167cd6ac624b8f8573fc281c165eeb093c7705f0c9d1ce383c8701d14fcde12ac700699f81e8
-41298a056fbf05326bc567de0a0b26ab9bb8bf1c727fffe1a769e825cf16eef0e80b165c6bf01f
-c921bca94f4af777d97a2f19e0a6ba590a7e6bb59956c28a9e498787adbe3de7e6d3fc47ff7726
-4b0c3148d711961ef450730e7d9c2a0f9a8a8f7848739b2b8d2d56196d23d6b0a070f7ac34e28f
-1949b3d9933bd71bf994c695728647fe1cf6384f74801dd45d812cb26587dcf820b46a68885bcd
-be76f7a022b91b2856413f8b472c291f6323e69460888d3cf8b748160f2e465f470393d943268b
-e792e635a8fd6619217c82809f6c96a1c9f9d29ad32faaaebfee0f7caa41b8bd0cb26e12ae0006
-88ed16f82ca7c86fa6dfcd1624fb95587b3f4af99d73d037e596049ed240cfc364725448a51776
-ac6f8704995692b4cfb620640c12fafe8bda7ad95960cba96348a26386586f689b88045f9d5c17
-e43924d6e512c17db975287c04f45268e5a9a97237ed2fbf40344d73de6125e201a21057af59b0
-2ebd555ff2f2a4fec3352b5f2224db9c832d06cce2408ec8547633e84867b3a73065ab9671a46f
-925533c889164deafa20f00ef1f3f3a6639bc9333208014faba60b13c7b07b41e98c88d797eeaf
-1109a75b204ee60000000000000000000000000000000000000000000000000000000000000000
-0000000000000000000000000000000000000000000000000000000000000000
-0000000000000000000000000000000000000000000000000000000000000000
-0000000000000000000000000000000000000000000000000000000000000000
-0000000000000000000000000000000000000000000000000000000000000000
-0000000000000000000000000000000000000000000000000000000000000000
-0000000000000000000000000000000000000000000000000000000000000000
-0000000000000000000000000000000000000000000000000000000000000000
-cleartomark
-%%EndResource
-%%BeginResource: font f-1-0
-%!FontType1-1.1 f-1-0 1.0
-11 dict begin
-/FontName /f-1-0 def
-/PaintType 0 def
-/FontType 1 def
-/FontMatrix [0.001 0 0 0.001 0 0] readonly def
-/FontBBox {0 -14 908 692                                     } readonly def
-/Encoding 256 array
-0 1 255 {1 index exch /.notdef put} for
-dup 73 /I put
-dup 82 /R put
-dup 101 /e put
-dup 109 /m put
-readonly def
-currentdict end
-currentfile eexec
-f983ef0097ece636fb4a96c74d26ab84185f6dfa4a16a7a1c27bbe3f1156aea698df336d20b467
-b10e7f33846656653c5ac6962759d3056cbdb3190bac614b984bf5a132dc418192443014ba63de
-800d392b6fea026574bb2535fd7bb5338f35bf15a88ea328fdaa49670c7852e3d060f3c5d6b07f
-2ef6d0f22646c5d18e19a2ae3ee120390f6dd96f76dcf1e127de5e9299077a00c17c0d71e36e5b
-9d5ec58fceda57739a6a4214d4b79d6c48d2784b60c320323c7acddddf34db833cac0cf109f799
-69d114a330d372e5c978a66acc84e3fe5557f6240856a013ffaa0199444e5c5036f775eba4a5c5
-8cde66cf604b9aca2178431127b8a1ff7ed633a65c04600af5f573483112251cabe8722c0ba224
-7e4445af50cf2457d0f320e3c97746456087766b4bf11115560ce328711eca3bd110d9edf8f723
-7690411035c2d2a4529eceb3758e9dfdf69937c82634682ddec349213e6cdca1236ff1e59fd7ad
-c509a9f3c257841b8053a86b38d617d963b24dfb3767bfc9b4af0288c9b0b8e2572d16601fc539
-50419b779278a6ee6aa2c6f6e88f16020db6e348845fd5b2cd9ac2bb9cc9caa74bac30ab845da5
-f651fffe8b245f374569b60b2520d5b091c2895daa06f7cacffa423bc29ca3a939660aef03f4ba
-db6c051bab9e97aa6f8b3423aee96ff61f682293fdb336288dbb885c46c5c6d7ca5c5a0cf84a99
-4b1ef4f098cdceee4559f76b71375ac1e48de97bc26d04e944bd8f7723aaca9bdeb0a55b4d8e30
-b9169a69c8b151f7e913240de4e7614c0ce99885f8de5ae8d0c7602bdba359c79247126be04fa0
-4837a74d4b1829aba24a81ace9429198af5c03ce00c992b95216dab9619da47da7550eca0ff6cd
-0ebc575021f16decb7f0d945e2c73764f06e1781806305825422f0f7ad20cee7de432128300693
-599dbdafc575e2f472140a927b4552e1cd714bd09871feab74613bf38b4117e1b2c870998d1584
-50ae3c9c1b184d5529d7092e102d713e1e4a8d02eb0fb3edc7ef054b7fbe323e488fbcf700dac6
-058c3eeb18d59888e42247d792f3cff694e14a0b69965054b8e811dc8ae391c9be575648546fef
-0365caa0b5334da60343169e20c6b1b8d51c5fbe17cfca3ec7f3bd1c61d09838b717c08ccfcbda
-2a43ce0a730162c3285d5185e5fa3f8c6aaa204a403cdae550e565dcaf3816e4f19a66fee5bb4d
-e532d49827c5c811b8c6effa17be7f7f897390f48ca0d11588bc17af153bec904639fcce603e9a
-fb7417deeba06beb6901c0fba586004121e1aa2dcab890d83326fd7ffca74c35e64a22c9434ef6
-7d7496180137f9c8705089856e54a802d541062de40941e37319ed189b6dd27b69783befae9725
-88dacdb39bfe000a0789e90bfdcc7a2187dbff723ba8a74bb2ececfee0a9ea34b01434890000000000000000000000000000000000000000000000000000000000000000
-0000000000000000000000000000000000000000000000000000000000000000
-0000000000000000000000000000000000000000000000000000000000000000
-0000000000000000000000000000000000000000000000000000000000000000
-0000000000000000000000000000000000000000000000000000000000000000
-0000000000000000000000000000000000000000000000000000000000000000
-0000000000000000000000000000000000000000000000000000000000000000
-0000000000000000000000000000000000000000000000000000000000000000
-cleartomark
-%%EndResource
-%%EndSetup
-%%Page: 1 1
-%%BeginPageSetup
-%%PageBoundingBox: 0 0 360 218
-%%EndPageSetup
-q 0 0 360 218 rectclip
-1 0 0 -1 0 219 cm q
-0.999985 0 0 rg
-1.310865 w
-2 J
-0 j
-[] 0.0 d
-3.25 M 8.371 116.121 m 32.953 116.121 l S
-49.336 117.352 m 49.336 115.176 48.473 113.094 46.938 111.555 c 45.402 
-110.02 43.316 109.156 41.145 109.156 c 38.973 109.156 36.887 110.02 35.352
- 111.555 c 33.816 113.094 32.953 115.176 32.953 117.352 c S
-295.125 116.121 m 319.703 116.121 l S
-295.125 117.352 m 295.125 115.176 294.262 113.094 292.727 111.555 c 291.188
- 110.02 289.105 109.156 286.934 109.156 c 284.758 109.156 282.676 110.02
- 281.137 111.555 c 279.602 113.094 278.738 115.176 278.738 117.352 c S
-49.336 117.352 m 155.844 117.352 l S
-172.23 117.352 m 172.23 115.176 171.367 113.094 169.832 111.555 c 168.293
- 110.02 166.211 109.156 164.039 109.156 c 161.863 109.156 159.781 110.02
- 158.246 111.555 c 156.707 113.094 155.844 115.176 155.844 117.352 c S
-172.23 117.352 m 205.004 117.352 l S
-221.387 117.352 m 221.387 115.176 220.523 113.094 218.988 111.555 c 217.453
- 110.02 215.367 109.156 213.195 109.156 c 211.023 109.156 208.938 110.02
- 207.402 111.555 c 205.867 113.094 205.004 115.176 205.004 117.352 c S
-221.387 117.352 m 278.738 117.352 l S
-165.266 21.145 m 165.266 58.523 l S
-162.809 21.145 m 162.809 58.523 l S
-172.23 66.715 m 172.23 64.543 171.367 62.457 169.832 60.922 c 168.293 59.387
- 166.211 58.523 164.039 58.523 c 161.863 58.523 159.781 59.387 158.246 60.922
- c 156.707 62.457 155.844 64.543 155.844 66.715 c 155.844 68.887 156.707
- 70.973 158.246 72.508 c 159.781 74.043 161.863 74.906 164.039 74.906 c 
-166.211 74.906 168.293 74.043 169.832 72.508 c 171.367 70.973 172.23 68.887
- 172.23 66.715 c h
-172.23 66.715 m S
-0 g
-0.36 w
-213.195 117.352 m 213.195 125.543 l S
-BT
-10.8 0 0 -10.8 210.748688 136.975703 Tm
-/f-0-1 1 Tf
-<01>Tj
-ET
-0.999985 0 0 rg
-1.152 w
-8.379 116.582 m 8.465 114.039 l 8.574 112.461 l 8.684 111.281 l 8.793 110.297
- l 8.902 109.434 l 9.012 108.656 l 9.117 107.941 l 9.227 107.281 l 9.336
- 106.66 l 9.445 106.074 l 9.664 104.988 l 9.773 104.477 l 9.883 103.988 
-l 10.098 103.062 l 10.207 102.621 l 10.316 102.191 l 10.535 101.371 l 10.973
- 99.844 l 11.082 99.484 l 11.188 99.133 l 11.406 98.449 l 11.844 97.148 
-l 12.062 96.531 l 12.277 95.934 l 12.715 94.785 l 13.586 92.66 l 13.789 
-92.191 l 13.992 91.73 l 14.398 90.84 l 15.215 89.141 l 16.844 86.051 l 16.945
- 85.867 l 17.25 85.328 l 17.656 84.625 l 18.469 83.266 l 20.098 80.719 l
- 20.199 80.57 l 20.297 80.422 l 20.496 80.125 l 20.895 79.543 l 21.695 78.41
- l 23.289 76.254 l 26.48 72.312 l 26.699 72.062 l 26.914 71.812 l 27.348
- 71.32 l 28.215 70.352 l 29.945 68.488 l 33.406 65.027 l 33.508 64.934 l
- 33.609 64.836 l 33.812 64.645 l 34.215 64.266 l 35.023 63.52 l 36.637 62.066
- l 39.871 59.328 l 46.875 54.008 l 53.75 49.457 l 60.164 45.695 l 67.117
- 42.066 l 73.613 39.039 l 79.977 36.379 l 86.883 33.793 l 93.328 31.641 
-l 100.312 29.574 l 107.168 27.793 l 113.566 26.34 l 120.5 24.984 l 120.703
- 24.945 l 121.312 24.84 l 122.121 24.695 l 123.738 24.422 l 126.977 23.91
- l 127.195 23.879 l 127.414 23.844 l 127.852 23.777 l 128.73 23.652 l 130.484
- 23.406 l 130.703 23.375 l 130.922 23.348 l 131.359 23.289 l 132.238 23.172
- l 133.992 22.953 l 134.098 22.941 l 134.207 22.926 l 134.422 22.902 l 134.852
- 22.848 l 135.715 22.75 l 137.434 22.559 l 137.543 22.547 l 137.648 22.535
- l 137.867 22.512 l 138.297 22.469 l 139.156 22.379 l 140.879 22.215 l 140.98
- 22.203 l 141.078 22.195 l 141.281 22.176 l 141.684 22.141 l 142.484 22.07
- l 144.09 21.938 l 144.293 21.922 l 144.492 21.906 l 145.699 21.812 l 147.305
- 21.699 l 147.414 21.695 l 147.523 21.688 l 147.738 21.672 l 148.176 21.645
- l 149.047 21.59 l 149.156 21.586 l 149.266 21.578 l 149.48 21.566 l 149.918
- 21.539 l 150.789 21.492 l 150.895 21.488 l 151.004 21.48 l 151.223 21.469
- l 151.66 21.449 l 152.527 21.406 l 154.27 21.332 l 154.676 21.316 l 155.082
- 21.305 l 155.898 21.273 l 156 21.273 l 156.305 21.262 l 157.523 21.227 
-l 157.625 21.227 l 157.727 21.223 l 157.93 21.219 l 158.336 21.207 l 158.438
- 21.207 l 158.539 21.203 l 159.148 21.191 l 159.25 21.188 l 159.352 21.188
- l 159.961 21.176 l 160.062 21.176 l 160.164 21.172 l 160.367 21.172 l 160.773
- 21.164 l 160.977 21.164 l 161.176 21.16 l 161.273 21.16 l 161.375 21.156
- l 161.672 21.156 l 161.773 21.152 l 162.172 21.152 l 162.371 21.148 l 162.77
- 21.148 l 162.867 21.145 l 165.258 21.145 l 165.359 21.148 l 165.758 21.148
- l 165.957 21.152 l 166.355 21.152 l 166.453 21.156 l 166.754 21.156 l 167.152
- 21.164 l 167.367 21.164 l 167.586 21.168 l 168.016 21.176 l 168.125 21.176
- l 168.234 21.18 l 168.449 21.184 l 168.883 21.191 l 168.988 21.191 l 169.098
- 21.195 l 169.312 21.199 l 169.746 21.207 l 170.609 21.23 l 170.719 21.23
- l 170.828 21.234 l 171.043 21.242 l 171.477 21.254 l 172.34 21.281 l 172.449
- 21.285 l 172.555 21.289 l 172.773 21.297 l 173.207 21.309 l 174.07 21.344
- l 174.273 21.352 l 174.473 21.359 l 174.875 21.379 l 175.684 21.414 l 175.887
- 21.422 l 176.086 21.434 l 176.492 21.453 l 177.297 21.492 l 177.398 21.5
- l 177.5 21.504 l 177.703 21.516 l 178.105 21.535 l 178.91 21.582 l 180.527
- 21.684 l 180.746 21.699 l 180.961 21.715 l 181.398 21.742 l 182.273 21.805
- l 184.023 21.941 l 184.242 21.957 l 184.461 21.977 l 184.898 22.012 l 185.773
- 22.086 l 187.523 22.246 l 187.629 22.254 l 187.738 22.266 l 187.953 22.285
- l 188.383 22.328 l 189.238 22.414 l 190.957 22.594 l 194.391 22.988 l 194.492
- 23.004 l 194.59 23.016 l 194.793 23.039 l 195.191 23.09 l 195.992 23.191
- l 197.594 23.406 l 200.797 23.863 l 200.906 23.879 l 201.016 23.898 l 201.23
- 23.93 l 201.668 23.996 l 202.535 24.133 l 204.273 24.414 l 207.746 25.016
- l 214.23 26.281 l 220.59 27.715 l 227.488 29.5 l 233.926 31.383 l 240.902
- 33.691 l 247.422 36.109 l 253.809 38.754 l 260.738 41.957 l 267.203 45.305
- l 274.215 49.387 l 281.094 53.93 l 287.512 58.766 l 294.473 64.84 l 294.574
- 64.938 l 294.676 65.031 l 295.285 65.617 l 296.098 66.414 l 297.719 68.059
- l 300.969 71.594 l 301.07 71.707 l 301.168 71.82 l 301.367 72.051 l 301.766
- 72.516 l 302.562 73.461 l 304.152 75.438 l 304.254 75.562 l 304.352 75.691
- l 304.551 75.949 l 304.949 76.469 l 305.746 77.535 l 307.34 79.773 l 307.445
- 79.93 l 307.555 80.09 l 307.77 80.41 l 308.203 81.059 l 309.066 82.398 
-l 310.793 85.27 l 310.902 85.457 l 311.012 85.648 l 311.227 86.035 l 311.656
- 86.82 l 312.523 88.465 l 314.25 92.105 l 314.352 92.336 l 314.449 92.57
- l 314.652 93.043 l 315.055 94.016 l 315.156 94.266 l 315.258 94.52 l 315.457
- 95.035 l 315.863 96.105 l 315.961 96.383 l 316.062 96.664 l 316.266 97.238
- l 316.668 98.441 l 316.77 98.754 l 316.867 99.074 l 317.07 99.73 l 317.473
- 101.125 l 317.574 101.492 l 317.676 101.871 l 317.875 102.652 l 317.977
- 103.062 l 318.078 103.484 l 318.281 104.367 l 318.379 104.832 l 318.48 
-105.316 l 318.684 106.352 l 318.785 106.906 l 318.883 107.492 l 319.086 
-108.789 l 319.188 109.516 l 319.289 110.32 l 319.387 111.227 l 319.488 112.297
- l 319.59 113.668 l 319.691 116.098 l 319.699 116.742 l S
-0 g
-0.36 w
-0 J
-[ 2.88 2.88] 0 d
-0.18 117.352 m 327.895 117.352 l S
-BT
-10.08 0 0 -10.08 333.65625 120.589891 Tm
-/f-1-0 1 Tf
-(Re)Tj
-10.8 0 0 -10.8 345.32625 120.589891 Tm
-/f-0-0 1 Tf
-(\()Tj
-/f-0-1 1 Tf
-<01>Tj
-7.2 0 0 -7.2 353.68125 116.145016 Tm
-<02>Tj
-10.8 0 0 -10.8 356.53875 120.589891 Tm
-/f-0-0 1 Tf
-(\))Tj
-ET
-Q q
-163 16 2 202.641 re W n
-0 g
-0.36 w
-0 J
-0 j
-[ 2.88 2.88] 0 d
-3.25 M 164.039 218.621 m 164.039 16.078 l S
-Q q
-0 g
-BT
-10.08 0 0 -10.08 150.290625 9.12 Tm
-/f-1-0 1 Tf
-(Im)Tj
-10.8 0 0 -10.8 163.111875 9.12 Tm
-/f-0-0 1 Tf
-(\()Tj
-/f-0-1 1 Tf
-<01>Tj
-7.2 0 0 -7.2 171.466875 4.675125 Tm
-<02>Tj
-10.8 0 0 -10.8 174.324375 9.12 Tm
-/f-0-0 1 Tf
-(\))Tj
-ET
-Q q
-163 16 2 52 re W n
-0 g
-1.44 w
-2 J
-0 j
-[] 0.0 d
-3.25 M 164.039 66.715 m 164.039 -46.508 l S
-Q q
-163 167 2 51.641 re W n
-0 g
-1.44 w
-2 J
-0 j
-[] 0.0 d
-3.25 M 164.039 167.984 m 164.039 281.207 l S
-Q q
-0 g
-161.141 63.816 5.793 5.797 re f
-1.44 w
-2 J
-0 j
-[] 0.0 d
-3.25 M 161.141 63.816 5.793 5.797 re S
-168.133 117.352 m 164.039 113.254 l 159.941 117.352 l 164.039 121.445 l
- h
-168.133 117.352 m f
-168.133 117.352 m 164.039 113.254 l 159.941 117.352 l 164.039 121.445 l
- h
-168.133 117.352 m S
-161.141 165.09 5.793 5.793 re f
-161.141 165.09 5.793 5.793 re S
-0.18 117.352 m 41.145 117.352 l S
-45.242 117.352 m 45.242 116.262 44.809 115.223 44.043 114.453 c 43.273 
-113.684 42.23 113.254 41.145 113.254 c 40.059 113.254 39.016 113.684 38.246
- 114.453 c 37.48 115.223 37.047 116.262 37.047 117.352 c 37.047 118.438 
-37.48 119.477 38.246 120.246 c 39.016 121.016 40.059 121.445 41.145 121.445
- c 42.23 121.445 43.273 121.016 44.043 120.246 c 44.809 119.477 45.242 118.438
- 45.242 117.352 c h
-45.242 117.352 m f*
-Q q
-286 116 42 3 re W n
-0 g
-1.44 w
-2 J
-0 j
-[] 0.0 d
-3.25 M 327.895 117.352 m 286.934 117.352 l S
-Q q
-0 g
-291.027 117.352 m 291.027 116.262 290.598 115.223 289.828 114.453 c 289.059
- 113.684 288.02 113.254 286.934 113.254 c 285.844 113.254 284.805 113.684
- 284.035 114.453 c 283.266 115.223 282.836 116.262 282.836 117.352 c 282.836
- 118.438 283.266 119.477 284.035 120.246 c 284.805 121.016 285.844 121.445
- 286.934 121.445 c 288.02 121.445 289.059 121.016 289.828 120.246 c 290.598
- 119.477 291.027 118.438 291.027 117.352 c h
-291.027 117.352 m f*
-211.898 117.773 m 211.59 119.559 l 213.195 118.715 l 214.801 119.559 l 
-214.496 117.773 l 215.793 116.508 l 214 116.246 l 213.195 114.617 l 212.395
- 116.246 l 210.598 116.508 l h
-211.898 117.773 m f
-1.44 w
-2 J
-0 j
-[] 0.0 d
-3.25 M 211.898 117.773 m 211.59 119.559 l 213.195 118.715 l 214.801 119.559 l 
-214.496 117.773 l 215.793 116.508 l 214 116.246 l 213.195 114.617 l 212.395
- 116.246 l 210.598 116.508 l h
-211.898 117.773 m S
-Q Q
-showpage
-%%Trailer
-end restore
-%%EOF
diff --git a/ising_scaling.tex b/ising_scaling.tex
index a1c8205..c454e43 100644
--- a/ising_scaling.tex
+++ b/ising_scaling.tex
@@ -245,7 +245,7 @@ s=2^{1/12}e^{-1/8}A^{3/2}$, where $A$ is Glaisher's constant
 
 
 \begin{figure}
-  \includegraphics{figs/F_lower_singularities}
+  \includegraphics{F_lower_singularities}
   \caption{
     Analytic structure of the low-temperature scaling function $\mathcal F_-$
     in the complex $\xi=u_h|u_t|^{-\Delta}\propto H$ plane. The circle
@@ -292,7 +292,7 @@ branch cuts beginning at $\pm i\xi_{\mathrm{YL}}$ for a universal constant
 $\xi_{\mathrm{YL}}$.
 
 \begin{figure}
-  \includegraphics{figs/F_higher_singularities}
+  \includegraphics{F_higher_singularities}
   \caption{
     Analytic structure of the high-temperature scaling function $\mathcal F_+$
     in the complex $\xi=u_h|u_t|^{-\Delta}\propto H$ plane. The squares
@@ -421,7 +421,7 @@ $\theta$. Therefore,
 The location $\theta_0$ is not fixed by any principle.
 
 \begin{figure}
-  \includegraphics{figs/F_theta_singularities}
+  \includegraphics{F_theta_singularities}
   \caption{
     Analytic structure of the global scaling function $\mathcal F$ in the
     complex $\theta$ plane. The circles depict essential singularities of the
@@ -478,7 +478,7 @@ Fixing these requirements for the imaginary part of $\mathcal F(\theta)$ fixes
 its real part up to an analytic even function $G(\theta)$, real for real $\theta$.
 
 \begin{figure}
-  \includegraphics{figs/contour_path}
+  \includegraphics{contour_path}
   \caption{
     Integration contour over the global scaling function $\mathcal F$ in the
     complex $\theta$ plane used to produce the dispersion relation. The
-- 
cgit v1.2.3-70-g09d2

