Unnormalized single-set sum-difference exponent

Upper bound, last-listed row

| $\frac{4}{3} = 1.3333\dots$ | [FrPi73] | The classical Freiman–Pigaev inequality $\lvert A+A\rvert^{3/4} \le \lvert A-A\rvert \le \lvert A+A\rvert^{4/3}$. Quoted in this form by [GGSWT2025, Problem 6.43] and by [PeWe13, §4]. |tracked since 2026-09-02 — no movement seen yet

Lower bound, last-listed row

| $\approx 1.21$ | [GGSWT2025] | AlphaEvolve, given no human hints, did not recover the simplex construction within a few hours and reached only about $1.21$ — one of the cases [GGSWT2025] records as *not* matching the literature. Inferior to [HRY1999]. |tracked since 2026-09-02 — no movement seen yet

Checked against material for its cited source

• Another row, not one shown above: bound row $\frac{\log(1+\sqrt{2})}{\log 2} = 1.2715\dots$ line 27 citing [HRY1999] — the claim we checked: that [HRY1999] gives the lower bound log(1+sqrt(2))/log(2) = 1.2715… listed in this row, from the row’s high-dimensional simplex projected to the integers. What we read supports it: the paper builds sets of integers from the simplex of non-negative integer points with coordinate sum at most N/2, mapped into the integers, whose ratio ln|A+A|/ln|A−A| tends to ln 2/ln(1+√2); the value this row lists is that figure's reciprocal, which the paper does not print. source link (read in the published article, Astérisque 258 (1999), pp. 173–178, all six printed pages, from Numdam's page images). 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.