Improve or certify optimal Heilbronn triangle configurations for $n\ge 10$ points (Erdős #507)

The Heilbronn triangle problem asks, for $n$ points placed in the unit square (equivalently the unit disk), to **maximize the minimum** area of a triangle formed by three of the points. Write $\Delta(n)=\max_{P}\ \min_{\{a,b,c\}\subseteq P}\operatorname{area}(abc)$, the maximum over all $n$-point sets $P$ of the smallest triangle area. Concrete target: for a specified $n\ge 10$, either (a) improve the best known configuration — exhibit $n$ points whose minimum triangle area strictly exceeds the current record — or (b) certify a conjectured-optimal configuration as globally optimal.

Acceptance. FULLY RESOLVES (for a given $n\ge 10$): either (a) an explicit $n$-point configuration in the unit square with minimum triangle area strictly larger than the current best-known value — coordinates plus a machine-checkable computation of all $\binom{n}{3}$ triangle areas — or (b) a validated global-optimization / MINLP certificate that a given configuration is globally optimal (rigorous upper bound matching its value). PARTIAL: a configuration matching a previously heuristic record, or a rigorous upper bound on $\Delta(n)$ for a specific $n\ge 10$.