Improve or prove optimal the packing of 40 equal circles in a circle

Pack $N=40$ non-overlapping unit circles into the smallest possible enclosing circle; let $R_{40}$ be the minimal radius of that container. Equivalently, place 40 points in a disk so that the minimum pairwise distance is maximized. The optimum $R_{40}$ is not known -- only a best-known (conjectured-optimal) configuration is recorded. Exhibit a valid packing of 40 unit circles into a container circle of radius strictly less than the current best-known $R_{40}$, or prove that the best-known configuration is optimal.

Acceptance. FULLY RESOLVES: a rigorous proof (e.g. interval-arithmetic global optimization) that the best-known 40-circle packing is optimal, determining $R_{40}$. PARTIAL (improve record): a list of 40 center coordinates and a container radius $R < R_{40}^{best}$ such that (i) every pair of centers is at distance $\ge 2$ and (ii) every center is within distance $R-1$ of the container center; verifier -- check all $\binom{40}{2}$ pairwise distances and all containment constraints. PARTIAL: a certified lower bound on $R_{40}$ narrowing the gap.