rename: coloring_nested_tire_graphs → coloring_nested_tire_dual_graphs

Renames the paper directory and updates:
  - \title in papers/coloring_nested_tire_dual_graphs/paper.tex:
    "Coloring Nested Tire Graphs" → "Coloring Nested Tire Dual Graphs"
  - bibliography reference in papers/plane_depth/paper.tex
  - rebuilt both PDFs

The new title reflects that the paper studies the cubic DUAL of
maximal planar graphs (nested tire structure on G^*), not the
primal triangulation.

Co-Authored-By: Claude Opus 4.7 <noreply@anthropic.com>

papers/plane_depth/paper.log

@@ -1,4 +1,4 @@
-This is pdfTeX, Version 3.141592653-2.6-1.40.24 (TeX Live 2022) (preloaded format=pdflatex 2022.10.5)  26 MAY 2026 14:17
+This is pdfTeX, Version 3.141592653-2.6-1.40.24 (TeX Live 2022) (preloaded format=pdflatex 2022.10.5)  27 MAY 2026 00:44
 entering extended mode
  restricted \write18 enabled.
  %&-line parsing enabled.
@@ -216,7 +216,7 @@ msy7.pfb></usr/local/texlive/2022/texmf-dist/fonts/type1/public/amsfonts/cm/cmt
 i10.pfb></usr/local/texlive/2022/texmf-dist/fonts/type1/public/amsfonts/cm/cmti
 8.pfb></usr/local/texlive/2022/texmf-dist/fonts/type1/public/amsfonts/symbols/m
 sam10.pfb>
-Output written on paper.pdf (4 pages, 193466 bytes).
+Output written on paper.pdf (4 pages, 193511 bytes).
 PDF statistics:
  87 PDF objects out of 1000 (max. 8388607)
  52 compressed objects within 1 object stream

papers/plane_depth/paper.tex

@@ -317,7 +317,7 @@ manuscript (math-research repository), 2026.
 
 \bibitem{bauerfeld-nested-tires}
 E.~Bauerfeld,
-\emph{Coloring Nested Tire Graphs},
+\emph{Coloring Nested Tire Dual Graphs},
 manuscript (math-research repository), 2026.
 
 \end{thebibliography}