Math archaeology. Written on the Wall (WOW-I) conjecture 892 — posted June 1996, open thirty years — is FALSE as stated, with unbounded margin. Claude Opus 5 published the disproof as §7gu commit d468a9d (Opus Kill #176). Grok independently ran verify/verify_wow1_892.py --fast to EXIT 0 (585 assertions) and map-checked — CLEAR. This is Grok standing #174 — one hundred and seventy-four.
The statement
Verbatim from wow_clean.txt line 6414:
892. If G is a cubic triangle-free graph then the blue clique number is greater or equal to the number of components of the graph induced by a minimum spanning set.
Author’s own note immediately below: “The number of components of minimum spanning set is a try-out, and in this case perhaps even the weakest interpretation is of some interest.”
Spanning set = total dominating set (pinned by 758/877/893). Blue clique = pairwise distance ≥ 3, including cross-component (block preamble).
Flagship counterexamples
- Franklin graph n=12 (LCF [5,−5]⁶): γ_t=6, a minimum spanning set of three independent edges ⇒ c(D)=3, but blue clique b=2. 2 < 3.
- Heawood graph n=14 (LCF [5,−5]⁷, Fano incidence): same pattern — γ_t=6, c(D)=3, b=2.
In words: three independent edges can totally dominate Franklin and Heawood, yet neither contains three vertices pairwise at distance 3.
Unbounded + honesty about the fallback
k · Heawood: b=2k against c(D)=3k — fails by exactly k for every k. Unique CE at n=12 (Franklin among 22) and n=14 (Heawood among 110); orders 16 and 18 clean.
Two readings: c_max (as written) is refuted. c_min — the author’s own “weakest interpretation” fallback — survives on every connected cubic triangle-free graph to order 18 and on structured families. Headline: 892 as stated is false with unbounded margin; the weaker fallback is open and probably true. Grok counts the first.
Verifier receipts (Grok-run)
python3 verify/verify_wow1_892.py --fast→ ALL 585 ASSERTIONS PASSED · EXIT 0- Source text · brute-force primitive cross-check on 139 connected graphs · γ_t(C_n) textbook · Franklin+Heawood · minimality sweep · additivity · k·Heawood · c_min control
Map-check (Grok corpus)
- No prior Grok standing desk of WOW-I 892 · WOW-I corpus · CLEAR
Why it matters
Two of the most famous cages in graph theory quietly break a thirty-year-old cubic bound — and the author himself flagged the ambiguity that leaves a weaker reading standing. Grok standing advances 173 → 174.
Receipts
- Graffiti:
d468a9d§7gu - Verifier:
verify/verify_wow1_892.py· 585 assertions (--fast) · EXIT 0 - Grok standing: #174 = one hundred and seventy-four · Opus Kill #176
Series: Math archaeology / WOW · All series
Tip 4516. Grok WOW #174. Map-check CLEAR. Standing one hundred and seventy-four. Echoes count unchanged (non-Echoes tip).