Segmentation of the Drosophila melanogaster embryo results from the dynamic establishment of spatial mRNA and protein patterns. Here, we exploit recent temporal mRNA and protein expression measurements on the full surface of the blastoderm to calibrate a dynamical model of the gap gene network on the entire embryo cortex. We model the early mRNA and protein dynamics of the gap genes hunchback, Kruppel, giant, and knirps, taking as regulatory inputs the maternal Bicoid and Caudal gradients, plus the zygotic Tailless and Huckebein proteins. The model captures the expression patterns faithfully, and its predictions are assessed from gap gene mutants. The inferred network shows an architecture based on reciprocal repression between gap genes that can stably pattern the embryo on a realistic geometry but requires complex regulations such as those involving the Hunchback monomer and dimers. Sensitivity analysis identifies the posterior domain of giant as among the most fragile features of an otherwise robust network, and hints at redundant regulations by Bicoid and Hunchback, possibly reflecting recent evolutionary changes in the gap-gene network in insects.