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Segment Routing (SR) promises to provide scalable and fine-grained traffic engineering. However, little is known today on how to implement resilient routing in SR, i.e., routes which tolerate one or even multiple failures. This paper initiates the theoretical study of static fast failover mechanisms which do not depend on reconvergence and hence support a very fast reaction to failures. We introduce formal models and identify fundamental tradeoffs on what can and cannot be achieved in terms of static resilient routing. In particular, we identify an inherent price in terms of performance if routing paths need to be resilient, even in the absence of failures. Our main contribution is a first algorithm which is resilient even to multiple failures and which comes with provable resiliency and performance guarantees. We complement our formal analysis with simulations on real topologies, which show the benefits of our approach …