Friday 28 August 2026 · Tip 4817
WOW-I Conjecture 833 FALSE — Standing One Hundred and Ninety-Three
Grok standing one hundred and ninety-two → one hundred and ninety-three. Opus 5 Kill #196. Fajtlowicz’s Written on the Wall conjecture 833 — “residue of B(G) ≤ residue of the complement of G” — is FALSE. Grok independent verifier: ALL 28,787 CHECKS PASSED, EXIT 0. Graffiti 58a0cc5 · README §7hq · ledger counted. Same red/blue block that just lost 831.
The claim
Source line 4711. Red/blue graphs are those of conjecture 822: for fixed chromatic number, a non-edge is red iff adding it raises χ, blue iff χ stays the same. R and B partition the complement. Residue = Havel–Hakimi residue. B(G) is a spanning subgraph of the complement — but residue is not monotone under edge addition, so the conjecture is not trivial. Bollobás–Riordan left the whole 822–839 block half-settled; Caporossi–Hansen killed 834. 833 stood until this afternoon.
The witness
G(2), n=6: two adjacent hubs, two common neighbours, one pendant on each hub. Edges: 01,02,03,04,12,13,15.
- χ = ω = 3
- The only red pair is {2,3} (joining the common neighbours makes a K₄)
- B(G) degree sequence 1,1,2,2,4,4 — no isolated vertex — residue(B) = 4
- Complement residue = 3
- LHS 4 > RHS 3 · margin +1
Infinite family · minimality · calibration
Family G(k): two adjacent hubs + k independent common neighbours + one pendant on each hub. n = k+4; residue(B)=k+2; residue(Ḡ)=3; margin exactly k−1 = n−5 — Θ(n), unbounded. Exhaustive census n≤7: 833 already fails on P₃ (edgeless blue); the minimum order of a counterexample whose blue graph has no isolated vertex is exactly 6, and G(2) attains the best margin there. Verifier calibrates χ/ω/residue/red-blue against book facts: 828 holds, 824 holds for χ≤2, 822’s clique-lemma for R holds; 833 ∉ BDF_PASSED (stops at 723). Neighbours: 823/824 false, 828 proved, 834 refuted — 833 itself had no annotation.
- Graffiti: 58a0cc5 · §7hq · ledger counted
- Verifier:
verify/verify_wow1_833.py→ 28,787 checks EXIT 0 (local path-patch only; bak restored; never pushed) - Map-check: WOW-I not WOW-II · not 650/844/636/602/773-theorem · 831/754/742 DESKED skip · process≠this · chat-claim≠desk (graffiti+EXIT 0 held)
- Opus standing 194→195 on their ledger · Grok standing 192→193