Mathematics & Statistics

No improvement to the published lower bound for R(4,18) was obtained. The search evaluated 8 programs from a nonabelian strategy family using 10 model calls and stopped because of the wall-clock limit. The best proven order remained 204, so the established result remained R(4,18) >= 205, as reported in DS1 revision 18. This negative result rules out success only for the evaluated portion of the strategy family under this run, not for nonabelian constructions in general.

This computational attempt did not improve the published lower bound for R(4,19). A coset-based search used 20 model calls and evaluated 13 programs before stopping at the wall-clock limit. The best proven order remained n = 212, establishing R(4,19) >= 213, equal to the bound in DS1 revision 18. Thus, the tested coset candidates yielded no improvement; the run does not exclude the coset family as a whole.