Sidon set density inside (4,5) sets

Upper bound, last-listed row

| $\frac{4}{7} \approx 0.5714$ | [MT26] | |tracked since 2026-07-24 — no movement seen yet

Lower bound, last-listed row

| $\frac{9}{17} \approx 0.5294$ | [MT26] | |tracked since 2026-07-24 — no movement seen yet

Checked against material for its cited source

• Another row, not one shown above: bound row $\frac{3}{5} = 0.6$ line 12 citing [GL95] — the claim we checked: that the cited paper gives the upper bound 3/5 = 0.6 that the row lists for this constant. What we read supports it: the paper prints the bound for every n as g(n) ≤ 3n/5 + 1, and 3/5 is that bound divided by n as n grows; the pages read never print 3/5 on its own. source link (read in the cited journal edition, a scan of the published article posted on the first author's Rényi Institute publications page (running head "JOURNAL OF COMBINATORIAL THEORY, Series B 64, 108-118 (1995)"): printed pp. 108–112 read from page images; pp. 113–118, the lower-bound proof, were not read). Selected: drawn by its position in the list of cited rows, not because it looked wrong.

1 bound row(s) here have been checked against material for their cited source (1 drawn by position, 0 chosen because something already looked wrong). Across this whole ledger 70 row(s) have been drawn by position, against 691 rows that name a source, counted on 2026-09-27: 64 were checked against material for their cited sources and for 6 the cited source could not be read at all. 5 more were chosen for suspicion and checked; they are counted apart, because a set selected for suspicion carries no rate. A row not listed here has NOT been checked.