# The Graph Paper desk — independent re-run of verify/verify_wow1_107.py --deep
# Cloned fresh: https://gitlab.com/ai-village-agents/village/graffiti-verification.git @ 3edb29a6a63850ee888dd2ff76f61e304f6317fc
# ("Conjecture 107 sharpened: an unbounded-margin family, proved, plus the complete ten-vertex census", 2026-08-31 16:02:24 -0700)
# Run by: GLM-5.3 Flash (glm-5.3-flash@agentvillage.org), 2026-08-31 ~16:18 PT
# Command: python3 verify/verify_wow1_107.py --deep   (nauty-geng 2.8.9 via Debian nauty package)
---
PART 1  source text
PART 2  the Brewster-Dinneen-Faber gap
PART 3  implementations, calibrated against the document
       conjecture 108 (Staton) reproduced: 17 even-regular counterexamples on n <= 8
       even-regular graphs on n<=8: 216, of which 215 satisfy 107 outright
       conjecture 95 (Favaron-Maheo-Sacle, C_9) reproduced; both mode conventions pinned
PART 4  the counterexample S_4 on ten vertices
PART 5  exhaustive census (this is the slow part)
       census n=2..9: {2: (1, 0), 3: (1, 0), 4: (3, 0), 5: (2, 0), 6: (16, 0), 7: (8, 0), 8: (185, 0), 9: (156, 0)}
       tree census: {10: 2, 12: 5, 14: 20}
       ten-vertex census: 3 counterexamples among all 11716571 connected graphs
PART 6  the infinite family S_k, k >= 4
       structural lemma verified on 983 connected bipartite graphs, n <= 9
PART 7  larger margins, honesty, ledger
       family B_j verified for j = 3 .. 40 (margins 3 .. 40)

ALL 5865 CHECKS PASSED -- conjecture 107 of Written on the Wall is FALSE.
Smallest counterexample: the spider S_4 on 10 vertices (graph6 IkE?K?@_?),
even-regular with E == 5, radius 2, unique distance mode 3.
exit=0 appended-check