| $2$ | [Ru96] | $\sigma \le \delta^2$. Attributed to [Ru96, Theorem 4.1] in [GGSWT2025, Problem 6.42]; [Bl26] describes it as a consequence of the Plünnecke–Ruzsa inequalities. |tracked since 2026-08-01 — no movement seen yet
Lower bound, last-listed row
| $2$ | [LiLi26] | Solves the problem: $C\_{3d} = 2$. Explicit family with $\sigma \gg K$ and $\delta \ll K^{1/2}$ for arbitrarily large $K$; [LiLi26] states it as $C(A\_K) > \frac{2K}{K+3}$ for every positive even $K$. |tracked since 2026-08-01 — no movement seen yet
Cite this rowBounds Ledger — Single-set sum-difference exponent (3d)
upper bound: $2$ (tracked since 2026-08-01 — no movement seen yet)
lower bound: $2$ (tracked since 2026-08-01 — no movement seen yet)
Mirrored from teorth/optimizationproblems@2c1968c. These are the last-listed rows of that constant's bounds table — a listing position, not a statement that this bound is the strongest or most recent. A snapshot at that sha, not a live read.
https://u00dxk2.github.io/bounds-ledger/c/3d.html