A Safe Dynamical Kernel for SIS-10 over Apache Kafk

This paper present a complete and irreducible formal specification for the SIS-10 safety kernel. The system satisfies totality, invariance, bounded causality, schedulability, feasibility, verifiability, machine-learning safety, compositional closure, and full observability. No additional axioms are required: the specification is dimensionally complete and closed under refinement. The tool is Apache Kafka. Kafka provides an ordered, durable, replayable event log with partitioned total order, replicated storage, and deterministic offsets. We show that Kafka's log semantics satisfy the requirements for totality, observability, compositionality, verifiability, and bounded causality. The resulting system is a closed and provably safe dynamical system. Keywords: safety kernel, formal methods, SIS-10, IEC 61508, Apache Kafka, event sourcing, compositional verification, zero-knowledge proofs, dynamical systems, functional safety.