Schur–Siegel–Smyth trace constant

Upper bound, last-listed row

| $1.8216$ | [SO24] | Explicit measures satisfying the conditions of [Smi24], optimized by gradient descent. Corollary 1.10 of [SO24] gives $\lvert \Lambda\_A - 1.8215998 \rvert \le 10^{-7}$ for $A = \\{x,\ 1-x,\ x^2-3x+1,\ x^3-5x^2+6x-1\\}$, and $C\_{86} \le \Lambda\_A$. Intermediate values in the same family: $\Lambda\_{\\{x\\}} \approx 1.898302$ (Serre's constant), then $1.84701204$ and $1.8224798$. Preprint; not listed as journal-published as of this writing. |tracked since 2026-07-28 — no movement seen yet

Lower bound, last-listed row

| $1.80203$ | [OSS25] | Adds constraints coming from the logarithmic energy of the limiting measure to Smyth's linear program, sharply reducing the number of variables required. The authors prove existence and uniqueness of an optimal solution, characterize it in terms of polynomials, and solve numerically by gradient descent. Schur's and Siegel's bounds are recovered as the two simplest cases. |tracked since 2026-07-28 — no movement seen yet