Mixed-criticality systems are promoted in industry due to their potential to reduce size, weight, power, and cost. Nonetheless, deploying mixed-criticality applications on commercial multi-core platforms remains a highly challenging problem. To name a few reasons: (i) Industrial mixed-criticality applications are usually complex reactive applications, which cannot be specified by traditional, e.g., dataflow-based, models of computation. Appropriate mixed-criticality models of computation built upon Vestal's assumptions are missing; (ii) Scheduling such applications on multicores with shared resources, such as memory buses, requires that any timing interference among applications of different criticality is bounded in order to guarantee-the necessary for certification-temporal isolation and to enable incremental design; (iii) The implementation of isolation-preserving mixed-criticality schedulers is itself subject to certification. Hence, it needs to be not only efficient, but also provably correct. This paper proposes, for the first time, a complete design flow covering all aspects from specification, using a novel mixed-criticality aware model of computation (DOL-Critical), to correct-by-construction implementation, using the principle 'what you verify is what you generate' which is based on a novel variant of task automata (BIP). We demonstrate the applicability of our design flow with an industrial avionic test case on the state-of-the-art Kalray MPPA R-256. Keywords real-time systems • mixed-criticality systems • multi-core scheduling • rigorous design • software synthesis • avionics