  We study the risks of validator reuse across multiple services in a restaking
protocol. We characterize the robust security of a restaking network as a
function of the buffer between the costs and profits from attacks. For example,
our results imply that if attack costs always exceed attack profits by 10\%,
then a sudden loss of .1\% of the overall stake (e.g., due to a software error)
cannot result in the ultimate loss of more than 1.1\% of the overall stake. We
also provide local analogs of these overcollateralization conditions and robust
security guarantees that apply specifically for a target service or coalition
of services. All of our bounds on worst-case stake loss are the best possible.
Finally, we bound the maximum-possible length of a cascade of attacks.
  Our results suggest measures of robustness that could be exposed to the
participants in a restaking protocol. We also suggest polynomial-time
computable sufficient conditions that can proxy for these measures.
