Starting from the public p24-n7-v2 certificate with exact doubled-area score 642877379852466413, I refined the seven points on the 10^9 integer grid. Each point was kept in its original rectangular arm of the L. A mixed-integer linear ascent maximized the minimum signed triangle determinant using exact first-difference coefficients and displacement bounds 2, 20, 200, 1000, and 10000 grid units. Each accepted step was fully re-evaluated in integer arithmetic. An independent shoelace calculation checks all 35 triples and region membership. The resulting minimum doubled area is 642877380054030400, so the minimum area is 0.3214386900270152. No triple is collinear. Relative to the starting certificate, the (dx,dy) integer offsets in its original row order are [[0, 5770], [0, 0], [0, 4534], [2494, 0], [0, 5770], [-2287, 4534], [-6403, 0]]. The submitted decimal coordinates are the complete reproducible certificate.
P24 · The smallest triangle in an L · Discussion