face_monochromatic_pairs: record graph6 + invariants of Conj-5.5 counterexample; drop partial proof attempt

- Disproof remark now records the canonical graph6 string (via
  G.canonical_label().graph6_string()) and the basic invariants
  (V=40, E=60, vertex/edge-conn 3, girth 3, trivial Aut, Hamiltonian,
  not bipartite, face-length distribution).
- The graph appears to be a fresh ad-hoc construction; the
  research-analyst literature search ruled out gen. Petersen,
  C40 fullerenes, snarks, Archimedean/Catalan polyhedra, McKay's
  cubic planar non-Hamiltonian catalogues, and the Foster census.
- counterexample_conj_5_5.py now prints the canonical graph6,
  girth, |Aut|, and hamiltonicity so the invariants are reproducible
  from the script.
- The "Partial proof attempt" (Steps 1-5: local CW structure, forced-
  crossing, mod-3 Heawood face-sum, lune-face Case A, Case B TBD) is
  removed --- the counterexample disproves the conjecture outright, so
  the partial structural arguments toward it are no longer needed.
  Paper drops from 19 to 17 pages.

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

papers/face_monochromatic_pairs/experiments/counterexample_conj_5_5.py

@@ -314,6 +314,9 @@ def main():
     G = build_graph(EDGES)
     col = edge_colour_map(EDGES)
     print(f"  |V(H)| = {G.order()}, |E(H)| = {G.size()}")
+    print(f"  canonical graph6 = {G.canonical_label().graph6_string()}")
+    print(f"  girth = {G.girth()}, |Aut| = {G.automorphism_group().order()}, "
+          f"hamiltonian = {G.is_hamiltonian()}")
 
     degs = sorted(set(G.degree()))
     print(f"  degree set = {degs}")