face_monochromatic_pairs: explicit counterexample to Conjecture 5.5

Adds the concrete construction (40 vertices, 60 edges, cubic + planar
+ proper 3-edge-coloured) on which h_φ is simultaneously constant on
two Kempe cycles sharing an edge:

  - K_{red, blue}  = 8-cycle (the outer frame): all h_φ = -1
  - K_{red, green} = 12-cycle (outer frame + upper-left ladder side):
                      all h_φ = -1
  - They share the colour-red edge (0, 7) (and others).

The graph is drawn in TikZiT and stored as
  papers/face_monochromatic_pairs/constant_heawood_counterexample.tikz

The Sage transcription + Heawood/Kempe verification + PNG renderer is
  papers/face_monochromatic_pairs/experiments/counterexample_conj_5_5.py

Rendered PNG (with the four bent outer-face / trapezoid arcs matching
the tikz drawing) is at
  papers/face_monochromatic_pairs/figures/no-two-constant-kempe-counterexample.png

Globally h_φ has 16 vertices at +1 and 24 at -1; the +1 vertices are
concentrated in the inner "tilted ladder" region, leaving the outer
and the K_{red,green}-extension all at -1. This is the structural
reason both Kempe cycles can be constant.

Also includes the TikZiT styles file default.tikzstyles defining the
red/blue/green edge styles used by the .tikz file.

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

default.tikzstyles

@@ -0,0 +1,12 @@
+% TiKZ style file generated by TikZiT. You may edit this file manually,
+% but some things (e.g. comments) may be overwritten. To be readable in
+% TikZiT, the only non-comment lines must be of the form:
+% \tikzstyle{NAME}=[PROPERTY LIST]
+
+% Node styles
+\tikzstyle{dot}=[fill=white, draw=black, shape=circle]
+
+% Edge styles
+\tikzstyle{green edge}=[-, draw={rgb,255: red,0; green,175; blue,0}]
+\tikzstyle{red edge}=[-, draw=red]
+\tikzstyle{blue edge}=[-, draw=blue]