Claims

../

1991_01_01_erdos_freud: Proposition 1 of Erdős and Freud (J. Number Theory 1991) gives a set of about root N integers up to N with (3/8 - o(1))N distinct sums up to N, the lower bound f(N) ≥ (3/8 - o(1))N; refereed and credited by the site.

2026_05_15_liu: A note of 2026-05-15 by Yu Leon Liu, found with OpenAI's GPT-5.5 and posted to the site's discussion thread, that the liminf of f(N)/N is at least (16 root 2 - 17)/12; not on the tab and unexamined by the site, so claimed.

---