PART 1: source text of Written on the Wall ok, 16 checks so far PART 2: 843 is not among the conjectures the book records as tested ok, 19 checks so far PART 3: implementations, calibrated against independently known facts calibration passed, 129 checks so far PART 4: the counterexample, C240 = GP(2,2) = leapfrog(GP(2,0)) C240: alpha <= 108, conjecture needs >= 112, margin -4. 508 checks so far PART 5: minimality -- 843 has NO counterexample among the small fullerenes per-order profile (n : isomers : certified bound on n/2-alpha): n=20 1 isomers deficiency <= 2 n=24 1 isomers deficiency <= 3 n=26 1 isomers deficiency <= 3 n=28 2 isomers deficiency <= 3 n=30 3 isomers deficiency <= 3 n=32 6 isomers deficiency <= 3 n=34 6 isomers deficiency <= 3 n=36 15 isomers deficiency <= 4 n=38 17 isomers deficiency <= 4 n=40 40 isomers deficiency <= 4 n=42 45 isomers deficiency <= 5 n=44 89 isomers deficiency <= 5 n=46 116 isomers deficiency <= 5 n=48 199 isomers deficiency <= 5 n=50 271 isomers deficiency <= 5 n=52 437 isomers deficiency <= 6 n=54 580 isomers deficiency <= 6 n=56 924 isomers deficiency <= 6 n=58 1205 isomers deficiency <= 6 n=60 1812 isomers deficiency <= 6 exhaustive to n = 60: 5770 isomers, deficiency always <= 6, 843 never fails theorem-based floor: any counterexample has n >= 136. 23692 checks so far PART 6: an infinite family, with margin tending to minus infinity GP(1,1): n=60 alpha <= 24 n/2-8 = 22 margin +2 GP(2,2): n=240 alpha <= 108 n/2-8 = 112 margin -4 GP(3,3): n=540 alpha <= 252 n/2-8 = 262 margin -10 GP(4,4): n=960 alpha <= 456 n/2-8 = 472 margin -16 GP(5,5): n=1500 alpha <= 720 n/2-8 = 742 margin -22 margin 8 - 6k -> -infinity. 24164 checks so far PART 7: honesty, provenance and ledger self-check ==================================================================== CONJECTURE 843 OF 'WRITTEN ON THE WALL' IS FALSE. Counterexample: C240 = GP(2,2), the leapfrog of C80. V(C240) partitions into twelve 5-cycles and twelve 15-cycles, hence alpha <= 12*2 + 12*7 = 108 = n/2 - 12 < 112 = n/2 - 8. Margin -4. The family GP(k,k) gives margin 8 - 6k -> -infinity. ==================================================================== all 24376 checks passed