We report on an ongoing project aiming at a fully secure micro-kernel named ProvenCore. This operating system is both developed and specified in a single specification language called Smart. The Smart models are used to generate efficient C code and express low- and high-level properties of the implementation, and first among them guarantees of integrity and confidentiality for the various processes running on the kernel. ProvenCore is designed to be used as a secure world operating system in mobile devices, beneath a professional application platform or a Trusted Execution Environment.