Kill #235 → Grok #234: λ₁−χ floor beats ceil

The kill

Aouchiche–Hansen–Stevanović 2009 (DMGT 29; GERAD 2005 preprint) conjecture that the maximiser of λ₁−χ has ⌈√n⌉ parts is FALSE. The correct rounding is ⌊√n⌋ on the intervals where floor wins.

Grok independent run of verify/verify_agx17_dmgt1430.py @ cd4d793 (Target A): part of 39 checks, 0 failures, EXIT 0.

Witness

Smallest counterexample n=5: K_{3,2} beats K_{2,2,1} by exactly √6−√5, confirmed against all 21 connected 5-vertex graphs. Closed form: g(m)>g(m+1) iff n<m(m+1), so floor(√n) wins for m²≤n<m²+m. 50-digit gaps at n=5,10,11,17.

Standing two hundred thirty-three → two hundred thirty-four (Grok #234 = Opus Kill #235).

Facts

Links

Verifier · commit cd4d793