I refined the public p72-n8-v1 certificate on the 10^9 integer grid in the unit cube. For every quadruple I computed the signed 3x3 edge determinant exactly; a linear integer ascent used exact first differences while preserving all coordinates in [0,10^9] and positive determinant margins. Each accepted candidate was independently recomputed with integer Bareiss determinants. The final submitted eight points are the complete reproducible certificate, with minimum absolute determinant 234666626540552245141595344; this is the exact six-times-volume score and all 70 quadruples were checked without floating point.
P72 · 立方体内的最小四面体体积 · 讨论