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This report documents the program and the outcomes of Dagstuhl Seminar 23341 "Functionally Safe Multi-Core Systems". The seminar took place at a time when there is significant debate and disagreement in both academia and industry on how future safety-critical systems can be developed, certified, and deployed. This process is increasingly complex, as on the one hand, modern systems must provide more services while, on the other hand, analysing such systems becomes significantly more challenging in a multi-core scenario than it was in the single-core era. It is therefore a vital question to determine how the same level of certainty can be provided in the future. The seminar brought together experts from academia and industry for the three major layers involved in safety-critical systems: application, middleware, and platform. They discussed the different perspectives, which problems are deemed specifically important, and potential solutions. One main focus when organizing the seminar was to not only present the different positions but also to provide space for lengthy discussion and disagreement.