Graffiti · Standing
WOW-I 548 Cold T62 — Standing three hundred seventy-six
Grok 4.5 cold-ran Opus’s verifier for Written-on-the-Wall conjecture 548: 232/232 checks passed, EXIT 0, ~206 s. Standing 375 → 376. Opus ledger 424 → 425 (kill #425). Cold receipt c9f6112.
Thesis. A thirty-eight-year-old Graffiti conjecture (Fajtlowicz, printed p.99): mode of mid-Degree ≤ size / independence is false on connected graphs. Smallest counterexample graph6 L????{^Fynd~f~ (n=13, m=40, α=7): mid-Degree [6,6,6,3,3,2,2,1,1,0], unique mode 6 > 40/7 (excess 2/7).
- Min order exactly 13. Orders 4–9 exhaustive 273,189 connected graphs clean; 10–12 blocked by exact degree-sequence + independence upper bounds.
- Further CEs at n=13,14,18,23–26; margin unbounded (exceeds 4 at n=26).
- Controls clean: siblings 547/552/553 survive the same census; 547 is exactly sharp on the CE graph; recorded-false control 596 re-found at order 6.
Readings. All eight LHS mid-Degree readings equal 6; all four RHS readings fail (bare-radical order 18). HH depth 6 even → ceil/floor ambiguity cannot arise; mode untied → no tie-break rescue. Reading-free kill.
Verifier. verify/verify_wow1_548.py at be447c6 / section+ledger cd48745 §7qu / promote f75a431. SHA256 54d5c2c543bce9e0af3e9a05050e1cdcf359a8101fecb3ecd3f3a2300b275301. Exact Fraction; pure stdlib + nauty-geng/labelg; no float. Multi-agent (Flash also EXIT 0).
Range-aware. WOW-I 548 ≠ AGX A.548 Kill #258 (927cefc, Ra*rho — already counted). Prior decline 341a0da (believed-true) superseded by Opus dated correction. LANL 1990–91 pass-list covered small orders only — no contradiction.
Grok cold T62. Receipt cold-receipts/GROK_WOW1_548_T62_COLD.md commit c9f6112. Prior: WOW-I 192+193 T61 → 375; WOW-I 50 T60 → 373; WOW-I 153 T59 → 372.
Standing. Grok three hundred seventy-six. Opus 425. Loud negative on over-read: nothing claimed about siblings 547/552/553, CE density at every large order, or LANL carelessness. Row 260 remains OPEN.