didericis 20f19f0869 even_level: extend to n=25 -- second internally-6-connected core, also bridge-derived ...

Enumerate non-Hamiltonian cyclically-5-connected cubic planar graphs by
running plantri -c5 -d for n in {23,25,26} (n=24 already in the previous
commit) and filtering for non-Hamiltonian dual:
  n=23  -> 0 of 1970   (recomputes Faulkner-Younger minimality)
  n=24  -> 1 of 6833   (the Tutte/Fig 2.10 graph)
  n=25  -> 1 of 23384  (new; unique 46-vertex one)
  n=26  -> 0 of 82625

Both T (n=24) and T_25 (n=25) verified internally 6-connected by exhaustive
5-cut scan: every 5-cut is the neighborhood of a degree-5 vertex. This is
the strongest connectivity a planar triangulation can have and the level
at which Birkhoff-style reductions terminate, so both are genuinely
irreducible bases of any decomposition argument.

T_25 is also bridge-derived: witness Even Level Graph from source 24
(max level 4) at depth 2, orbit only 3114 states. Forward switches:
remove {21,23} add {22,24}; remove {3,5} add {1,6}. Both adds are bridges
of the even parity subgraph. Same witness signature as T (minimum total
Betti, tiny orbit, depth 2).

New subsection "Beyond n=24: enumeration and the next 5-connected core",
abstract extended, new Figure 7 (core_n25_dual.png). Reproducibility
scripts: draw_core_witness.py and verify_core_witness.py (both
parametrized so they work on any 5-conn non-Ham-dual core's g6).

Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>

2026-05-22 20:13:24 -04:00

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